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THE THEORY OF CONSTRAINTS
SummaryThe theory of constraints is a philosophy that has a lot in common with Just-in-Time but also has some critical differences. There are two basic differences. The first is that the theory of constraints accepts the existence of a constraint, at least temporarily, and focuses the improvement effort on the constraint and related workstations. The second is that the theory of constraints uses overlapped production (transfer batch not equal to the process batch) to schedule work through a batch production environment, while Just-in-Time provides no scheduling mechanism for a batch environment. Thus, the theory of constraints scheduling approach has wider applicability than Just-in-Time (although Just-in-Time's continuous improvement philosophy and quality emphasis clearly is applicable to batch production environments).
There are five steps to the theory of constraints: identify the constraint, exploit it, subordinate everything else to it, elevate the constraint, and avoid inertia when the constraint shifts. In exploiting the constraint, the drum-buffer-rope scheduling technique and buffer management are used. In finding ways to elevate the constraint, the techniques of effect-cause-effect and the cloud diagram often are useful.
What is TOC? / Why is Theory Of Constraints Important?
Thus far we have examined two approaches to production planning and control system design, material requirements planning (MRP) and Just-in-Time (JIT). In this section we examine a third approach, the theory of constraints (TOC). Developing a production planning and control system would be simple except for the existence of seemingly random problems (machine breakdowns, tool breakage, worker absenteeism, lack of a component, scrap, rework, customers who change their order timing or quantity, etc.) and the fact that operations are linked, with Operation A dependent on Operation B (the output of Operation B is all or part of the input into some Operation A). Henceforth, we shall refer to these problems as the problem of random fluctuations and dependent events.
The traditional, or MRP, approach to the problem of random fluctuations and dependent events is to eliminate the dependence by having a large inventory buffer at every workstation. The JIT approach is to eliminate the random problems by seeking out the root cause of each problem and correcting it. For example, machine breakdown may be eliminated by the use of preventive maintenance.
Both MRP and JIT practitioners believe that an ideal plant is a balanced plant, i.e., one in which every resource has the same output capability relative to the plant's need. The TOC approach is to accept the existence of an unbalanced plant, one in which some resource has less relative output capability than the others. The most limited resource is called the constraint. TOC breaks dependencies by creating a material buffer, but TOC buffers only the constraint. Non-constraint stations have a capacity buffer, i.e., excess capacity. Non constraints usually do not need a material buffer in addition to the existing capacity buffer. To add inventory to a non constraint station causes lead time to increase (a cost) and work-in-process inventory to increase (a cost) while providing little tangible benefit. TOC thus agrees with JIT that inventory is waste, if the inventory is planned at a non constraint station. However, by buffering the constraint from random problems at other stations, therefore permitting the constraint to work all the time, an inventory buffer at the constraint does add value and hence is not waste.
TOC does not try to eliminate all problems, only those that threaten the constraint in spite of the constraint's inventory buffer. To use JIT terminology, excessive effort in problem elimination is a waste. There must come a point when it is much less expensive to provide a small buffer against a problem at the constraint than it is to eliminate the problem. The constraint buffer also frees management time to solve problems against which no buffer can be provided,
SIMULATION MODEL: COMPARING MRP, JIT, AND TOC
The following discussion is intended to illustrate the differences in the traditional, JIT, and TOC approaches. An extremely simple shop was simulated so that it is easier to explore the implications of each approach.
Consider a shop that has a two-station assembly line and produces one product. Station 1 can produce either 2, 3, or 4 units of product each day; each outcome is equally likely. Station 2 has an identical capacity. There can be a maximum of 2 units of work in process between Station 1 and Station 2. Station 1 has an unlimited supply of raw material. There are presently 2 units of WIP between the stations. The shop is to operate for 200 days. What is the expected output of this system? How can the system be improved?
It might surprise you to learn that the expected output from this system is 2.806 units per day. You can estimate this result using Lotus 1-2-3 to simulate the shop. When we simulated this shop, we obtained approximately 2.80 units per day, averaged over the 200 days. Results of 10 replications of 200 simulated days are shown in Table 1. Single replication results varied from a low of 2.72 units to a high of 2.91 units and averaged 2.80 units. Since each station is capable of averaging 3 units per day of output, our results are about 7 per cent below what we expect to produce. Traditional thought, JIT, and TOC have different approaches to solving this problem. The traditional approach would add WIP between stations, JIT would reduce variability at each station, TOC would unbalance the line, add WIP at one station, and reduce variability slightly. Let's explore the implications of each of these approaches.
Table 2 shows a portion of the spreadsheet used to perform the Monte Carlo simulation. This particular spreadsheet was used only to prepare this example and is not one of the 10 replications reported. Random numbers determine the production output for each station. A random number between 0 and 0.33 yields an output of 2, one between 0.33 and 0.67 yields a 3, and one between 0.67 and 1 yields a 4. In the first row of the main body of the table, Station 1 drew a random number of 0.519239, so Station 1 has a possible production of 3. There are 2 units of inventory available (beginning condition). Station 2, therefore, has 5 units of inventory potentially available. Station 2 drew a random number of 0,006+, yielding an output of 2 (because it is between 0 and 0.33). The output of the line is 2, the output of Station 2 is 2, and the actual output of Station 1 is limited to 2 since there is not room to store the additional potential unit between the stations. However, for collecting data for the Station 1 column, the value 3 is used. The unused inventory available for the next trial is 2. You may wish to verify the next line, in which Station 1's output is 3, Station 2's is 4, and the output of the line is 4. The inventory available for the third trial therefore drops to 1.
To understand how Station 2's output may be limited, assume at a given time no WIP exists between stations and Station I draws a potential of 2 while Station 2 draws a potential of 4. Then the output of the WIP would be 2, because Station 2 is furnished only 2 units to process, despite its own potential to process 4 units. The output of the line would be 2, the value recorded for Station 1 would be 2, and the value recorded for Station 2 would be 4.
Observe in Table 1 that, in isolation, both Station 1 and Station 2 produced the theoretical average of 3 units per day, with some minor fluctuation around these averages for most replications of the simulation. However, the output of the line was consistently about 2.8 units per day because of the interaction of random fluctuations and the station dependencies.
Traditional Approach and Results
The traditional approach to production and inventory system design would eliminate the limit of 2 units of WIP between the two stations. (For convenience of notation, we will designate this traditional approach the MRP approach, although no MRP logic is actually present in the example.) Assume we permit an unlimited amount of WIP and begin the simulation by having 5 units of WIP available between the two stations. The results are shown in Table 3. Average line output is up to about 2.96 units per day, not quite to the theoretical average of 3.00 units. This result may be surprising, but it is correct. It would take much more than S units of WIP in position initially to completely decouple the two stations. Note that ending inventory fluctuates quite a lot, implying that lead times also fluctuate quite a lot. In Table 1, ending inventory was not shown because ending inventory was limited to 2 pieces and would therefore have to be 0, 1, or 2. Ending inventory can fluctuate substantially only when we relax the policy that at most 2 units of WIP are permitted.
