A theory of constraints fable: part 1.

While I was perusing the classified advertisements in a metropolitan newspaper, the following caught my attention: "Plant Manager for Plant 10; Knowledge of modern mang. tech. rqrd. Salary neg. Rspd. to Box 114."

Since I am an engineer, I was actually looking for a management position such as director of R & D. But this advertisement aroused my curiosity, because I was currently taking a course in Industrial Management at the local university, and we were studying several new management theories and systems. One such philosophy, "Theory of Constraints," was particularly exciting to me, and I thought it would be challenging to try to apply it in a real company. Therefore, I decided to send a resume to Box 114. All I had to lose was a stamp.

Several weeks passed before I received a call from the personnel director of Numbers, Inc. He said that the president of the First Decade Division of Numbers, Inc., Mr. Six, wanted to discuss the position at Plant 10 with me. He suggested that we meet at Mr. Six's corporate office in Chicago on the last Thursday in March. I agreed to his plans.

Numbers, Inc., was a large corporate conglomerate with hundreds of plants worldwide. It had the reputation of not being very creative and made money by buying existing manufacturing facilities, operating them until they became unprofitable or outdated, and then either selling or closing them and liquidating the assets. Even the company's names for its plants lacked creativity. Plants were called "Plant 1 ," "Plant 2," and so forth. They grouped ten of these plants together to form divisions known as "First Decade," "Second Decade," etc.

I flew into Chicago on the Wednesday before my interview. That night I visited with an old college friend now living and working in the Chicago area. Roger had heard of Numbers, Inc., and knew its reputation for buying small companies and running them into the ground. By the end of the evening, I wondered if I had made a mistake in even considering working for such a corporation. Since I was already there, however, I decided that it offered an opportunity for me to gain valuable experience.

The next morning I met with the personnel director, and we discussed my background. At ten o'clock he took me to see Mr. Six, an older gentleman who was a little rough around the edges. When the personnel director introduced us, Mr. Six said he was glad to meet me and began describing his problems with Plant 10. He had authorized the purchase of Plant 10 about two years ago. At that time, the plant was profitable and had a very strong market potential, but it also had either considerable excess capacity or very poor resource utilization. He replaced the plant manager with one of his own men, Mr. Four, to run the plant. Mr. Four, as it tums out, was a tough executive who was supposed to light a fire under Plant 10's "inefficient" workers. Mr. Four had successfully improved the plant's efficiency, but it still was not making a noticeable profit. Therefore, Mr. Six was not a very happy man. He turned to me and posed a question: "Can you make me money?"

I started to explain diplomatically that I thought a management philosophy called Theory of Constraints could be applied to this plant. Mr. Six cut me off abruptly and said, "I don't want to hear any philosophical mumbo jumbo. I want to know if you can make me some money in that plant."

At that point, I decided to change my approach. I looked him directly in the eye and announced that if I could not make the plant profitable, nobody could. I really had no idea whether I could make the plant profitable or if I was even the best person to try, but that was the answer Mr. Six wanted to hear. "Good, I like an individual with confidence," he said. I looked around for the person he was talking about, but I was the only person in the room.

Mr. Six suggested lunch, and I agreed. During that time, I realized that Mr. Six not the cold-hearted man he seemed. Instead, he was a man being pressured by the CEO, Mr. Century, to explain why he had purchased a company that was not turning a profit. He told me that he was the sixth president of this division and that a Mr. Seven, a good friend of the CEO, wanted his job. It was imperative that he make plant 10 profitable if he wanted to keep his job.

After lunch, we returned to Mr. Six's office. By this time, the conversation was much lighter, and we were able to discuss some of the specifics of the job. He informed me that I was competing for the job against Mr. Biff, the son of Mr. Eighteen, the president of the Second Decade Division. Mr. Biff had recently received an MBA from Harvard and was looking for a career boost from his father. Mr. Six did not have much use for Mr. Biff, but he agreed to give him a chance to secure the job.

Mr. Six wanted me to visit Plant 10 next week. (A visit was also planned for Mr. Biff.) While I was there, I would also meet with the controller for a briefing on the company's financial operations. After the visit, I was to prepare a business plan for the plant for the next month. Mr. Biff would also be making a plan, and Mr. Six would use our plans to decide which of us would be hired. Mr. Six then took me down to the personnel director to make the necessary arrangements. The plant's financial information was sensitive, so we spent about an hour filling out numerous non-disclosure agreements.

