Optimal Control of a Production System with Information on the Production and Demand Status: Application to Vendor Managed Inventory

we consider a system consisting of a manufacturer serving several retailers. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers. Orders from the retailers arrive in batches which sizes follow a discrete distribution. The production time is assumed to follow a k0Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a kl-Erlang distribution. Work-inprocess as well as finished units incur a per unit per unit of time carrying cost. Unsatisfied units from an order from a particular retailer are assumed lost and incur a retailer-specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total cost. We show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy among retailers is a rationing policy with rationing levels non-decreasing in the demand stages. We offer managerial insights such as the effect of variability on the operating cost and the benefits of such contracts as VMI or CPFR.