As WIP increases, at some point, according to theory, Station 2 is decoupled from Station 1 - The line output should then equal the output of Station 2. As can be seen from Table 3, the average line output was 2.96 units per day, varying from a low of 2.91 to a high of 3.05. It appears that an initial WIP much higher than 5 is necessary to completely decouple Stations 1 and 2. Only 2 of the 10 replications achieved an average of) units per day output.
To achieve the traditional approach, the only change made to the simulation is that the limitation of 2 that was placed on the inventory column is relaxed; inventory is permitted to vary without limit. A negative side effect of the traditional decoupling approach is that lead times become highly variable. Note that ending inventory at the end of the 200th trial varied from 3 units to 28 units, which implies that lead time for a job entering the system varies from 1 day to 10 days. Fluctuating lead times make it difficult to establish the time to order needed raw materials and/or the time to promise delivery to specific customers.
Thus, the traditional approach does not quite achieve the desired output and has a highly undesirable side effect. If you ponder the implications of the variation in ending inventory to managing lead times and producing a specific order to a specific due date, perhaps you will' comprehend why many western managers believe their shop is controlling them rather than vice versa.
JIT, Approach and Results
The JIT approach to production and inventory management would greatly reduce the variability of the system, attacking causes of variability (breakdown, scrap, etc.) at both stations while maintaining the WIP at only 2 units between stations. Assume JIT is able to reduce variability to the point that there is an 80 percent chance of getting exactly 3 units from each station, with a probability of 10 percent of getting only 2 units and a probability of 10 percent of getting 4 units. WIP between stations is limited to 2 units. The results of this simulation are shown in Table 4. Note that the average output of the line is about 2.94 units per day, slightly below the traditional approach, but with minimal in-process inventory and a consistent one day lead time. (If we produce 3 units per day and there are 2 units in process, a new unit will start at Station 1 on one day and complete Station 2 the next day.)
Note from Table 4 that the JIT approach greatly reduces the variability of line output. Line output is in a narrow band around the average of 2.94, with a low of 2.92 and a high of 2.97. WIP varies from 0 to 2, so lead time is always one day or less; a unit may enter this morning and finish this afternoon. Unfortunately, JIT achieves a smaller average output than the traditional approach. Also, quite a lot of effort may be required to achieve the reduction in variability at both stations. For example, variability may be due to scrap, the scrap may be a function of incoming raw material variability, and the incoming raw material variability may be inherent (for example, mineral ores and other natural resources have inherent variability’s that cause the number of defects to vary). Output variability may be due to having an occasional worker absent due to illness, vacation, or other unavoidable event.
Despite the high cost of reducing variability, when system predictability is considered, the JIT approach seems clearly superior to the traditional approach for this simple two-station, one-product situation.
TOC Approach and Results
TOC's approach to production and inventory system design is somewhat of a hybrid of the traditional and the JIT approaches. TOC would declare one of the two stations to be a constraint, buffer that station, eliminate the worst of the variability at the constraint, and try to expedite at the non constraint whenever the constraint buffer becomes small. The concept of what TOC is doing is quite simple. The details of how this is accomplished can be a bit confusing.
Assume TOC declares Station 2 to be the constraint. (The choice is arbitrary. In this instance, choosing Station 1 would actually produce better results.) TOC would reduce the variability of Station 2, but not to the extent JIT does. Assume TOC is able to reduce variability at Station 2 so that there is a 60 percent chance of getting 3 units, a 20 percent chance of getting only 2 units, and a 20 percent chance of getting 4 units. Because TOC permits more variability than JIT, TOC requires somewhat more WIP. Assume WIP is permitted to go to a maximum of 4 units, with 4 units initially in the system.
Since Station 2 is the constraint, TOC tries to prevent the constraint from being idle. As the traditional results demonstrate, having ~ units of WIP initially is not enough to prevent Station 2 from being idle if the output of Station 1 is not changed. TOC would therefore expedite material at Station 1 whenever the buffer at Station 2 becomes small (i.e., whenever Station 2 is threatened with lack of work). Assume the following strategy is employed: If WIP is 3 or 4, no expediting is performed at Station 1. Output is therefore 2, 3, or 4 units, each equally likely (the original situation). However, if only 1 or 2 units of WIP exist at the beginning of a day, additional management attention is placed on Station I. For that day, for Station 1 only there is a 50 percent probability of getting 3 units and a 50 percent probability of getting 4 units. Finally, if WIP ever hits 0, more attention is given to Station 1 50 that 4 units of output are guaranteed from Station I.
As Table 5 shows, the TOC approach achieves the theoretical average of 3 units per day output while maintaining a reasonably steady two-day lead time (1/3 day at Station 1, 4/3 day in queue, 1/3day at Station 2).
The TOC approach is to unbalance the line. As Table 5 shows, the average capacity at Station 1 is up to about 3.2 units per day, because on days when Station 2's WIP is less than 3, Station 1's average output increases to 3.5 or 4.0. The result of increasing Station 1's capacity is to maintain sufficient buffer to decouple Station 2 from Station 1. TOC thus achieved the theoretical capacity of Station 2, approximately a 2 percent increase in output compared to JIT. TOC also required less effort than JIT at Station 2, where variability was not reduced as much. (Recall that initially the outcomes 2, 3, and 4 had probabilities of 0.333,0.333, and 0.333, respectively; JIT changed these to 0.1, 0.8, and 0.1, respectively, while TOC changed them to 0.2, 0.6, and 0.2, respectively.) Not only is the change in variability due to TOC about half that of the change due to JIT, but if you assume that the easiest sources of variability to change were attacked first, you can argue that the work required to achieve the TOC result at Station 2 must be much less than half of the effort required to achieve the JIT result.
The relative effort required to change Station 1 is less clear. How much effort does it require to eliminate a result of 2 units output on a few critical days? Does that require more or less effort than that needed to reduce the probability of getting only 2 units to 0.1 on all days? Let's assume the change made at Station 1 by TOC requires the same effort as the change made at Station I by JIT. TOC still requires less overall effort because there is clearly less effort needed at Station 2. Thus, TOC improves the results obtained by JIT by about 2 percent while requiring less effort.
But are the TOC results superior to the JIT results? Probably so. An additional 2 units of WIP and one day of lead time seems a small price to pay for 2 percent additional output. This example actually distorts the difference in WIP that JIT and TOC would achieve. TOC has more WIP at constraints but less at non constraints. A system with several stations will still have only one constraint station, so for a line with four or more stations, TOC probably has less WIP than JIT in addition to its other benefits.
An important secondary point is that both MRP and JIT agree that this assembly line is well balanced, because both stations have identical characteristics. TOC does not agree with this notion; it insists that a balanced plant is inefficient. Note that most assembly lines have more than two stations. An interesting exercise would be to simulate a three or more station line for one or more of the cases and compare the output of the three-station line to the two-station results. You will find that the three-station line consistently achieves less output and that the longer the line the less the output.
Clearly TOC requires more effort than the traditional approach. But in addition to increasing output by slightly more than 1 percent compared to the results of the traditional approach, TOC also stabilized the amount of WIP in the system and, hence, stabilized the due date performance. There is a definite competitive advantage to having a short lead time as well as to having a consistent lead time.
