Dynamic Lot Sizing with Deterministic Demand

Abstract

To this point we have examined environments in which demand was assumed to occur at a known, constant rate over an infinite horizon.We now turn our attention to developing a finite-horizon, discrete-time model with deterministic but non-stationary demand for a single product at a single stage. In a finite-horizon discrete-time model, as the name suggests, the length of the planning horizon is finite and the order placement decisions are made at discrete intervals of time. Inventory is reviewed only at the beginning of a period, hence we can call this model a periodic review model. Backorders are not permitted.

There are three types of costs considered in this environment, the fixed ordering cost, the variable procurement cost (or payment to the supplier) and the hol ding cost. If there were no fixed cost, it would be optimal to place an order in every period. The fixed cost provides an economic incentive to combine several periods’ demands into a single order. The variable procurement cost is also incurred only when an order is placed. The magnitude of this cost is proportional to the order quantity. Unlike the fixed and variable costs of order placement, the holding cost is not incurred when an order is placed. The holding cost is charged every period in proportion to the amount of on-hand inventory at a period’s end.