A forward algorithm for a solution to the following dynamic version of the economic lot size model is given: allowing the possibility of demands for a single item, inventory holding charges, and setup costs to vary over N periods, we desire a minimum total cost inventory management scheme which satisfies known demand in every period. Disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full N periods.
A forward algorithm for a solution to the following dynamic version of the economic lot size model is given: allowing the possibility of demands for a single item, inventory holding charges, and setup costs to vary over N periods, we desire a minimum total cost inventory management scheme which satisfies known demand in every period. Disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full N periods.
In spite of the high level of interest in inventory control that has sprung up recently among statisticians, economists, and businessmen, very little has been written that indicates the fundamental connection between price theory and inventory control. Most of the inventory control systems now in operation assume a given price structure. The analysis is frequently restricted to cost minimization. Economic theorists, on the other hand,~have concerned themselves with profit maximization but have not ordinarily concerned themselves with the realistic details underlying the construction of their curves. Only in the event that other variables external to the cost minimization problem are assigned optimal values will the cost minimization problem be equivalent to profit maximization.
An inventory control model in which the state of the system is reviewed only at discrete, equally spaced time intervals is studied. A procurement is made if at the review period the inventory position of the system is less than or equal to a number k. The quantity procured is an integral multiple of a number Q. The total expected cost of review, procurement, holding inventory, and stockouts is determined under the assumption that all demands are ultimately met. The cost of a stockout is taken to consist of a fixed cost per unit out of stock plus a variable cost which is proportional to the time out of stock. Specific expressions for all the cost expressions are found for the case of (1) Poisson demands and fixed lead times, and (2) Poisson demands and gamma lead times. It is shown that many of the inventory models discussed in the literature are special cases of the model here described.
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