This simulation illustrates the philosophical differences between the traditional, the JIT, and the TOC approach to dealing with the problem of random fluctuations and dependent events. The traditional approach is to buffer everything, which leads to high inventory costs and long lead times. The JIT approach is to eliminate the random fluctuations. The superiority of the JIT approach compared to the traditional approach for situations in which one product is manufactured continuously is evident in this simulation. From this simulation, it is evident why repetitive manufacturers in the West are rapidly changing to the JIT approach. At the same time, it appears from this simulation that TOC can offer some improvements to the JIT approach to managing a line. TOC reduces some of the fluctuations, buffers only the constraint, and expedites elsewhere when the constraint buffer is less than it should be. TOC produced greater output with less effort and only marginally greater inventory than JIT. For larger plants, TOC requires less WIP than JIT because JIT maintains a small buffer between every station while TOC focuses the buffer at the constraint and permits less WIP than JIT at all other stations.
In the remainder of this section we discuss the theory of constraints; We present a brief history of the development of TOC. We define constraint and delineate the five steps of the theory of constraints. We describe the scheduling technique TOC uses for job shops, known as drum-buffer-rope. We describe the use of buffer status information as the shop floor control information system We discuss performance measurement in a TOC system. We discuss the implementation of TOC via the Socratic method. Finally, we briefly describe the results achieved by some companies that are using TOC.
DEVELOPMENT OF THE THEORY OF CONSTRAINTS
The creation of the theory of constraints is primarily the effort of one man, Eliyahu Moshe Goldratt. Goldratt is a physicist by education who became involved with production system design to help a friend who operated a plant that made chicken coops. The friend asked Goldratt to design a scheduling system. His system tripled the output of the plant (Jayson 1987). Goldratt eventually marketed the scheduling system in the United States under the trade name OPT.
OPT was effective, but controversial, The controversy arose from the fact that a plant had to execute the OPT schedule without understanding it, because Goldratt refused to release details of his scheduling algorithm. Because many of the schedules were counterintuitive, some plants had difficulty getting super-visors to perform tasks in the sequence called for by the schedule. In an effort to alleviate this problem, Goldratt wrote a book, The Goal: A Process of Ongoing Improvement (1986), which explains the philosophy underlying the algorithm in the form of a novel,
With the publication of The Goal came the issue of what to call the philosophy underlying the scheduling algorithm. At first the term OPT Thought-ware was used, but this resulted in confusion between the philosophy and the proprietary software. Then the term Synchronous Production was used, but that terminology proved confusing also because there are other approaches that occasionally are called synchronous production. The term that finally emerged is theory of constraints. The theory of constraints represents a refinement of the ideas presented under the names OPT Thoughtware and Synchronous Production. Despite the name changes, the philosophy itself has remained basically the same, although refinement has occurred as experience with the philosophy in a variety of environments has created feedback on how the methods might be improved.
The theory of constraints is being refined and expanded at the Avraham Y. Goldratt Institute (named after Dr. Goldratt's late father) and elsewhere. The Goldratt Institute publishes The Theory of Constraints Journal on an irregular, approximately quarterly, basis. Most transfer of the theory to industry occurs through a series of seminars provided by Goldratt, Bob Fox, Dale Houle, and Donn Novotny. At the time of this writing, the institute had entered into agreements with the University of Georgia and Lehigh University to offer theory of constraint courses as continuing education courses on campus. More universities were expected to participate. Other major contributors to the development of the theory include Alex Kiarmon, Eli Schreigenheim, and Avraham Mordoch. Other sources of written material on the theory include chapters in books by Blackstone (1989), and Cohen (1988), and a book by Umble and Srikanth (1989). Portions of the theory of constraints have not yet appeared in print, but are transmitted through workshops. Some of the material in this section is based on material not documented elsewhere.
THE FIVE STEPS OF THE THEORY OF CONSTRAINTS
In order to define the theory of constraints, it is first necessary to define the concept of a constraint. A constraint may be defined as anything that prevents a system from achieving a higher performance relative to its goal. This definition indicates that the theory of constraints may have a wider application than simply production planning and control systems. It also begs that we define what we mean by "goal" and how we measure performance. The goal of any business is to make more money, now and in the future. A finance professor might say that the goal of a business is to maximize the net present value of stockholders' wealth. The two definitions are essentially the same, especially if you recognize that the finance definition requires the estimation of the amount of money to be made in the future. The performance measures needed are both absolute and relative, e.g., net profit (absolute) and return on investment (relative).
There are three broad categories of constraints, internal resource constraints, market constraints, and policy constraints. Each of these can be illustrated using the simple two-station assembly line described earlier. Suppose for a moment that the demand for the single product made on the line is 4 units per day. Then using the theory of constraints approach to managing the line, Station 2 is an internal resource constraint. Station 2 has a capacity of 3 units per day, which is less than both Station 1(3.2 units per day) and the market (4 units per day). When an internal resource constraint exists, it dictates the pace to be used for all resources in the plant. If, on the other hand, market demand is only 2.5 units per day, there is a market constraint. A market constraint exists when the market demand for an item is less than the capacity of the machine having the least capacity available to produce that item When the market is the constraint for an item, the market should dictate the pace of production. In the simulation results shown in Table 1, there is a policy constraint. The constraint is the policy of permitting only 2 units of WIP between the two stations. As Table 2, Table 3, and Table 4 illustrate, changing this policy results in increased throughput for the system.
The five steps of the theory of constraints are as follows:
1. Identify the constraint.
2. Decide how to exploit the constraint.
3. Subordinate everything else to the action taken in 2.
4. Elevate the constraint. (The term elevate is used in TOC to mean to make possible a higher performance relative to the goal, usually by acquiring additional capacity at the constraint.)
5. WARNING: If in Step 4 the constraint is eliminated, do not let inertia become the new constraint.
To illustrate the five steps in action, assume that we are operating the facility with the conditions that produced Table 1, a simple assembly line with an output averaging 2.81 units per day, and that market demand is 3.10 units per day. We are operating the Tine permitting only 2 units of WIP. Having learned a little about TOC, we decide to move to the TOC approach. In Step 1, we identify the constraint to be Station 2. In Step 2, we decide to exploit this constraint by protecting the constraint with a buffer of material, by reducing the variability at Station 2, and by increasing the capacity of Station 1 by selective expediting. Recall that we expedite at Station 1 whenever Station 2's queue drops below 3 units.
In Step 3, we subordinate Station 1's output to Station 2. This is accomplished by forcing Station 1 to go idle whenever Station 2's queue is full. If we did not subordinate Station 1 to Station 2's pace, Station 1 would continue to build inventory so that the WIP awaiting Station 2 would grow without limit.
Step 4 usually requires the acquisition of additional resources by buying a new machine, subcontracting work outside the plant, or rerouting work within the plant. Suppose that we are able to subcontract work to another vendor who delivers to us 1 unit of the finished item every other day The output of the entire plant is thus raised by 0.5 units per day to an average of 3.5 units per day. Step 5 now becomes important because by elevating the constraint from 3.0 units per day to 3.5 units per day, the new constraint becomes the market (3.1 units per day). If we continue to let Station 2 dictate the pace, we will accumulate finished goods inventory at the rate of 0.4 units per day. Since accumulating this inventory adds cost but does not add value, we have allowed inertia to limit our profitability. It is important to recognize that the way a plant is operated, even a simple two-station assembly line, changes when the constraint moves from an internal resource to the market.