The following Tuesday, I arrived at Plant 10 at 9 o'clock. The first order of business was a detailed tour of the facility. The controller, George Peabody, and the plant engineer, Frank Smith, accompanied me. George explained that the plant only produced three products at this time: A, D, and F. All three were manufactured from four basic raw materials: A, C, E and F.

I started taking notes in preparation for my assignment. I asked George the price of each of the products. George responded, "Product A sells for $180 each, and our sales forecast calls for 40 per week. Product D has a sales forecast of 80 per week at $240 per unit. He explained that product D was their most profitable product, and the sales department was working hard to sell it.

"What about product F?" I asked. He told me, like product A, it sold for $180 with has a sales forecast of 40 units per week. George added that they had not been able to produce enough of the products to satisfy the customer needs. Seldom did they deliver a product by the due date. George's comments led me to believe that there might be some hope for making a profit in this business. Obviously, the products were in high demand. Otherwise, there would be no customers left.

I asked Frank if he could show me how these products were manufactured. Frank's face brightened as he realized he was going to be able to show off the manufacturing facility he had built from the ground up. Frank was one of the plant's two original employees and knew it better than anyone. He started his explanation with product A, which is manufactured from raw materials A and C. First, both raw materials were processed through the green machine. There were two green machines, each of which had one operator. It took two hours to set up the machines, but once they were, they basically ran themselves. At one time they had tried having one person operate both machines, but it had not worked out very well. Both machines, it seemed, needed to be set up at the same time, a task for more than one operator.

I asked Frank if I could see raw materials A and C. He stared at George for a few minutes before he asked if I would refrain from any more questions about raw material supplies until he had a chance to explain. I agreed, and Frank continued. Once the raw materials passed through the green machine, they were assembled in the red machine to form subassembly B, which was used in products A and D. The red machine had one operator, and considerable physical effort was needed to operate it. The operator was not busy on a continuous basis, but Frank did not think anyone could run it continually for eight hours. He went on to say that it now took only eight minutes to process a part on this machine, when only a month before, it had taken eighteen minutes. George took that opportunity to explain that Frank's excellence in reducing the processing time and eliminating all set-up time at this station had greatly reduced the cost of products A and D.

As I looked around the machine, I noticed a considerable inventory of subassembly in the aisle and on the shelves. I asked Frank about this. Frank replied proudly that this inventory was the proof that his modifications really worked; the material really flew through the red machine now. I smiled, all the while thinking, "There must be a constraint somewhere around here."

I asked Frank where the subassembly went from here. He answered that some of the subassemblies are processed through the green machine again to produce A. Others were routed to the Blue machine for product D. I suggested that we continue to follow through on Product A and return later to follow product D.

As we walked over to the Green machine, I felt that I might have identified the system constraint. The machines had a long set-up time and were used for three different operations just to produce product A.

"How much time does it take to process one subassembly through this machine?" I asked.

Frank answered, "Fifteen minutes, plus or minus a few."

"And how long does it take to process the raw materials?"

"Processing raw material A takes four minutes and raw material C takes five minutes."

I did some quick math in my head: "15 plus 4 plus 5 equals 21 minutes, or 3 parts per hour. We can sell 40 units per week. That's approximately 40 divided by 3, or 14 hours. There are 80 product Ds: 4 plus 5 is 9, or 6 per hour; therefore, 80 divided by 6 equals 13 hours. That's a total of 14 plus 13, or about 27 hours. If I add at least three set-ups of two hours each, that is 33 hours."

I began to smile, confident that I had found the system constraint. "Is this machine used for any other products?" I asked.

Frank nodded, explaining it was also used to manufacture product F. "That's why there are two of these old work horses," he added.

My smile disappeared. I realized that I might have jumped to a conclusion too soon. Frank suggested that we move on to the Cyan machine, which was the next step in the production of A.

As we walked toward the shipping dock, Frank explained that two cyan machines were used to perform the last step in the manufacture of all the products. These machines were located near the shipping docks. Frank went on to say that they were used throughout the production of all the products. Since I no longer wanted to jump to unwarranted conclusions, I erased all previous thoughts about constraints and concentrated on the operation of the cyan machine.

