A Production–Inventory Problem for an Energy Buy-Back Program

This paper considers a production–inventory problem in which the manufacturer participates in an energy buy-back program, which offers 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 $M+1$ states: normal (i.e., nonpeak), peak type $1, \ldots$, peak type $M$, and the reward amount in the period will be $0,$ $K_1, \ldots$, and $K_M$, 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 $m=1, \ldots, M$. The numerical experiment demonstrates 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.