A few generalizations can be made regarding the five steps for a firm that has never implemented the theory of constraints. Most facilities have policy constraints that need to be eliminated before the identification of resource constraints begins, The most common policy constraints are the use of work station utilization or efficiency as a performance measure and the use of individual incentives based on output. Since the pace of work will be dictated by the slowest station or by the market, whichever is smaller, almost all work stations will have a certain amount of planned idle time, To attempt to utilize this idle time by building products would result in excess inventory. Workers will not willingly be idle, however, if their performance evaluation will suffer as a result of the idleness. Workers certainly will not willingly be idle if they lose incentive pay as a result. Any policy that is in conflict with having planned idle time at non constraint resources must be changed before the constraint begins to dictate the pace of work.
A plant may or may not have an internal resource constraint. A resource is an internal constraint if and only if the resource can produce less output than the market wilt demand when the resource is working 24 hours per day 7 days per week. A plant that can increase output by adding a shift or working over-time does not have a resource constraint. Many production planners claim that their plants have many constraints and that the location of the constraint changes as the product mix changes. This claim is rarely, if ever, true. Very often a plant appears to have many constraints simply because every station attempts to work all the time because of performance measures and/or incentive bonuses. Also, the existence of large lots or batches may create temporary bottlenecks as the large lot is processed at first one station and then a second. To determine whether a plant truly has a constraint it may be necessary to eliminate machine utilization as a performance measure and to implement drum-buffer-rope scheduling, described in the next section, as though the market were the constraint. If a true resource constraint exists, it will quickly be identified by the amount of work that accumulates at the station.
Step 2 is to decide how to exploit the constraint. If the market is the constraint, we should exploit the fact that we have excess capacity. With excess capacity we should be able to eliminate almost all work in process, which will cause lead times to diminish. With shorter lead times, we should be able to aggressively pursue additional business. We are exploring the fact that we have a market constraint. Whenever a true internal resource constraint is found, we exploit that constraint by operating it at all times and by protecting the constraint from problems at other stations by means of an inventory buffer. Another way to protect the constraint is to perform an inspection immediately prior to the constraint operation, so the constraint never wastes time on a part that already is defective. Another way to exploit the constraint is by adjusting our product mix to recognize the constraint. Most firms decide what to produce based on profitability per unit. TOC points out that if Item A has a profit of $2 per unit and requires 5 minutes of constraint time while Item B has a profit of $1 per unit but requires 1 minute of constraint time, then Item H is more profitable than Item A.
Consider the following example. Suppose the market for Item A is 1,000 units per week while the market for Item B is 8,000 units per week. Suppose Item A requires $2 of raw material and sells for $4 while Item B requires $1 of raw material and sells for $2. Both A and B require a single operation. Item A requires 5 minutes of machine time while Item B requires 1 minute. In any week there are 10,000 minutes of machine time available. If we consider Item A to be the more profitable, we can build all 1,000 units of A plus 5,000 units of B for a total revenue of $14,000 and a profit of $7,000. If, however, we recognize that B is more profitable per constraint minute, we will produce 8,000 units of B and 400 units of A for a revenue of $17,600 and a profit of $8,800. The two alternative product mixes are summarized in Table 6.
An interesting feature of theory of constraint implementation is that a firm can realize an almost instantaneous increase in profitability by (1) achieving an increase in output by buffering the constraint properly, as shown in the two-station line example, or (2) slightly altering the product mix, as shown in the Product A and B example.
Step 3 is to subordinate everything else to the decision made on how to exploit the constraint. This means that the schedule of work is determined by the constraint and that a buffer is created to protect the constraint. Material release is dictated by the needs of the constraint. Early release of material to prevent a non constraint from going idle must be prohibited. The workers on non constraint machines must be educated that they are working at non constraints, They should use time not needed for production to maintain the machine, cross train on a second machine, improve quality, or any other useful nonproductive tasks. Expediting is performed only when the condition of the buffer indicates that expediting is needed. Expediters should regularly check the status of the material in the constraint buffer. If a significant amount of work is missing from the constraint buffer, the expeditor should locate the material, expedite its production, and then try to identify why the material was late and, if possible, correct the cause of the delay. By eliminating the largest causes of delay of material moving to the constraint buffer, one can eventually reduce the size of the constraint buffer. Thus, the effort to improve the shop floor is subordinated to the constraint as welt as the effort to schedule and control the shop floor.
Step 4 is to elevate the constraint. This step should be taken with caution, because when the constraint shifts, the way in which the shop is operated must also shift. Everyone affected (which means everyone in the plant) should know in advance that the constraint will shift, and therefore the way in which the shop will operate will also shift. Many firms have found that their constraint is their newest, most expensive, and most highly automated piece of equipment. This machine is the constraint because a great deal of work was moved to it in order to eliminate lengthier operations on other equipment. Sometimes the older equipment may even be moved into storage. Once the fact that this machine is a constraint is recognized, the jobs with the least profit per constraint minute often can be moved back to older equipment, which now is recognized to be a non constraint. By shifting work from the constraint to a nonconstraint, the revenue generated by the shop is increased with little or no increase in operating expense. At a recent conference of theory of constraint implementors, most attendees reported eliminating all internal constraints within one to six months of TOC implementation. Many eliminated the internal constraints without investing in additional capacity. This result is not surprising when you realize that many operations can be performed on alternate equipment and that when constraints and non constraints have been identified, it is a fairly simple matter to offload some of the work currently performed at the constraint onto non-constraint stations.
DRUM-BUFFER-ROPE SCHEDULING
Drum-buffer-rope scheduling has one distinctive feature that must be emphasized---a process batch size that is not equal to the transfer batch size. A process batch is defined to be the number of units run after a station sets up to produce some Part A and before the station sets up to produce some other Part B. A transfer batch is defined to be the number of units of an item physically transported from some Work Station X to some other Work Station Y. In most job shop operations the transfer batch and the process batch are the same, i.e., an entire process batch is completed at one station and then materials handling personnel are called to transfer the job to the next station on the routing. It is not at alt uncommon for a lob requiring one hour of work at each of three stations to require a three-week lead time---roughly one week in queue and one hour in process at each station. The long queue time is due to the large amount of work in process maintained at each station. However, if the plant manager decides to put this job on a truck in two hours, the job can be completed. All three stations set up for the job and pieces are carried from station to station whenever one piece is completed. In this situation the transfer batch is one and the process batch is the order size, The third station is able to complete its operation a few minutes after the first station completes the last piece, with a little over one hour elapsed, total.
TOC assumes that a transfer batch of one is used whenever it is needed. Because most operators work at non constraints, there is no reason not to have the worker pull material forward from feeding stations whenever the worker runs out of work. Each station is furnished with a schedule of work that should be coming through the station in the near future. It is therefore a relatively minor task for an idle worker to check possible feeding stations for completed work and to bring forward any items that are ready to be transferred, In this situation the transfer batch is usually variable---however many happen to be ready when the next operator checks, The process batch size usually is equal to the order size. The transition to a smaller transfer batch can be made with no change in plant layout---provided one recognizes that non constraint workers can move materials. However, Shigeo Shingo (1987) has several comments on shop layout that might be helpful.