Product A passed through the cyan machine in fifteen minutes. The product then traveled to the magenta machine and returned to the cyan machine for the final, eighteen-minute manufacturing stage. The cyan machine had a one hour set-up time, and one operator was assigned to run the machine. As we moved from the cyan to the magenta, I noticed two large piles of inventory, or works in progress (WIP), piled beside each machine. The magenta machine took twenty minutes to process each A. It had a half-hour set-up time with one operator stationed at each machine. Frank then pointed at the shipping dock and said, "From here, it goes back through the cyan machine and out the door." He paused and added, "Usually about two days late."

Frank then suggested that we go through the manufacturing stages for product D. I nodded with approval as Frank again pointed at the shipping and receiving dock. "Raw material E is brought in by truck, processed through the cyan machine right by the dock, and then brought over here and run through the magenta machine." It took nine minutes to process E through the cyan machine and another eighteen minutes to pass through the magenta machine. Frank reached into the pile of pans beside the aisle and handed me one. "At this stage we have a part that looks like this," he said. I put it back.

The parts then went to the blue machine. As we walked that way, Frank stopped and introduced me to Tom Jones. Frank bragged that Tom was one of the company's brightest and most talented young employees. Tom seemed slightly embarrassed by Frank's fulsome comments, but I could see that he was also pleased. Tom's fellow employees had chosen him to be the first participant in a new cross-training program. Frank had designed this program, which would eventually train all employees to operate all machines.

I was impressed. "There just might be some hope for this company, after all," I thought. I was encouraged that Frank seemed willing to try new approaches to solving old problems. Tom said it was nice to meet me, but that he really had to run. He was scheduled to be trained on the Green machine, and he did not want to waste any time. He was only allowed to cross train for an hour a day, then he had to return to his work station.

The three of us waded through all the partially finished parts to the blue machine. George seemed unhappy about this multitude of parts, and he made an unintelligible comment to Frank. Frank shrugged it off the comment and continued to talk about the Blue machine, which took an hour to set up before processing one part of Raw Material E in thirty minutes. There was only one Blue machine.

"Tom Jones is the only person who can run this old machine," he said. "From here, the parts go to the Red machine, where they are assembled with subassembly B, which has also gone through the Blue machine." Subassembly B, which was the same subassembly used in product A, took six minutes to pass through the Blue machine.

I noticed that the blue machine was not operating at the moment, but I did not give it much thought. I knew Tom Jones was cross-training on the green machine and would be back in an hour.

From the red machine, the part went to the cyan machine for a final six minutes of processing. I asked Frank to back-track a bit and tell me how long it would take for the Red machine to perform the assembly. Frank smiled. "Nine minutes," he said. George commented that Frank's recent modifications had shortened the time from eighteen minutes. Producing D was now more cost-effective.

Because it was nearly time for lunch, Frank suggested giving me only a quick run-down of F's production process, particularly since I had now seen all the equipment. I agreed. Raw material F was processed through the green machine first, in about fifteen minutes. It then was sent to the cyan machine, where it was processed in twelve minutes. From there, it went through the magenta and blue machines, which have processing times of twenty and fifteen minutes, respectively. It then flowed back to the magenta machine for a second, seven-minute processing. Its final stop was the cyan machine for a final, ten-minute processing before it went out the door.

As I was hastily taking notes, Frank asked if I had any questions. "Not at the moment," I said. I asked him if he would mind reviewing my notes after I had organized them. I wanted him to see if I was on the right track. Frank said he would be glad to help any way he could.

George suggested lunch. Frank said he was unable to join us because he had scheduled an employee luncheon for feedback on his new cross-training program. As we said our good-byes, I told him I would probably fax an organized version of my notes over to him in the morning for his comments.

On the way to the restaurant, George asked me what I thought of Mr. Six. I commented that I felt his bark was worse than his bite. George then announced that he hated Mr. Six with a passion. He said that Mr. Six had offered him the plant manager position, but he had declined because he disliked the idea of "that monster" breathing down his back every minute. During lunch, George explained that up until two years ago they were a very profitable little company. Then they were purchased by Numbers, Inc., and had to meet their requirements for efficiency and resource utilization.

We returned to George's office, ostensibly to discuss Plant 10's financial status. Instead, George shut the door behind us, and in a very serious voice announced that there were some things about the company that I needed to know. He reminded me of my request asked to see raw materials. He continued, "Well, the truth of the matter is that we're having cash flow problems right now and we can't afford to buy any raw materials." I had no reply. The situation was worse than I had imagined. George said that all the WIP in the plant had become a cash flow drain and they were not able operate the plant the way it should be. Unless some of the WIP was converted to finished products and sold, they would be unable to make payroll on Friday. That was why Mr. Six had asked for a plan for the next month. "He wants to find somebody who can get the plant out of this mess in a hurry, before it's too late," George said.

