On lot-sizing problem in a random yield production system under loss aversion

Based on the framework of prospect theory, this paper studies the optimization problem for a random yield production system under loss aversion preference. The objective is to determine production quantity to maximize the expected utility considering loss aversion. We formulate the problem under the scenarios of multiplicative and additive random yield risks, respectively, and prove the uniqueness of the optimal production quantity under each scenario. This optimal production quantity is compared with the one in risk-neutral case, and its relationship on the loss-aversion degree is analyzed. We also explore the sensitivities of the production quantity to the system parameters. It is shown that the optimal production quantity is increasing with shortage penalty and decreasing with holding cost, whereas the sensitivities to market price and production costs are conditional.