The TOC approach raises two interesting questions. First, the JIT approach advocates reducing setup time until a shop can afford a process batch of one. If the transfer batch has been lowered to one unit to speed the order through the shop, what additional benefit is to be gained by reducing the process batch down to one unit? Second, since the order will be shipped to the customer as a batch, does it ever make sense to have the process batch be less than the order size (or the delivery size in the case of a blanket order with several deliveries)? Unless there is some clear benefit to be obtained by continuing to reduce the setup time beyond that needed to support a process batch equal to the order size for all orders, JIT is creating wasted effort by forcing the transfer batch to equal the process batch.
The concept of drum-buffer-rope is as follows: Ideally, all non constraint stations preceding the constraint on a part's routing should begin production of the part as soon as the part is released to the first station on its routing. Thus, parts move very quickly from material release to the constraint buffer. The parts then wait for an indeterminate time in the constraint buffer until the constraint begins to process the part. Once the constraint begins to process the part, ideally all non constraints on the routing between the constraint and the shipping dock should also set up for the part, so the part is moved one unit at a time to the shipping point. Thus, drum-buffer-rope schedule development consists of two stages. First, develop a derailed schedule for the constraint itself, this schedule is called the drum. Second, determine how much time is to be allowed for material to move from material release to the constraint and, for each end item, how much time should be allowed for material to move from the constraint to shipping. This time offset is called the rope, because it links material release to the constraint so the constraint can pull forward the material as it needs it. A rope also pulls material forward from the constraint to shipping (or, in the case of a good that does not require processing at the constraint, the rope pulls material from release to shipping). The material that is scheduled to be at the constraint at any point in time is called the constraint buffer. Material that is scheduled to be at shipping at any point in time is called the shipping buffer. This description should make clear the origin of the name drum-buffer-rope.
The unit of measurement for the constraint buffer is standard time, i.e., time estimated to be required for the constraint to process all items in the buffer. The time represented by the internal constraint buffer is equal to the lead-time offset of the rope connecting the constraint to material release. Because of the assumption of a transfer batch of one, TOC assumes that all non-constraint stations will begin processing material as soon as it is released, so the delay in moving to the constraint buffer is minimal TOC recognizes that some time is required to move from material release to the constraint buffer, so material is not considered to be overdue until a time equal to one-half the buffer size has passed. If material that should be in the first half of the buffer is missing, corrective action will be taken to expedite material and to determine and correct the cause for the delay.
There is a second rope that pulls material from the constraint to the shipping dock. The length of this rope is equal to the length of the shipping buffer, which is a buffer maintained to protect the shipping schedule. Although each product may have a distinct shipping buffer size, there is usually only one internal constraint and, hence, only one internal constraint buffer size. The unit of measure for the shipping buffer is units of end item.
Drum-buffer-rope scheduling thus reduces to: (1) identify the constraint, (2) sequence jobs on the constraint, (3) decide on the size of the constraint buffers (which fixes the length of the rope from the constraint to material release), and (4) decide on the size of the shipping buffers (which, in effect, forward schedules material from the constraint to shipping and fixes the promise date to the customer). The job of shop scheduling, thought by most researchers to be extremely complex, is thus reduced to a simple single machine scheduling problem. The simplicity of the problem is conditional on the shop having one or no internal constraints.
A common objection to theory of constraints is the notion that there are many interacting constraints in a shop. This notion really is not true. Although most companies that have implemented TOC initially believed they had many constraints, all have found that they had few resource constraints, that they rarely interacted, and that moving the constraint to the market is much simpler than they thought.
If demand can be forecast with accuracy over the planning horizon (and all scheduling procedures make this assumption), then the load required from every resource can be predicted. One resource will be more heavily loaded than all others. This statement can be made with confidence, since it is extremely unlikely that two or more resources will have exactly the same load. The most heavily loaded resource is treated as the constraint; all other resources are subordinated to it. If a shop has a highly seasonal demand for several items, such that the most heavily loaded resource shifts from season to season, then the planning horizon should be one year. By having a one-year planning horizon, the effect of seasonality is eliminated and the most heavily loaded resource for the entire year is selected as the constraint. Of course, an unanticipated shift in product mix may cause the constraint to move. But such a shift would cause replanning in any system.
The schedule created by drum-buffer-rope is entirely feasible provided that the constraint is never permitted to go idle and the efficiency and utilization of the constraint are approximately as predicted. Buffer management, discussed in the next section, is intended to insure the constraint is used as planned, assuring schedule performance.
BUFFER MANAGEMENT
There are three types of buffers present in the theory of constraints, two of which have been discussed. The constraint buffer protects the constraint; the shipping buffer protects the promised due date delivery. There is also an assembly buffer, which stages non constraint parts at assembly points with constraint parts so that constraint parts are never delayed for lack of non constraint parts. If all buffers in the shop have the correct material in them at all times and never have material that is not supposed to be there, the shop must be operating on schedule. Any schedule deviation will cause expected material to be missing from the buffer. Management using the theory of constraints is a type of management by exception that reacts only when material is missing from the buffer.
Suppose the constraint is scheduled to produce the following parts in the next week:
Part Time Units A 7.5 hours 150 B 8.5 hours 200 C 7 hours 100 D 17 hours 300 Suppose further that the constraint buffer is set to 16 hours. Then, at present, all 150 units of A and all 200 units of B should be in the buffer.
For buffer management purposes, the buffer is logically divided into thirds. At present, one-third of the buffer is about 5 hours. We might choose to call Region I--- 5 hours, Region II--- 6 hours, and Region III--- 5 hours. We could represent this buffer as a visual display as shown in Figure 1.
In Figure 1, the vertical axis shows minutes, each letter represents a vertical distance of 15 minutes; the horizontal axis shows hours, the numbers on the next to last row represent hours in the future, from 1 to 16. Note that the hours 10 through 16 are identified only by the last digit. Figure 1 indicates that for the next 7,5 hours the constraint will process A and for 8.5 hours after that it will process B, consistent with the schedule presented earlier. Assume that the letter (A or B) is colored green if the required material is present in the buffer and red if the material has not yet been reported as being present at the buffer.
Note that this visual could be kept up to date at all times simply by having a PC or a terminal in the constraint area and having the material handler log material in and out as material is moved. Then anyone walking by the constraint area and glancing at the display could determine in a glance whether the constraint was properly protected. For that matter, with the computer at the constraint hooked to a network of PCs or to a central computer, it would be possible for anyone in the plant having access to a PC or a terminal to check the status of the constraint buffer at any time.
A red letter occurring in Region I of the buffer would literally raise a red flag that immediate expediting is required. A red letter occurring in Region II indicates material is taking somewhat too long to move to the constraint. Investigative and corrective action is required, although expediting is not yet indicated. In theory of constraints terminology a hole in the buffer occurs whenever material that should be in the buffer is missing.
