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2024-10-25 02:13本頁面
【正文】 door with aluminum framing。 Koopmans為此呼吁當(dāng)時年輕的經(jīng)濟(jì)學(xué)家要關(guān)注線性規(guī)劃。 1975年，康托洛維奇與 T . C . Koopmans 一起獲得了諾貝爾經(jīng)濟(jì)學(xué)獎。Chapter 3 Introduction to Linear Programming Linear programming is a widely used model type that can solve decision problems with many thousands of variables. Generally, the feasible values of the decisions are delimited by a set of constraints that are described by mathematical functions of the decision variables. The feasible decisions are pared using an objective function of the decision variables. For a linear program the constraints and objective functions are required to be linearly related to the variables of the problem. Prototype Example The circles show the raw materials used, and the rectangles indicate the operations that the products must pass through in the manufacturing process. Each rectangle designates a machine used for the operation and the time required. Example: The figure represents a manufacturing system producing two products labeled P and Q. The rounded rectangles at the top of the figure indicate the revenue per unit and the maximum sales per week. For instance we can sell as many as 100 units of P for $90 per unit. For example product P consists of two subassemblies. To manufacture the first subassembly, one unit of RM1 passes through machine A for 15 minutes. The output of machine A is moved to machine C where it is processed for 10 minutes. The second subassembly starts with RM2 processed in machine B for 15 minutes. The output is taken to machine C for 5 minutes of processing. The two subassemblies are joined with a purchased part in machine D. The result is a finished unit of P. Product Q is manufactured by a similar process as indicated in the figure The rectangle at the upper left indicates that one machine of each type is available. Each machine operates for 2400 minutes per week. OE stands for operating expenses. For this case the operating expenses, not including the raw material cost is $6000. This amount is expended regardless of amounts of P and Q produced. Z= 45P + 60Q The optimum solution is to produce 100 units of P and 30 units of Q. The profit of this solution is $300. Results: Find the optimum product mix From the value column for the constraints, we see the amounts of time required by the optimum production quantities. Clearly, the time on m
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