Linear Programming Case Statement
Q: What is going on with this case?
A: A company that has focused on research has decided to become a production company. They need a production and financing plan (how much of each product to make and how to pay for it) for the first three months of 1986.
Q: 1986?
A: OK, yes, that was before you were born, but the case has some nice features and moving it up to the present would ruin some of those features, so, 1986.
Q: What kind of research did the company do?
A: The company still does research in genetic engineering; they have simply decided to produce some of the products they have developed rather than selling them to pharmaceutical companies.
Q: This company produces genetically engineered drugs?
A: Yes. That is rather old news today, but in 1986 it was new and exciting. If you remember the movie “Jurassic Park,” that is the kind of work this company does.
Q: They are making dinosaurs?
A: No, but they are playing with gene sequences to create new drugs.
Q: What drugs have they produced?
A: In the past ten years they have had a lot of success with altering growth hormones for various animals. One of the drugs in this case, CGH (Chicken Growth Hormone) is a result of that research. When used as a feed supplement for chickens, it results in faster growing and ultimately larger chickens, which chicken farmers like (“faster growing” means quicker turnover and “larger” means you can sell the chicken for more).
Q: You said, “one of the drugs.” Are there others?
A: One other: DL (Delta Lymphokine). This drug is for humans and is supposed to help with immunosuppressed patients. You may not realize that when a person receives an organ transplant (heart, liver, whatever), the immune system has to be shut down to prevent the body from killing the “foreign” organ. Similarly, chemotherapy (for cancer patients) shuts down the body’s immune system. Now, without your immune system, you get sick a lot and could die from something really simple. DL may be able to boost the immune systems of patients like these.
Q: Since this is 1986, does this case have anything to do with AIDS?
A: Very good, yes, it does. In 1986, AIDS was a scary, new, worldwide epidemic. Nobody knew anything about it, except that its kill rate was nearly 100% once it went active (the disease can lie dormant for years). Anyone who found a cure for AIDS was guaranteed a trip to Sweden to pick up a Nobel Prize. DL shows a lot of promise to be the first drug to have any success in treating AIDS.
Q: How many AIDS patients have been treated with DL?
A: None. Before a drug can be used on humans, the FDA spends five to seven years testing it to see whether the helpful effects are greater than the harmful ones. The FDA has agreed to test DL and is asking for 250,000 milligrams of the drug each quarter for testing. Right now, that is the only market for DL.
Q: That’s a pain. What about CGH?
A: CGH, as an animal feed supplement, does not require FDA approval and we can sell all we can make.
Q: Where do we make these drugs?
A: Up to now, we have produced small amounts in our labs. With our decision to become a drug production company, we did an IPO (Initial Public Offering) and raised a lot of money. Unfortunately, we spent most of that money renovating a brewery to become a continuous-flow manufacturing facility.
Q: What is continuous-flow?
A: Actually, what it says – product flows out of the system as a semi-solid which is processed into the final product. It only works for products that can be semi-liquid, so they flow from one part of the system to the next, such as drugs, many chemical processes, and even some foods.
Q: Anything else we need to know about CF systems?
A: Yes. They are extremely expensive to set up, so they only way they pay for themselves is to run at 100% of their capacity so they produce a LOT of product and the cost is spread out, reducing the cost per unit. Second, your system is basically four vats. Raw materials are pumped in at the bottom and as they move toward the top (taking a couple of hours to get there), they “cook” so they are finished when they get to the top and are skimmed off. That means that when you start up, and the vat is empty, the first vat-load doesn’t cook properly, and has to be thrown out. In a similar way, if you shut down, you have a whole vat of partially cooked product that has to be thrown out. In other words, starting up and shutting down the system is wasteful and expensive.
Q: Anything else we need to know about the products?
A: The spreadsheet that accompanies this shows the revenue and cost data for each product, and gives you other information, such as the processing time required, the anticipated payment schedule, and all sorts of financial information.
Q: What about the financing part of the case?
A: Well, the most important point is that we are cash-strapped. Having spent most of our IPO money on re-fitting the brewery, we are down to $218K (“K” means “thousands,” if you don’t know that abbreviation) in cash.
Q: How are we going to pay for everything?
A: That’s the problem. In your accounting class, you should have come across the phrase “net 30,” which means you have 30 days to pay for something after you receive it (this is called “trade credit”). So, you order a bunch of raw materials, they show up, and you have 30 days to turn the raw materials into products and sell them. You theoretically use the money from the sale to pay for raw materials, hopefully making a little profit that you get to keep.
Q: Why did you say “theoretically”?
A: Just like you take 30 days to pay your suppliers, your customers take 30 days (longer, actually, see the payment schedule referenced earlier) to pay you. This leaves a one to two-month gap where you have to pay for raw materials and operating expenses before much money flows in from product sales.
Q: Will $218K cover that?
A: Not even close. We are going to need millions of dollars.
Q: What do we do?
A: As much as I hate to say it, borrow the money using a Line of Credit (LoC). It is usually a really terrible idea to borrow money to cover operating expenses, but as a start-up, we kind of have to.
Q: What is a line of credit?
