W e investigate a two-stage serial supply chain with stationary stochastic demand and fixed transportation times. Inventory holding costs are charged at each stage, and each stage may incur a consumer backorder penalty cost, e.g. the upper stage (the supplier) may dislike backorders at the lower stage (the retailer). We consider two games. In both, the stages independently choose base stock policies to minimize their costs. The games differ in how the firms track their inventory levels (in one, the firms are committed to tracking echelon inventory; in the other they track local inventory). We compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs, i.e., the optimal solution. We show that the games (nearly always) have a unique Nash equilibrium, and it differs from the optimal solution. Hence, competition reduces efficiency. Furthermore, the two games' equilibria are different, so the tracking method influences strategic behavior. We show that the system optimal solution can be achieved as a Nash equilibrium using simple linear transfer payments. The value of cooperation is context specific: In some settings competition increases total cost by only a fraction of a percent, whereas in other settings the cost increase is enormous. We also discuss Stackelberg equilibria.

We present an inventory model, where the demand rate varies with an underlying state-of-the-world variable. This variable can represent economic fluctuations, or stages in the product life-cycle, for example. We derive some basic characteristics of optimal policies and develop algorithms for computing them. In addition, we show that certain monotonicity patterns in the problem data are reflected in the optimal policies.

Consider a central depot (or plant) which supplies several locations experiencing random demands. Orders are placed (or production is initiated) periodically by the depot. The order arrives after a fixed lead time, and is then allocated among the several locations. (The depot itself does not hold inventory.) The allocations are finally received at the demand points after another lag. Unfilled demand at each location is backordered. Linear costs are incurred at each location for holding inventory and for backorders. Also, costs are assessed for orders placed by the depot. The object is to minimize the expected total cost of the system over a finite number of time periods. This system gives rise to a dynamic program with a state space of very large dimension. We show that this model can be systematically approximated by a single-location inventory problem. All the qualitative and quantitative results for such problems can then be applied.inventory and production, approximations, stochastic models

We have an inventory to manage. The scenario is standard in all respects save one. Instead of arriving unannounced, customers provide advance warning of their demands. How should we use this information, and what is its effect on system performance? The answers turn out to be strikingly simple. There are very simple policies which perform effectively, in some cases optimally. Also such "demand leadtimes" improve performance, in precisely the same way that replenishment leadtimes degrade it.value of information, customer supplier relations, inventory control

We provide a new approach to the structural analysis of the standard lost-sales inventory system. This approach is, we think, easier to work with than the original one. We also derive new bounds on the optimal policy. Then, we show that more variable demand leads to higher cost. Finally, we extend the analysis to several important variations of the basic model.