Economic lot scheduling problem

The economic lot scheduling problem (ELSP) is a problem in operations management and inventory theory that has been studied by many researchers for more than 50 years. The term was first used in 1958 by professor Jack D. Rogers of Berkeley, 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 a 1956 paper from Welch, W. Evert. 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. 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.

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The dynamic lot-size model in inventory theory, is a generalization of the economic order quantity model that takes into account that demand for the product varies over time. The model was introduced by Harvey M. Wagner and Thomson M. Whitin in 1958. We have available a forecast of product demand dt over a relevant time horizon t=1,2,...,N (for example we might know how many widgets will be needed each week for the next 52 weeks).

Newsvendor model

The newsvendor (or newsboy or single-period or salvageable) model is a mathematical model in operations management and applied economics used to determine optimal inventory levels. It is (typically) characterized by fixed prices and uncertain demand for a perishable product. If the inventory level is , each unit of demand above is lost in potential sales. This model is also known as the newsvendor problem or newsboy problem by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be worthless at the end of the day.

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Economic Order Quantity (EOQ), also known as Financial Purchase Quantity or Economic Buying Quantity (EPQ), is the order quantity that minimizes the total holding costs and ordering costs in inventory management. It is one of the oldest classical production scheduling models. The model was developed by Ford W. Harris in 1913, but R. H. Wilson, a consultant who applied it extensively, and K. Andler are given credit for their in-depth analysis.

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