INTRODUCTION TO MANAGEMENT SCIENCE

Linear Programming

A financial analyst must select an investment portfolio from a variety of stock and bond investment alternatives.  The analyst would like to establish the portfolio that maximizes the return on investment.

A marketing manager wants to determine how best to allocate a fixed advertising budget among alternative advertising media such as radio, television, newspaper and magazine.  The manager would like to determine the media mix that maximizes advertising effectiveness.

A company has warehouses in a number of locations throughout the United States.  For a set of customer demands, the company would like to determine how much each warehouse should ship to each customer so that total transportation costs are minimized.

MANAGEMENT SCIENCE IN ACTION (Linear Programming)

 

TIMBER HARVESTING MODEL AT MEADWESTVACO CORPORATION*

MeadWestvaco Corporation is a major producer of premium papers for periodicals, books, commercial printing, and business forms.  The company also produces pulp and lumber, designs and manufacturers packaging systems for beverage and other consumables markets, and is a world leader in the production of coated board and shipping containers.  Quantitative analysis at MeadWestvaco are developed and implemented by the company’s Decision Analysis Department.  The department assists decision makers by providing them with analytical tools of quantitative methods as well as personal analysis and recommendations.

MeadWestvaco uses quantitative models to assist with the long-range management of the company’s timberland.  Through the use of large-scale linear programs, timber harvesting plans are developed to cover a substantial time horizon.  These models consider wood market conditions, mill pulpwood requirements, harvesting capacities, and general forest management principles. Within these constraints, the model arrives at an optimal harvesting and purchasing schedule based on discounted cash flow.  Alternative schedules reflect changes in the various assumptions concerning forest growth, wood availability, and general economic conditions.

Quantitative methods are also used in the development of the inputs for the linear programming models.  Timber prices and supplies as well as mill requirements must be forecast over the time horizon, and advanced sampling techniques are used to evaluate land holdings and to protect forest growth.  The harvest schedule is then developed using quantitative methods.

*Based on information provided by Dr.Edward P. Winkofsky of MeadWestvoco Corporation.

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MANAGEMENT SCIENCE IN ACTION (Linear Programming)

 

ASSIGNING PRODUCTS TO WORLDWIDE FACILITIES AT EASTMAN KODAK*

One of the major planning issues at Eastman Kodak involves the determination of what products should be manufactured at Kodak’s facilities located throughout the world. The assignment of products to facilities is called the “world load”. In determining the world load, Kodak faces a number of interesting trade-offs. For instance, not all manufacturing facilities are equally efficient for all products, and the margins by which some facilities are better vary from product to product.  In addition to manufacturing costs, the transportation costs and the effects of duty and duty drawbacks can significantly affect the allocation decision.

To assist in determining the world load, Kodak developed a linear programming model that accounts for the physical nature of the distribution problem and the various costs (manufacturing, transportation, and duties) involved.  The model’s objective is to minimize the total cost subject to constraints such as satisfying demand and capacity constraints for each facility.

The linear programming model is a static representation of the problem situation; the real world is always changing.  Thus, the linear programming model must be used in a dynamic way. For instance, when demand expectations change, the model can be used to determine the effect the change will have on the world load.  Suppose that the currency of country A rises compared to the currency of country B?  How should the world load be modified?  In addition to using the linear programming model in a “how-to-react” mode, the model is useful in a more active mode by considering questions such as the following: Is it worthwhile for facility F to spend d dollars to lower the unit manufacturing cost of product P from x to y? The linear programming model helps Kodak evaluate the overall effect of possible changes at any facility. 

In the final analysis, managers recognize that they cannot use the model by simply turning it on, reading the results, and executing the solution.  The model’s recommendation combined with managerial judgment provides the final decision.

*Based on information provided by Greg Sampson of Eastman Kodak.