What To Turn In

For the sake of this project consider your group to be a ledgling operations research consulting irm. StoAgra is your irst big client and you want to impress them in hopes of getting future contracts with them and to get good press so other large companies will notice you and provide you with interesting work and huge consulting fees.

Your report to StoAgra will be done in three parts. The irst, a one page cover memo addressed to the company’s CEO, should thank the CEO for the opportunity to work on StoAgra’s problem, express your willingness to follow up on this project if necessary, and your eagerness to be of further assistance should similar questions arise in other areas of StoAgra’s business operations. If you discover anything particularly stunning or important in your analysis that you think the CEO should be aware of, this should also appear in the cover memo.

The second part will be an executive summary of your results.  This should be addressed to mid-level managers who know the language of operations research but are not active practitioners or experts.  This is where, in narrative form, you should describe your results.  This should be done in a way that presents a“story”for the reader.  Answering the company’s speciic questions should be done here, as well as any additional insight you have reached that is not specically part of the company’s request.   These added insights are particularly important because this kind of creativity is what sets consulting irms apart and you deinitely want to impress StoAgra with your analytical skills.

While OR language can be used in this section, do NOT refer to speciic variable names, etc., in this section. Tell your story without making speciic reference to the details of your mathematical model.  (You may, of course, mention that you used a linear program or an integer program, but do not spell out exactly what variables you used, etc.)

The third and last section will be a technical appendix for StoAgra’s technical staf. These are well trained staf who know as much about mathematical programming as you do.  Perhaps they are even graduates of Math 266. This is where your complete program should be listed, fully anotated, along with any alternative mathematical programs you used in sensitivity analysis or other investigations you may have undertaken. Fully anotated means, among other things, that all decision variables and constraints are fully described. The idea here is to show technical experts that your analysis is correct and to show them how you came to the management conclusions presented in the executive summary. Your technical appendices should give StoAgra’s technical staf a irm description of your general approach to the problem and enough information to answer any question mid and upper level management might have about your analysis, and be well enough organized and presented that technical staf can ind supporting material quickly.

Grading

This project counts for 15% of your course grade. The project grade will be based on three components.

1. The quality and mathematical correctness of your formulation.

2. The correctness, creativity and completeness of your analysis and answering of StoAgra’s stated ques- tions. Your abililty to formulate and address important matters not speciically suggested by StoAgra will also be considered here.

3. The quality of your writing and presentation of results within all three sections of the report.

Annualizing One-Time Expenses

One important concept in this project is an appropriate way to convert large one time expenses, like building a factory that is expected to last many years, into a stream of annual (or daily) expenses. There are many ways of doing this, as any quick look at an accounting text will conirm.  For the purposes of this project I suggest a simple technique for converting large one time expenses into annual costs. The idea is that the company could have earned interest on the money it instead spent on building the facility. Thus, the true cost to the irm is the string of interest payments it could have received had it not built the building. Thus, to convert a one time expense of E into an ininitely long stream of annual expenses, simply multiply E by an appropriate interest rate i.

For example, suppose a facility, say a new residence hall, is going to cost $85,000,000. If the prevailing interest rate seems to be about 6.5%, then the building can be conceived of as costing the sponsoring organization $85, 000, 000 0.065 = $5, 525, 000 every year. Similarly, if a daily expense is desired, the daily interest rate can be used. While not technically correct, the daily interest rate is often computed by dividing the annual interest rate by 365, 1  keeping in mind that several signiicant digits must be used for this result to be meaningful. For the purposes of this project, you can assume that an annual interest rate of 6.5% is appropriate for planning purposes.

Introduction to the Project

StoAgra, Incorporated, plans to produce, can and distribute a food supplement called NorskeCorn.  Aside from secret formula binders, food colorings and preservatives, the main raw materials for NorskeCorn are corn and milk. The resulting product will be placed in steel cans and sent to wholesale warehouses. StoAgra’s responsibility for the products will end with its arrival at the wholesale warehouse.

Purity is a major concern for StoAgra and a major component of the projected advertising campaign. For this reason, StoAgra wants to build its own corn and milk processing plants from scratch.

The processed corn and milk, along with steel for cans, will all be shipped to one or more inal processing plants which will actually create the NorskeCorn, produce the cans, and ill these cans with the NorskeCorn. The resulting canned goods will then to shipped to one or more wholesale warehouses.  All production, assembly and warehousing operations are located within the state of Minnesota.

Transportation is likely to be a substantial cost to StoAgra. The company has decided to use railroads to transport its raw materials to whatever inal processing plants StoAgra decides to build.  Trucks, using regular highways, will transport the inished canned goods to the wholesale warehousing facilities.

Company Goals

The company has several goals in mind and seeks your guidance in helping them move forward with their plan. The goals are:

Determine whether this venture can be proitable. Perhaps it is a bad idea and should be abandoned.

If potentially proitable, determine how many and which of the potential corn processing plants should

be constructed.

Determine how many and which of the potential dairy processing plants should be constructed.

Determine how many and which of the potential steel producers should be suppliers to the NorskeCorn

project.

Determine which railroads should be utilized for raw material transport.

Determine which wholesale warehouses should receive the NorskeCorn product.

Determine the optimal NorskeCorn recipe at each of the inal assembly plants.

Table 1: Corn Processing Plants

Management also realizes there may be other important questions it should be asking, and hopes your irm will include important information beyond what is speciically addressed above.

Corn Processing Plants

StoAgra has identiied four communities as good sites for its corn processing plants. Each site has associated with it a one-time ixed cost of building the plant, a non-labor cost of production (dollars/ton produced), a labor utilization factor (hrs/ton of production), a standard labor wage rate (dollars/hour) and an overtime labor wage rate.  Limits also exist on the amount of standard labor and overtime labor that are available at each plant.  Lastly, each site has a maximum production (in tons) that that plant can sustain.  The information for each potential plant is shown in Table 1.

Dairy Processing Plants

StoAgra has identiied four good sites for Dairy Processing Plants. These have the same parameters as corn processing plants, except the output is dairy product, instead of corn. Dairy product output is measured in tons. The relevant parameter values are shown in Table 2.

Steel

StoAgra will purchase its canning supplies from existing companies, so there will be no ixed construction or labor costs for it to consider. The ive canning supply sites, along with their prices and shipping options, are given in Table 3.

Assembly

The assembly plants are charged with combining the raw materials into NorskeCorn and canning the food. As with raw material processing plants, each assembly plant has associated with it an annualized ixed cost of construction, non-labor ixed expenses, various wage rates and availabilities, labor eciencies and limited railroad service.

Unlike processing plants, assembly plants must also deal with wastage.  A certain small percentage of each plant’s output is wasted due to equipment failure, compromised sanitation, etc. The projected wastage rates for each assembly plant are given as a percentage of inputs.  For example, if a plant has a wastage

Table 2: Dairy Processing Plants