A: Basically, a credit card. You are given a limit (your bank gave you a three-million-dollar line), and you pay interest on only the amount you draw (not the whole amount). You can pay the balance down, or draw more and pay interest on more, as long as you make the interest payment each month.
Q: Anything else?
A: Well, your bank is a little nervous. You are a start-up production company with no cash and you have up to $3,000K of their money. To make themselves feel better, they have set two limits on you: you must keep at least $120K in cash in the bank, and total debt (defined as line-of-credit balance plus the trade credit (money owed to your suppliers for raw materials) must be less than $4,000K.
Q: Have we stopped being a research company?
A: No, there is data (on the spreadsheet) showing the on-going revenues and costs from existing business.
Q: What are we supposed to do with all of this?
A: The spreadsheet shows you a linear programing formulation that uses all this data. The decision variables are the production levels (per month) for each of the two products, and also cash on hand (monthly) and LoC balance (again, for each month). The objective is to maximize contribution, and the constraints are DL demand (no more than the 250K mg needed by the FDA), LoC cap ( 250K), total debt (< 4,000K), cash flow (more on that below) and production capacity (4 vats * 24 hours per day * days per month, either 31 or 28).
Q: What is “cash flow”?
A: Something I hope you covered in Accounting. Simply put, cash flow is monitoring the movement of CASH (not money owed by you or to you). The basic equation is:
(Beginning Cash) + (Cash In) – (Cash Out) = (Ending Cash)
That sounds really simple but applying it can be tricky. Fortunately, you don’t have to. In the formulation is a Cash Flow constraint (that looks nothing like that formula, but, trust me, it does the same thing) and on a separate page of the spreadsheet there is a Cash Flow Table linked to each solution. You should look at that table to see where the money is going and where it is coming from. This will tell you a lot about the risks and rewards of each solution.
Q: If we are using LP, which gives one, optimal solution, how can you say, “each solution,” implying more than one?
A: This is important – “optimal” is an EXTREMELY (caps for emphasis) limited idea. “Optimal” doesn’t mean “best,” it means “best for whatever data you typed in.” If you change the data, as I have, you get a different, but also optimal, solution. You have to decide which of the optimal solutions you prefer.
Q: What are these different solutions?
A: The first optimal solution is simply using the data provided in the case. In the video, I explain why this is a truly bad solution that will probably bankrupt the company within the first three months, even though it does make a lot of money (maximizes contribution). I show you two alternate solutions, one emphasizing CGH production over DL, and the other emphasizing DL, then using the remaining resources to make whatever CGH you can.
Q: Shouldn’t we just pick the one that has the most profit (contribution)?
A: Not necessarily. The LP formulation gives you the highest contribution for each scenario, but there are other factors you have to consider.
Q: What other factors?
A: We call these factors “criteria,” and this type of problem (most problems, actually) are “multiple criteria” problems. The criteria you must consider for the two alternate solutions (DO NOT recommend the first solution – it is terrible) are contribution, cost/borrowing, market penetration, and capacity utilization.
Q: Contribution is pretty obvious, but what is “cost/borrowing”?
A: Cost and borrowing are closely related in this problem, so you might as well think of them as one criterion. Since we have very little cash, and must keep $120K of in an account, to make the bank happy, the higher your costs, the more you will have to borrow from the LoC. If you max out your LoC and money doesn’t flow in as you expect, then you won’t be able to pay your trade credit, there will be no more raw material shipments, and you go out of business. The LP solution will assume the payment schedule is 100% correct, so you will have to worry about that on your own. The only thing you can do, though, is keep enough of the LoC available for you to cover a month of late payments. You may not be able to do that, but you have to do the best you can.
Q: Ok, what about “market penetration”?
A: For DL, since the FDA is the only market that just means “How quickly do you get the 250K mg of DL delivered?” For CGH, it means a little more: you can sell all you can make, so you want to make all you can (to get customers used to buying your brand) but you also want to sell more each month, to keep all current customers happy and bring on new customers.
Q: What about “capacity utilization”?
A: This goes back to the continuous flow process, where I told you that you had to run at 100% to make a lot of product and spread the high cost out. It turns out that you don’t have enough cash to run at 100% every month starting in January. If you try, you will have to shut down vats (as explained, that is very wasteful and expensive). So, you want the capacity used to increase from month to month, reaching 100% as quickly as possible.
Q: None of that sounds really hard. We just pick the solution with the highest contribution, lowest cost, highest production amounts (market penetration), and highest capacity used. What’s the problem?
A: No one solution has all of those. You have two solutions, and each wins some criteria and loses others. Some of them are pretty close. You have to decide which tradeoffs to make.
Q: What do you mean by “tradeoffs”?
A: Suppose you pick the solution with the highest contribution. How much extra cost/borrowing did you take on? What did that do to capacity utilization? You have to decide not only which criteria are most important to you, you have to explain to me WHY that is more important than another and why the differences in the criteria are significant.
Q: How do we do that?
A: Listen to the recording. I will talk about each solution and each criterion for each solution. You have to take notes, write down the relevant numbers, and then think about it and figure out which one is right for you and why. Then you explain that to me in a one-page summary. What could be easier?
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