Joint inventory and pricing decisions: reference effects and delay sensitive customers

Abstract

We consider joint inventory and pricing problem of a single product with stochastic demand in two different contexts. In the first one, we study a periodic review problem where the demand of the product is subject to reference effects. Randomness is introduced with additive and multiplicative random terms. The customers have different attitudes such as loss-aversion or loss-neutrality. For the demand models with an additive random term, we show that the problem can be decomposed into two subproblems and a steady state solution exits for the infinite horizon problem. Defining the modified revenue as revenue less production cost, we show that a state-dependent order-up-to policy is optimal for concave demand models with concave modified revenue functions. We also show that the optimal inventory level increases with the reference price. For the demand models with an additive and a multiplicative random term, we show that a state-dependent order-up-to policy is optimal for demand models and expected revenue functions which are concave after a transformation. We also provide an extensive computational study. For the second context, we consider a capacity constrained manufacturer who serves several classes of delay sensitive customers. We model the problem as an M/M/1 queueing system with non-preemptive priorities. We give closed form solutions for the inventory decisions. Using an approximation on to the problem we provide explicit solutions when there is a single customer type. We also show that the optimal prices are incentive compatible in the sense that they optimize the profit of the manufacturer even if the manufacturer does not have any information about an arriving customer and let the customer choose a price from a provided menu of prices.