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James E. Reeb, Extension forest products manufac- turing specialist; and Scott Leavengood, Extension agent, Klamath County; Oregon State University. Using the Simplex Method to Solve Linear Programming Maximization Problems J. Reeb and S. Leavengood EM 8720-E October 1998 $3.00 A key problem faced by managers is how to allocate scarce resources among activities or projects. Linear programming, or LP, is a method of allocating resources in an optimal way. It is one of the most widely used operations research (OR) tools. It has been used successfully as a decision- making aid in almost all industries, and in financial and service organiza- tions. Programming refers to mathematical programming. In this context, it refers to a planning process that allocates resources—labor, materials, machines, and capital—in the best possible (optimal) way so that costs are minimized or profits are maximized. In LP, these resources are known as decision variables . The crite- rion for selecting the best values of the decision vari- ables (e.g., to maximize profits or minimize costs) is known as the objective function . The limitations on resource avail- ability form what is known as a constraint set. For example, let’s say a furniture manufacturer pro- duces wooden tables and chairs. Unit profit for tables is $6, and unit profit for chairs is $8. To simplify our discussion, let’s assume the only two resources the company uses to produce tables and chairs are wood (board feet) and labor (hours). It takes 30 bf and 5 hours to make a table, and 20 bf and 10 hours to make a chair. PERFORMANCE EXCELLENCE IN THE WOOD PRODUCTS INDUSTRY About this series According to the Operations Research Society of America, “Operations research [OR] is concerned with scientifically deciding how to best design and operate man-machine systems, usually under conditions requiring the allocation of scarce resources.” This publication, part of a series, should be useful for supervisors, lead people, middle managers, and anyone who has planning responsibility for either a single manufacturing facility or for corporate planning over multiple facilities. Although managers and planners in other industries can learn about OR techniques through this series, practical examples are geared toward the wood products industry.
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2 O PERATIONS R ESEARCH Decision variables. . . “The resources available.” Constraint set. . . “The limitations on resource availability.” Objective function. . . “The criterion for selecting the best values of the decision variables.” There are 300 bf of wood available and 110 hours of labor avail- able. The company wishes to maximize profit, so profit maximiza- tion becomes the objective function . The resources (wood and labor) are the decision variables . The limitations on resource availability (300 bf of wood and 110 hours of labor) form the constraint set, or operating rules that govern the process . Using LP, management can decide how to allocate the limited resources to maximize profits.
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