The shipping buffer and assembly buffer can be created and managed in a fashion analogous to the constraint buffer. The size of the buffer is a function of the degree of variability that exists within the shop and of the extent to which non constraints are loaded. If the shop has some machines with long setup times, others that break down quite frequently, and non constraint machines that are loaded quite heavily, then a large buffer is required to protect the constraint and to permit ample time for jobs to move from shipping to the constraint. Whenever a hole occurs in Region I or Region II of the buffer, the cause of the hole is investigated and recorded. Those problems that most frequently appear on the list of causes, such as long setups at Machine X or long breakages at Machine Y, are high priority items for corrections.
Like JIT, TOC advocates continuous improvement, but TOC wishes to focus the continuous improvement effort on those things that cause the most frequent and most severe holes in the buffer. Once these problems are eliminated, so that a hole in Region I of the constraint has not occurred for some time, then the size of the buffer can be reduced. Note the sequence of events. JIT removes inventory and then attacks the problems that surface. TOC uses buffer management information to identify the most critical problems, corrects the problem, and then reduces the inventory. It therefore seems logical that one should get more output from a TOC-run plant as problems are corrected than from an identical plant run by JIT. A JIT-run plant causes disruptions in flow in order to identify problems; a TOC plant identifies potential disruptions in flow and attempts to correct them before flow is actually disrupted. Because of continuous flow, other things being equal, the TOC plant should have more output.
It is also important to note that buffer management is a complete shop floor control system, provided that non constraint stations are evaluated on their ability to keep material moving on schedule into the buffers. In the next section we discuss the use of local performance measures that are consistent with global objectives.
TOC & PERFORMANCE MEASUREMENT
As has been noted, the present system of performance measurement used by most western companies is not consistent with either TOC or JIT operations. The most common problem is machine utilization and efficiency measures at non constraint stations. Because we desire non constraint stations to produce only what is needed to support the schedule, nonconstraints must have some idle time. However, if the machine utilization performance measure is retained, the machine operators and their supervisors will literally beg, borrow, and steal material to prevent idle time. Thus, machine utilization must be eliminated as a performance measure. Anything that would cause an operator to want to be busy, such as incentives based on the number of pieces produced, must also be eliminated.
A logical question then becomes: What performance measures should be used by a company operating under the theory of constraints? It is easy to criticize existing measures, but some performance measure is necessary so that management can properly do its job. The most important performance measure is performance to schedule. Performance to schedule implies that pieces are not made early and they are not made late. Therefore, two performance measures are required, one to measure things done ahead of schedule and a second to measure things done behind schedule. The theory of constraints suggests inventory dollar days as a measure of things done ahead of schedule (and hence inventoried) and throughput dollar days as a measure of things done behind schedule.
A dollar day is simply one dollar held for one day. If you borrow money from a bank to finance your education or a car, you pay for the use of that money on the basis of the amount you borrowed and the length of time you held the money--dollar days. It makes sense to value inventory that is built ahead of schedule on the basis of dollar days. In essences the company has loaned the using department the resources needed to make the inventory. The department should repay the company based on the dollars tied up in inventory and the length of time the money is held as inventory. It also makes sense to measure shipments that are delayed on the basis of dollar days. The delay in shipment will probably result in delay in payment. The cost to the company of receiving payment late is measured by the size of the payment and the number of days that payment is delayed because of late shipment.
Both inventory dollar days and throughput dollar days arc measured relative to a buffer. Let's first consider the shipping buffer To consider the shipping buffer in isolation, assume the market is the constraint so that only a shipping buffer exists. Inventory dollar days would be accrued if material is present at the shipping dock (or finished goods inventory) and the material is not required by the shipping buffer. This material should not yet have been released to the floor. Having been released, it should not have been processed by any station since all stations should have noted that the material was not being pulled into the shipping buffer. Thus, the stockroom that released the material and every station that processed the material is charged with inventory dollar days equal to the cost of the material held in inventory times the length of time until that material will be needed. As time passes, the time until needed will diminish and so the penalty will diminish.
Note that this process has two important features, First, the measure is consistent with the actual cost to the company for the mistake that was made. Second, as the problem becomes corrected, the penalty for the mistake is eliminated. Consistency is important so that decisions made on the basis of local interest do not have a negative impact on the entire company. The problem with machine utilization as a measure at non constraint stations is that it is not consistent; there is incentive for the station to produce inventory that is not needed. The elimination of the penalty as the mistake is eliminated is important because it provides an incentive for the work station to operate efficiently whenever there is work available.
The effect of using inventory dollar days and throughput dollar days on a non constraint is as follows: When work arrives, the worker will verify that the job appears on one of the buffer documents. As long as the job appears on one of the buffer documents, the worker will not be charged inventory dollar days for processing it. Throughput dollar days are computed from the midway point in the buffer. If the work on hand has not reached the midpoint of the time buffer, the worker can avoid any dollar day penalty by processing the job and passing it along before the halfway mark is reached. If the work has reached the halfway mark, the worker is charged throughput dollar days until the work is passed to the next station. The worker has incentive to work quickly either to avoid throughput dollar days or to eliminate an existing dollar day charge.
The use of inventory dollar days is particularly effective in eliminating a tendency on the part of workers to get material early in order to avoid idle time, This tendency is a habit in most shops that have been evaluated on the basis of machine utilization, and the habit will require some effort to break. With the new measure, the worker should soon realize that not only is it not good to work ahead of schedule but that such action will actually incur a penalty.
A worker also has incentive to work carefully. If work is done improperly, the station causing the defect is charged throughput dollar days until the defect is corrected or a replacement unit can be made. If a part that has constraint time embedded in it is scrapped, that part can never be replaced. The constraint has no time to spare to devote to the replacement part. Thus, throughput dollar days can be charged to some arbitrary future point in order to arrive at a finite penalty that emphasizes the cost to the firm of losing a part that has been processed by the constraint.
Sometimes a worker will have two jobs in the station at the same time. Throughput dollar days wilt cause the worker to process the job that is closest to its due date first (assuming approximately equal order value). If the worker acts in a manner to minimize the throughput dollar day charge to the local station, he or she is doing precisely what top management wants done. A consistent performance measure provides excellent shop floor control without the need for management intervention.
If a constraint exists, the constraint station will be provided with a schedule. The use of throughput dollar days and inventory dollar days encourages the constraint operator to keep precisely to the schedule and to produce with perfect quality. If the station for some reason runs out of work, the station is not charged with throughput dollar days while it is idle; the station holding the material needed is charged. However, when work arrives, the operator has an incentive to work quickly and carefully. The constraint operator has a double incentive to do work in the proper sequence: If a job is done early, that job creates inventory dollar days while throughput dollar days accrue on the job that should have been processed.
To summarize this section, throughput dollar days and inventory dollar days provide an incentive for workers to follow the schedule and to work quickly and carefully. They are consistent performance measures in that if the performance of a particular station improves with respect to a measure, the performance of the entire shop must also improve. The performance measures would also work well with an MRP system or a JIT system provided that all workers are made aware of the schedule to be followed.
