[管理學(xué)]運(yùn)籌學(xué)課件4_線性規(guī)劃-文庫吧
2025-09-20 02:13 本頁面
【正文】 s the upper bound for P. If either the time on machine B or the market for product P are increased, the profit will increase . Find the bottlenecks 康托洛維奇和丹捷格 1939年著名數(shù)理經(jīng)濟(jì)學(xué)者康托洛維奇發(fā)表了 《 生產(chǎn)組織和計劃中的數(shù)學(xué)方法 》 這一運(yùn)籌學(xué)的先驅(qū)性名著，其中已提到類似線性規(guī)劃的模型和 “ 解乘數(shù)求解法 ” 。但是他的工作直到 1960年的 《 最佳資源利用的經(jīng)濟(jì)計算 》 一書出版后，才得到重視。 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。 1947年 G . B. Dantzig 在研究美國空軍軍事規(guī)劃時提出了線性規(guī)劃的模型和單純形解法，并很快引起美國著名經(jīng)濟(jì)學(xué)家 Koopmans的注意。 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。今天，單純形法及其理論已成為了線性規(guī)劃的一個重要的部分。 Case 1 The WYNDOR GLASS CO. produces highquality glass products, including windows and glass doors. It has three plants. Aluminum frames and hardware are made in Plant 1, wood frames are made in Plant 2, and Plant 3 produces the glass and assembles the products. There are two products. Product 1: an 8foot glass door with aluminum framing。 Product 2: a 4*6 foot doublehung woodframed window. The table summarizes the data gathered. P r o duc t i on t i m e ( H our s ) P r o duc t P l ant 1 2 P r o duc t i on t i m e av ai l abl e p er w ee k 1 1 0 4 2 0 2 12 3 3 2 18 P r of i t pe r b at ch $3000 $5000 Formulation as a linear programming problem To formulate the mathematical model for this problem, let: x1=number of batches of product 1 produced per week x2=number of batches of product 2 produced per week Z=total profit per week (in thousands of dollars ) from producing these two products. Formulation as a linear programming problem Thus, x1 and x2 are the decision variables for the model. Using the bottom row of the table above, we obtain Z=3x1+5x2 The objective is to choose the values of x1and x2 so as to maximize Z=3x1+5x2 , subject to the restrictions imposed on their values by the limited production capacities available in the three plants. Maximize Z=3x1+5x2 Subject to the restrictions X1=4 2X2=12 3x1+5x2=18 And X1 =0, X2 =0 Briefly, the most mon type of application of LP involves the general problem of allocating limited resources among peting activities in a best possible (., optimal) way. More precisely, this problem involves selecting the level of certain activities that pete for scarce resources that are necessary to perform those activities. The choice of activity levels then dictates how much of each resource will be consumed by each activity. Linear Program
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