A Production-Inventory Problem under an Energy Buy-Back Program

Abstract

This paper considers a production-inventory problem in which the manufacturer participates in an energy buy-back program, which offers him probabilistic opportunities with rewards for not using electricity. That is, the manufacturer will get paid for stopping production to save on electricity. The amount rewarded in a period will depend on the electricity market condition at that time. The market condition in any given period is represented by three states: normal (i.e., non-peak), semi-peak, or peak, and the reward amount in the period will be 0, K1; and K2, respectively. The occurrence of each state in a period is dictated by a known probability distribution. The objective is to determine from the manufacturer's perspective, whether to take such an offer when it arises. Under a mild assumption, we show that in the normal market condition, the production decision is partly a base-stock policy, whereas under semi-peak and peak conditions, the manufacturer, upon accepting the offer, produces according to (s1; S) and (s2; S) policies, corresponding to K1 and K2; respectively. Two variants of the model are also discussed.

Keywords: Production-inventory model, (s; S) policy, dynamic programming, electricity use in production, energy buy-back program

JEL Classification: C61, M11, Q40, Q41