IMPLEMENTATION TECHNIQUES of TOC
A doctrine of the theory of constraints is that any person responsible for decision making in a particular area is a potential constraint. The chief of purchasing can become the constraint by ordering the wrong material; the chief of personnel can become the constraint by hiring the wrong type of workers; marketing can become the constraint by emphasizing the wrong product(s); many different sections of manufacturing can become the constraint by processing jobs in the wrong sequence or the wrong quantity. It is therefore important for the decision makers to feel a sense of ownership of the global decision-making process. This can best be accomplished by having each decision maker invent the specific system to be used in his or her area.
At the same time, it is important that all areas of a firm are pulling in the same direction) that is, all areas must agree on what constraints exist and what should be done to exploit or elevate the constraints.
T6 accomplish both goals simultaneously, theory of constraint implementation should proceed from the top of the organization down. At each level, a manager who has just received education on the theory of constraints makes a presentation of an implementation plan for his or her area of responsibility to a superior. Unless some gross error in identifying the nature of the constraint has been made, the superior will accept the plan and request the manager to provide for education in the theory of constraints for any subordinate decision makers. This implementation procedure is called Socratic because, like Socrates, the manager must ask questions, not provide answers. It is often difficult for a manager to avoid the temptation to "correct" a subordinate's implementation plan. Nevertheless, this temptation must be avoided. If a manager changes the solution, the implementation becomes the manager's, not the subordinate's. The feeling of ownership is lost. The feeling of ownership is far more important than the precise sequence in which improvement actions are taken. If the manager has patience, the subordinate will eventually find the correct solution---and retain ownership of the solution.
The theory of constraints emphasizes a continual process of improvement. Improvement should be focused on the constraints so that improvement proceeds as rapidly as is practical. Every decision maker should therefore know what the constraints' are, how his or her area of responsibility interfaces with the constraints, what the next constraints are expected to be if a given constraint is broken, and how his or her area interfaces with the anticipated constraints. With this knowledge, the decision maker should be able to identify the set of problems experienced by his or her area that have the greatest impact on the business.
In a sense, the theory of constraints makes the decision-making process much easier. Most managers have an almost endless set of data to track and potential improvement efforts to consider. By identifying those problems that have the greatest impact on the constraint, a manager can limit the amount of data that must be monitored and also postpone consideration of certain improvement efforts. At the same time, the amount of information that must be passed around the organization can be reduced, as a lot of detail concerning non constraint activities can simply not be transmitted.
The theory of constraints provides two useful techniques for use in developing and refining implementation plans. The first is effect-cause-effect and the second is a cloud diagram.
Effect-Cause-Effect
In order to create a good implementation plan, it is necessary to identify those problems that create or contribute to constraints and to understand their underlying causes. For example, the market for a product might be a constraint. When analyzing performance versus competition, we might note that although we are competitive on cost, we have poorer quality and longer lead time than the competition. We should therefore identify the causes of the poor quality and/or long lead time. The long lead time might be caused by a lack of certain components at assembly. It should be easy to verify that assembly jobs arc often held due to lack of a full. set of components. There are many reasons that components might be missing. One is that a constraint exists in the system. A second is that workers may be taking components allocated to one assembly in order to complete a second assembly. Another is that the inventory records are poor and the component never existed in the first place. In order to find a solution we need to understand why the parts are missing. If inventory records are the problem, we need a much different implementation plan than if a constraint is the problem.
At this point we have three hypothesized causes of the problem, any one of which could take quite a bit of time to pursue. Are any of the hypothesized causes worth pursuing? Here is where effect-cause-effect comes in. If any of the three hypothesized causes of the problem really is the cause, there should be some subsidiary effect that exists and that we can verify. For example, if inventory records are the problem, we should find that many of the components do not have correct on-hand quantities recorded. We can verify this subsidiary effect by identifying several components, counting the on-hand quantity, and determining whether the count is correct. If all of the parts tested have accurate counts, it is unlikely that poor inventory records are causing a persistent problem with missing parts. If there is a constraint in the system, a subsidiary effect would be that several of the parts that are supposed to be at the assembly area are sitting at the constraint awaiting processing. We could check this by examining the routings of the missing parts for common stations, then checking the stations that appear on all or most routings to see if one of them has a lot of the missing parts. If there is no concentration of parts at any one station, we are less comfortable pursuing the notion that a constraint exists than if one station has all the parts.
The key feature of effect-cause-effect is that before we spend a lot of time tracing cause and effect we find a way to test whether or not a hypothesized cause is a likely candidate. If we can find no verifiable subsidiary effect, we are likely to waste time by pursuing the present hypothesized cause. Our search is likely to be more effective if we give further thought to possible causes and find one that has subsidiary effects that can be verified. The use of a testable hypothesis is a technique of scientific method that is taught to scientists but, for some reason, is not a standard part of the manager's tool kit. Because it is important for a manager to make effective use of problem solving time, the use of effect-cause-effect to avoid spending time on dead ends is recommended.
Cloud Diagrams
Once the cause of a problem is understood, its solution may not be obvious. The cloud diagram is a useful technique for trying to identify a solution to an intractable problem. For example, the most common topic of articles discussing inventory management is the topic of batch size, indicating that there is no agreement on the ideal batch sizing procedure. Figure 2 shows a cloud diagram of the batch sizing decision. The first task is to identify the objective of the decision to be made. In this case, we wish to find a way to minimize inventory costs. Since inventory costs are composed of the costs associated with holding inventory and the costs associated with processing orders, two requirements for minimizing inventory costs are minimizing holding costs and minimizing order processing costs.
To complete the cloud diagram it is necessary to identify the prerequisite(s) of each requirement. To minimize our holding costs, a prerequisite is that we order in small batches. To minimize our order processing costs, a prerequisite is that we order in large batches. A conflict exists because we cannot both order in large batches and order in small batches. The usefulness of the cloud diagram as a problem solving technique is that it forces us to understand the nature of the problem. To understand that we cannot order in both small batches and large batches is to achieve a much better understanding of the problem than merely to understand that we should minimize inventory costs but that we need inventory.
Once we have clarified the nature of the problem, we can check that the assumptions used in defining the problem are appropriate. The task of determining underlying assumptions is the most difficult and the most critical part of the cloud diagramming process. It is easy to identify a trivial assumption that merely restates a requirement. For example, we might say that it is necessary to minimize inventory holding costs because holding inventory costs money. That is not an underlying assumption; it merely restates the requirement. If we cannot find the true underlying assumption, the technique will be useless. To find the underlying assumption, ask why is this requirement a requirement? Why does it absolutely have to be? In this case, a good statement of the assumption relating holding cost to inventory cost is that we assume that we must pay our vendor for our material before our customer will pay us. Note that this way of stating the assumption does not merely restate the requirement, it truly explains the requirement. If we could find a way to get our customer to pay for the raw material, we wouldn't care how much inventory we kept. (As the amount of inventory held by defense contractors that are paid on a progress payment basis amply demonstrates?)
Figure 3 gives the cloud diagram with an underlying assumption for each of the five arcs. There must exist at least one assumption per arc. If any of the assumptions can be shown to be invalid, the conflict disappears, and the problem is solved. As was mentioned in the previous paragraph, if a contractor can have the customer agree to pay the vendor, the contractor is happy to work with large batches.
