A Production-Inventory Problem for 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 of 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 depends on the electricity market condition at that time. The market condition in any given period is represented by M+1 states: normal (i.e., nonpeak), peak type 1,..., peak type M, and the reward in the period will be 0,K₁,...,  or K_M, 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 peak type m condition, the manufacturer, upon accepting the offer, produces according to an (s_m,S) policy, where m=1,...,M. Our numerical experiment suggests that the cost savings due to buy-backs can be substantial. It also shows that the always-participating strategy, i.e., the firm shuts down production whenever the buy-back program is activated, can perform much worse than the never-participating strategy.