Decision Analysis WK4A
1. Read the referenced article that fully describes the management science study summarized in the application vignette presented in Section 7.1. Briefly describe how mixed BIP was applied in this study. Then list the various financial and nonfinancial benefits that resulted from this study.
7.1 A CASE STUDY: THE CALIFORNIA MANUFACTURING CO. PROBLEM
The top management of the California Manufacturing Company wants to develop a plan for the expansion of the company. Therefore, a management science study will be conducted to help guide the decisions that need to be made. The president of the company, Armando Ortega, is about to meet with the company’s top management scientist, Steve Chan, to discuss the study that management wants done. Let’s eavesdrop on this meeting.
Armando Ortega (president): OK, Steve, here is the situation. With our growing business, we are strongly considering building a new factory. Maybe even two. The factory needs to be close to a large, skilled labor force, so we are looking at Los Angeles and San Francisco as the potential sites. We also are considering building one new warehouse. Not more than one. This warehouse would make sense in saving shipping costs only if it is in the same city as a new factory. Either Los Angeles or San Francisco. If we decide not to build a new factory at all, we definitely don’t want the warehouse either. Is this clear, so far?
Steve Chan (management scientist): Yes, Armando, I understand, What are your criteria for making these decisions?
Armando Ortega: Well, all the other members of top management have joined me in addressing this issue. We have concluded that these two potential sites are very comparable on nonfinancial grounds. Therefore, we feel that these decisions should be based mainly on financial considerations. We have $10 million of capital available for this expansion and we want it to go as far as possible in improving our bottom line. Which feasible combination of investments in factories and warehouses in which locations will be most profitable for the company in the long run? In your language, we want to maximize the total net present value of these investments.
Steve Chan: That’s very clear. It sounds like a classical management science problem.
Armando Ortega: That’s why I called you in, Steve. I would like you to conduct a quick management science study to determine the most profitable combination of investments. I also would like you to take a look at the amount of capital being made available and its effect on how much profit we can get from these investments. The decision to make $10 million available is only a tentative one. That amount is stretching us, because we now are investigating some other interesting project proposals that would require quite a bit of capital, so we would prefer to use less than $10 million on these particular investments if the last few million don’t buy us much. On the other hand, this expansion into either Los Angeles or San Francisco, or maybe both of these key cities, is our number one priority. It will have a real positive impact on the future of this company. So we are willing to go out and raise some more capital if it would give us a lot of bang for the buck. Therefore, we would like you to do some what-if analysis to tell us what the effect would be if we were to change the amount of capital being made available to anything between $5 million and $15 million.
What is the most profitable combination of investments?
Steve Chan: Sure, Armando, we do that kind of what-if analysis all the time. We refer to it as sensitivity analysis because it involves checking how sensitive the outcome is to the amount of capital being made available.
Armando Ortega: Good. Now, Steve, I need your input within the next couple weeks. Can you do it?
Steve Chan: Well, Armando, as usual, the one question is whether we can gather all the necessary data that quickly. We’ll need to get good estimates of the net present value of each of the possible investments. I’ll need a lot of help in digging out that information.
Armando Ortega: I thought you would say that. I already have my staff working hard on developing those estimates. I can get you together with them this afternoon.
Steve Chan: Great. I’ll get right on it.
The California Manufacturing Company is a diversified company with several factories and warehouses throughout California, but none yet in Los Angeles or San Francisco. Because the company is enjoying increasing sales and earnings, management feels that the time may be ripe to expand into one or both of those prime locations. A basic issue is whether to build a new factory in either Los Angeles or San Francisco, or perhaps even in both cities. Management also is considering building at most one new warehouse, but will restrict the choice of location to a city where a new factory is being built.
The decisions to be made are listed in the second column of Table 7.1 in the form of yes-or-no questions. In each case, giving an answer of yes to the question corresponds to the decision to make the investment to build the indicated facility (a factory or a warehouse) in the indicated location (Los Angeles or San Francisco). The capital required for the investment is given in the rightmost column, where management has made the tentative decision that the total amount of capital being made available for all the investments is $10 million. (Note that this amount is inadequate for some of the combinations of investments.) The fourth column shows the estimated net present value (net long-run profit considering the time value of money) if the corresponding investment is made. (The net present value is 0 if the investment is not made.) Much of the work of Steve Chan’s management science study (with substantial help from the president’s staff) goes into developing these estimates of the net present values. As specified by the company’s president, Armando Ortega, the objective now is to find the feasible combination of investments that maximizes the total net present value.
To the left of the following problems (or their parts), we have inserted the symbol R whenever RSPE can be used. The symbol T indicates that the Excel template for posterior probabilities can be helpful. Nearly all the problems can be conveniently formulated in a spreadsheet format, so no special symbol is used to designate this.
2. You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem without probabilities.
State of Nature
Alternative S1 S2 S3
A1 6 2 4
A2 3 4 3
A3 8 1 5
a. Which alternative should be chosen under the maximax criterion?
b. Which alternative should be chosen under the maximin criterion?
3. Barbara Miller makes decisions according to Bayes’ decision rule. For her current problem, Barbara has constructed the following payoff table (in units of hundreds of dollars) and she now wishes to maximize the expected payoff. Use the attached excel spreadsheet to show work, there are two tabs.
State of Nature
Alternative S1 S2 S3
A1 2x 50 10
A2 25 40 90
A3 35 3x 30
Prior probability 0.4 0.2 0.4
The value of x currently is 50, but there is an opportunity to increase x by spending some money now.
What is the maximum amount Barbara should spend to increase x to 75?