The other assumptions present in the usual batch sizing model are now briefly explained. The requirement to minimize setup or order costs assumes that setup costs are variable, that is, the cost varies directly with the number of setups or orders. For a manufactured part this assumption may or may not be true. There is always a real setup cost at the constraint. There often is not a setup cost at a non constraint, although there may sometimes be an expediting cost if a setup causes a deep hole in the constraint buffer. Order cost also may not be a variable cost. We usually include in the order cost the cost of filling out the paperwork for the order and the cost of offloading the truck and storing the goods received. One might ask whether the offloading and storage costs are a function of annual volume or a function of the size of shipments. One can make an argument that the cost is a function of annual volume and is independent of the size of an individual shipment. The process of filling out the paperwork is largely computerized and perhaps is more correctly treated as a fixed cost. The cost of negotiating the purchase may also be fixed. Many firms negotiate a blanket purchase order once a year. For a firm having setup or order costs that virtually are fixed costs, the use of small batches, as JIT advocates, is clearly indicated.
The notion that a large batch is a prerequisite to a small setup cost (accepting the assumption that setup costs are variable) assumes that there is an inverse relationship between the batch size and the number of setups. This assumption is expressed explicitly in the total cost equation used to derive the economic order quantity. The total cost equation has a term stating that the total setup cost is equal to the cost of setup times the annual demand divided by the batch size. Annual demand is assumed to be a constant, independent of batch size. One could argue that the batch size determines the lead time, the longer the lead time the less demand there will be, and therefore the batch size should be chosen based on annual volume considerations, not on setup cost considerations. The Japanese essentially used this line of reasoning to arrive at the practice of JIT and then took their reasoning a step further: Given that volume considerations determine the batch size, Jet's force the setup cost down to something that is consistent with the desired hatch size.
The notion that a small batch is a prerequisite to minimizing holding cost involves a similar assumption-that the batch size is directly related to the holding cost. Again the economic order quantity formula makes the assumption explicit: Holding cost is equal to one-half the batch size times the unit cost times the holding cost percentage. In this instance, the assumption seems unassailable. A change in volume does not affect the average on-hand quantity in the long run. If the order size is Q, the average number on hand is Q / 2, independent of the rate of sales.
The fifth arc, the arc indicating the conflict between the small batch and the large batch, involves an assumption that the concept of a batch is the same in both the large batch prerequisite and the small batch prerequisite. This assumption can be invalidated because the large batch prerequisite refers to the process batch size and the small batch prerequisite refers to the transfer batch size. Although batch production environments traditionally have treated these two batches as being the same, there is no inherent reason that we cannot choose to use a Large process batch to minimize setup cost and a small transfer batch to minimize holding cost. As was stated earlier, the differentiation between the concept of a process batch and the concept of a transfer batch is one of the features that distinguishes the theory of constraints from the traditional approach to production planning.
The act of diagramming a problem in a cloud diagram does not guarantee that an underlying assumption can be broken. Sometimes the best one can achieve is to recognize that there are conflicting prerequisites and accept the best available compromise. (Compromise is the approach that underlies the economic order quantity formulation-accepting a trade-off between holding cost and setup cost.) If a compromise is the only solution, so be it. However, the cloud diagramming technique will often expose an unstated, underlying assumption that is erroneous. The process of exposing the erroneous assumption eliminates the problem; it evaporates the cloud. Because exposing an erroneous hidden assumption usually leads to a marked increase in performance, the time taken to formulate a problem as a cloud diagram before accepting a compromise is well spent.
Let's briefly summarize this section. The implementation process for the theory of constraints relies on managers at each level creating an implementation plan. This approach is used because of a belief that a feeling of ownership of the plan is more important than the short run specifics of the plan. In order to implement, a manager needs to understand the five steps and to understand where the firm's constraints presently are and where they are likely to go in the foreseeable future. Two problem solving techniques, known as effect-cause-effect and the cloud diagram, are useful to managers preparing an implementation plan.
REPORTED RESULTS
Because the theory of constraints is quite new, only a few firms are actively using the concepts and only a portion of those have reported results. Firms that have reported results, discussed briefly below, include General Motors, DuPont, and AT&T. The reason we have elected to report on a technique that is still quite young and not thoroughly tested is that it appears to offer a method of moving the Just-in-Time philosophy of keeping material moving, never idle, from the sequential flow environment to the batch production environment. By having a small transfer batch, a large process batch can be moved through a shop rather quickly. A necessary consequence is that some machines have idle time. We accept that we cannot perfectly balance an assembly line. Perhaps we should also accept an unbalanced shop and learn to exploit the constraint rather than trying to create interacting constraints.
The plant that has reported the most complete set of statistics concerning theory of constraint implementation is GM's Windsor, Ontario, trim plant. Their results were reported in an article in Automotive Industries (Callahan 1989). Windsor calls their approach to production planning synchronous manufacturing, which they describe as an amalgam of theory of constraints and Just-in-Time concepts. Synchronous manufacturing implementation began in 1986, at which time the company was achieving 17.3 inventory turns per year. Their goal was to achieve 35 turns, By December 1988 the plant had achieved 50.4 turns. The company also achieved a 94 percent reduction in lead time and a $23 million reduction in annual costs, while increasing output by 16.8 percent.
An interesting aspect of these numbers is that lead time was reduced by 94 percent WIP inventory was reduced by 68 percent. For most companies employing JIT, the lead time reduction is usually one percentage point different, at most, from the inventory reduction. The reason for the difference is that JIT uses a transfer batch equal to the process batch while TOC does not.
AT&T's microelectronics division reports results achieved with what they call common sense manufacturing (CSM) at their Reading plant (Cannon and Kapusta 1989). Common sense manufacturing is described as including an end-to-end pull system, strategic buffers, constraints management, drum-buffer-rope scheduling, and total employee involvement. Like GM, AT&T's approach apparently is to merge the theory of constraints and Just-in-Time concepts. The Reading plant's reported results include a 50 percent reduction in inventory, a 70 percent reduction in lead time, a 60 percent increase in rework, and a five-fold increase in turnover. They do not report their change in output, however, since turns are defined as annual sales divided by inventory, and since inventory went down only 50 percent, for turns to increase five-fold, annual sales must have increased by 250 percent. They do report, "The results left no doubt that CSM techniques did, in fact, work---and work well beyond our greatest expectations."
DuPont reports some short-term results achieved early into a theory of constraints implementation (Davis and Fox 1989). The implementation team identified the constraint and proceeded to implement the-five steps. First, they noticed that the operator was manually counting parts, delaying the machine. A counter was moved from an unused machine, saving one hour per eight-hour shift. Next, the team noted that part of the time the constraint was performing rework for a non constraint machine. This activity probably made sense using traditional cost accounting but it made no sense from a theory of constraints perspective. The rework activity was moved back to the non constraint. This change freed another hour per eight-hour shift. Next, the team noted that the three operators (one per shift) had quite different methods- A conference was held and a standard method was agreed on and implemented. Within five weeks the output of the constraint had moved from 3,000 units per shift (on average, varying from 2,000 to 4,000) to 8,000 units per shift. The production rate was then backed down to 5,000 units per shift, with little variation, to meet the needs of the market. The original constraint was broken and the market is pacing production, with a different machine than the original constraint identified as the next constraint.
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