Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s,S,p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s,S,p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions and apply it to provide a characterization of the optimal policy.

Modeling and Analysis of Two-Part Type Manufacturing Systems

This paper presents a model and analysis of a synchronous tandem flow line that produces different part types on unreliable machines. The machines operate according to a static priority rule, operating on the highest priority part whenever possible, and operating on lower priority parts only when unable to produce those with higher priorities. We develop a new decomposition method to analyze the behavior of the manufacturing system by decomposing the long production line into small analytically tractable components. As a first step in modeling a production line with more than one part type, we restrict ourselves to the case where there are two part types. Detailed modeling and derivations are presented with a small two-part-type production line that consists of two processing machines and two demand machines. Then, a generalized longer flow line is analyzed. Furthermore, estimates for performance measures, such as average buffer levels and production rates, are presented and compared to extensive discrete event simulation. The quantitative behavior of the two-part type processing line under different demand scenarios is also provided.