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The economic lot scheduling problem (ELSP) is a problem in operations management and inventory theory that has been studied by a large number of researchers for more than 50 years. The term was first used in 1958 by professor Jack D. Rogers of Berkeley,〔Jack D. Rogers: A Computational Approach to the Economic Lot Scheduling Problem, Management Science, Vol. 4, No. 3, April 1958, pp. 264–291〕 who extended the economic order quantity model to the case where there are several products to be produced on the same machine, so that one must decide both the lot size for each product and when each lot should be produced. The method illustrated by Jack D. Rogers draws on 1956 paper from Welch, W. Evert.〔Welch, W. Evert, A Case of Simple Linear Programming, Management Methods 1956〕 The ELSP is a mathematical model of a common issue for almost any company or industry: planning what to manufacture, when to manufacture and how much to manufacture. ==Model formulation== The classic ELSP is concerned with scheduling the production of several products on a single machine in order to minimize the total costs incurred (which include setup costs and inventory holding costs). We assume a known, non-varying demand for the m products (for example, there might be m=3 products and customers require 7 items a day of Product 1, 5 items a day of Product 2 and 2 items a day of Product 3). Customer demand is met from inventory and the inventory is replenished by our production facility. A single machine is available which can make all the products, but not in a perfectly interchangeable way. Instead the machine needs to be set up to produce one product, incurring a setup cost and/or setup time, after which it will produce this product at a known rate . When it is desired to produce a different product, the machine is stopped and another costly setup is required to begin producing the next product. Let be the setup cost when switching from product i to product j and inventory cost is charged based on average inventory level of each item. N is the number of runs made, U the use rate, L the lot size and T the planning period. To give a very concrete example, the machine might be a bottling machine and the products could be cases of bottled apple juice, orange juice and milk. The setup corresponds to the process of stopping the machine, cleaning it out and loading the tank of the machine with the desired fluid. This product switching must not be done too often or the setup costs will be large, but equally too long a production run of apple juice would be undesirable because it would lead to a large inventory investment and carrying cost for unsold cases of apple juice and perhaps stock-outs in orange juice and milk. The ELSP seeks the optimal trade off between these two extremes. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Economic lot scheduling problem」の詳細全文を読む スポンサード リンク
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