Inventory Management

Basically, all effort on inventory management is dedicated to answering two questions: When to order and how much to order. In general, a decision maker will pursue three possibly contrary objections: Low inventory holding costs, low purchase costs and high inventory availability, or rather an inventory availability that satisfies the need of the subsequent production, distribution or transportation process. For tight model assumptions, the two basic questions are easily answered. For example, let us assume a constant demand per period (D) that occurs at a constant rate, zero replenishment lead times, i.e. material will be immediately on hand when ordered and all relevant expense ratios (price per unit, costs per order (s), inventory holding costs per unit (h)) independent of the order quantity, then we derive the well known EOQ formula (figure).

q is the optimum order size and r=q/D the time between two consecutive orders. However, there will hardly be any real world system that satisfies the assumptions. In most real systems we find that lead time, demand per period or both are subject to stochastical influences and should therefore be modelled as random variables. In this case, it is no longer appropriate to follow a rigid decision rule such as ordering q units every r periods, but we should rather incorporate some adaptive component into our purchasing policy, i.e. instead of ordering q units every r period, we could order the amount that is currently missing to some target level. Early research on stochastic inventory systems goes back into the 1950s and a broad body of knowledge has been established nowadays. Nonetheless it seems somewhat impossible to present a general approach that covers all systems one might reasonably think of. Therefore, research in this area is focussed on analyzing inventory systems that appear representable for real world applications.