This paper treats a depot-warehouse system in which demand occurs at the warehouse or retail level. This work differs from a number of other studies in that we allow item demands to be correlated both across warehouses and also correlated in time. Our motivation for this generalization arises from our experience with an actual system of this type used by a major national producer and distributor of consumer products. We observed both high correlations between successive monthly demands (around 0.7) and correlations between demands for an item at different locations (also about 0.7) in a given time period. We derive an explicit expression for the optimal safety stock as a function of the level of correlation through time. The analysis requires two assumptions: 1) the allocation assumption and 2) the equal coefficient of variation assumption. (Similar assumptions have been used by other researchers.) Finally, numerical evaluations are included to illustrate the impact of the various magnitudes of correlation.inventory, multi-echelon, issuing policies, stochastic model

Multi-echelon inventory systems are often controlled as a network of single-echelon inventory systems for simplicity of managerial authority, organizational control, and performance monitoring. This paper explores the amount of suboptimization in such a situation, using an actual demand data set provided by other researchers. We consider low-demand, high-cost items controlled on an (S - 1, S) basis, with all warehouse stockouts met on an emergency-ordering basis. We demonstrate that the suboptimality penalty for this data set is 3% to 5% when single-echelon systems are appropriately parameterized.inventory/production, multi-echelon systems

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We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives' information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable.

We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the demand of a period is satisfied from at most three distinct production (dispatching) epochs. We devise a dynamic programming algorithm to compute the production/dispatching quantities and times.