The plan at that point was to try to push as many products as possible out the back door without purchasing any new supplies of raw materials. If everything went as planned, they might generate enough cash to make payroll ($11,000) and have some money (approximately $2,500) left over to buy the raw materials needed to operate the plant next week. According to his projections, they would have reduced WIP to 20 subassembly Bs, 10 subassembly Es, and 8 subassembly Fs to be processed through the Blue machine. Purchasing had to know what raw materials were needed for the next week by Friday afternoon for there to be any chance of receiving them in time for next week's production.

He stated, "I have no clue what to tell them. Raw materials A and E are the cheapest at $30 a piece. I could order them to keep the production people busy, but I can't sell any product unless we process some raw material C at $35 per unit. The only thing I'm reasonably sure we don't want to process is raw material F. It costs us $65 per unit."

After hearing all this, I was beginning to feel overwhelmed. I wondered what had ever possessed me to send a resume to this company in the first place. I did not feel much better when George told me that Mr. Biff, who was in the plant the day before, and I had to submit our plans for the plant to Mr. Six first thing Thursday morning, and he would respond by Thursday evening. George made sure to stress that he needed to know what raw materials to order by Friday afternoon.

George walked me to the front door, wished me good luck, and said he would be available all day Wednesday if I had any questions. As I drove away from the plant and boarded the plane, I knew that I had my work cut out for me if I wanted to get a plan to Mr. Six by Thursday morning. Leaving the airport parking lot, I mulled over the process that Frank had described in such detail. My first step, once I got home, would be to organize my notes so that I could use them to work through this problem.

FIGURE 2
               Minutes/Unit

Resource        A        D         F

Blue            0        36       15
Green          24         9       15
Cyan           33        15       22
Maroon         20        18       27
Red             8        17        0
Total          85        95       79

By the time I pulled into my driveway, I had already identified my first constraint as time. I knew I had better exploit it by starting on this plan immediately. After sifting through my notes for several hours, I created a flow diagram [ILLUSTRATION FOR FIGURE 1 OMITTED]. I would have liked to fax a copy to Frank for confirmation, but that would postpone any further work. until morning. I decided to proceed with the assumption that my model was correct.

Since my next step was to identify the system's constraint, I constructed several tables. The first two (Figures 2 and 3) showed that the blue machine was the system constraint; it was where the WIP was located. Now that I knew the system constraint, I needed to exploit it. To do so, it was necessary to identify which products yielded the highest throughput per constraint minute. I created another table (Figure 4).

FIGURE 3
                                  Minutes/Week
Resource         A        D     F      Total    # Machines    %
Load

Units/Week       40      80      40     160
Blue              0    2880     600     3480       1
145%
Green           960     720     600     2280       2            48%
Cyan           1320    1200     880     3400       2            71%
Maroon          800    1440    1080     3320       2            69%
Red             320    1360       0     1680       1            70%
FIGURE 4

Throughput per constraint minute (TOC)
                                    Product
                             A         C          F

Sales                     $180.00    $240.00    $180.00
Raw Materials Cost         $65.00     $95.00     $65.00
Throughput                $115.00    $145.00    $115.00
Minutes on Constraint           0         36         15
Throughput/Constraint
-minute                      FREE    $4.03      $7.67

I then realized that it was well past midnight and this step could be completed later in the morning. I also felt it would be a good idea to ask Frank to look over my model before I went too much further. In the morning I would fax Frank a copy of the model and ask George for any confirmed orders they had in the pipe line.

I awoke early Wednesday morning and immediately faxed a copy of my plant model to the plant. I knew Frank was not there yet, but I wanted it to be waiting for him when he walked in the door. At the bottom of the diagram, I attached a note asking George to make a list of all confirmed orders they currently had for the next two weeks and fax it back to me.

I then got to work on my plan for the next week based on the sales forecasts George had given me yesterday. After an hour of sifting through notes and calculating, I came up with yet another table (Figure 5). Although I was starting to feel better about the profitability of this company and the Theory of Constraints, several things still bothered me about my calculations. The plan was based on simulated orders and did not include any time for setting up the blue machine. I was also a bit concerned that if I ran the blue machine at full capacity, it might create load problems on other machines. However, the low utilization of the other machines indicated that my latter concern was not a serious one.

