Inventory Models with Deterministic Demand

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INVENTORY MODELS WITH DETERMINISTIC DEMAND It is extremely difficult to formulate a single general inventory model which takes into account all variations in real systems. In fact, even if such a model were developed, it may not be analytically solvable. Thus inventory models are usually developed for some specific situations. In this section we shall deal with situations in which demand is assumed to be fixed and completely known. Models for such situations are called economic lot size models or economic order quantity models. Model 1 (a) Classical EOQ Model (Demand Rate Uniform, Replenishment Rate Infinite) This is one of the simplest inventory models. A stockist has order to supply goods to customers at a uniform rate R per unit time. Hence demand is fixed and known. No shortages are allowed, consequently, the cost of shortage, C2 is infinity. He places an order with the manufacturer every t time units, where t is fixed; and the ordering cost per order is C3. Replenishment time is negligible i.e., replenishment rate is infinite so that. Replacement is instantaneous (lead time is zero). The holding cost is assumed to be proportional to the amount of inventory as well as the time inventory is held. Thus the cost of holding inventory I for time T is C1IT, where C1 is the cost of holding one unit in inventory for a unit of time. The cost coefficients C1, C2 and C3 are assumed to be constants. The stockist’s problem is to determine (0 How frequently he should place the order. (if) How many units should be ordered in each order. This model is illustrated schematically in figure. If orders are placed at intervals t, a quantity q = Rt must be ordered in each order. Since the stock in small time dt is Rtdt, the stock in time period t will be [pic] Area of inventory triangle OAP. [pic] Fig.1-Inventory situation for model 1 (a). - Cost of holding inventory

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