FIGURE 5

Budget & Product Mix - TOC

Product                              A        C        F      Total

Throughput/Constraint Minute       FREE     $4.03   $7.67
Units per Constraint Minute           0        36      15
Number of Units per Week             40        50      40
Minutes per Week or Constraint        0      1800      600    2400
Sales Price per Unit               $180      $240     $180
Total Sales of all Units Sold    $7,200   $12,000   $7,200
$26,400
Raw Material Cost                   $65       $95      $65
Total Raw Material Cost          $2,600    $4,750   $2,600
$9,950
Weekly Expenses
$11,000
Net Profit
$5,450

I knew I needed to investigate the other two questions further. I thought of the Goldratt Institute Simulators and The Goal Software, two computer programs we had used in my Industrial Management class to solve these types of problems, but I did not have time to locate such software and run it. Anyway, Plant 10 did not have enough money to buy raw materials, much less an expensive computer program. I would have to think of a methodology for performing the simulation manually.

I dug out a copy of The Haystack Syndrome, by Dr. Eliyahu Goldratt, and read the section in which he discusses how these programs work. As I read that chapter, I realized suddenly that I could use my favorite toy to solve this problem. As they had other times in the past, Legos would come to my rescue. I had used them to build a model for viscoelasticity in graduate school and to develop the hyperbolic function used to control a robotic filament winder. So, off I went to the closet to find those amazing blocks.

By the time I returned to my office, the fax machine was printing a copy of the confirmed orders for the next two weeks.

My next item of business was to develop a system to model the load on the constraint: the blue machine. I created a time line using each row or peg on a Lego block to represent one hour. Eight pegs equaled one day. I then created a paper time line that corresponded with the pegs and placed the Lego base plates on the time line.

I used yellow blocks to represent the when the blue machine's operating time for processing subassembly Bs. Therefore, at six minutes per unit, I could process ten subassemblies per Lego peg. White blocks represented the time for processing the semi-processed raw material E through the blue machine. That operation took thirty minutes per part, so each peg represented two parts. Blue blocks represented the time that the constraint was processing raw material F. A process time of fifteen minutes per unit corresponded to four units per Lego peg. Finally, I chose red blocks for the set-up time, which was one hour and corresponded to one Lego peg.

I stacked a set of blocks together in a line long enough to equal twelve hours, my designated shipping buffer. I marked the center to represent the point when I had used half of my shipping buffer. I systematically transferred each order from the table that George had sent me to the time line, writing the shipping date on the block. I then laid one end of my shipping buffer block at the shipping date on my time line and placed the end of the order block onto the Lego plates.

I began to place the orders that were due on the seventh day of operation. The right edge of the shipping buffer was placed on orders due to be shipped on the seventh. The bottom blue block represented an order for 24 Fs. White and yellow blocks represented the order for 10 Ds. The red block represented the setup time for each operation. All orders were due at the same time, so the right edge of each set was lined up with the left edge of the shipping buffer.

The next step was bulldozing the runs backwards in time as shown above. Care should be taken to keep the latest shipping date to the right of any early shipping dates. In this case, orders for the tenth day are to the right of the orders for the ninth.

Since it is impossible to do work in the past, I then turned the Lego bulldozer around and pushed all the orders to the present day. The orders extended beyond the left end of the timeline. Obviously, there would be some late orders.

Next, I identified all late orders with a red flag. I placed the right edge of the shipping buffer on each due date. If any order extended past the mid-point of the shipping buffer, it received a flag.

I combined like orders to eliminate any unnecessary set-ups. I made sure I only moved the orders to earlier dates to avoid trading one late order for another. Some red flags disappeared. To remove the remaining red flags, my only option was to schedule overtime on the blue machine. Based on the distance the last order hangs beyond the right edge of the time line, I saw that I would need at least twelve hours of overtime. At two hours of overtime a day, Tom Jones would have to work overtime all next week. If the overtime were started early, a set-up or two might be eliminated and some of the overtime reduced.

Now that I felt confident that all the orders could be met, it was time to go back to adjust my early predictions based on firm orders and overtime requirements.

Editor's note: Part 2 of this fable will appear in the May/June issue of Industrial Management.

Sam Osten is a research and development engineer employed by Vetrotex Certainteed. Mike Patterson, Ph.D., is a professor of management at Midwestern State University, located in Wichita Falls, Texas.