On maximizing a loss-averse buyer’s expected utility in a multi-sourcing problem

Abstract

The paper studies optimal purchasing policies for buyers in a multi-sourcing problem. For a multi-souring problem, the study first obtains the optimal purchasing policy for a loss-neutral buyer to maximize expected profit. In a multi-sourcing, we find that a loss-neutral buyer could purchase no commodities and can rely only on spot buying to meet the whole market demand if the wholesale price is larger than the spot price. Further, the research finds that a loss-neutral buyer’s optimal purchasing quantity is independent of the retail price. To reveal the loss aversion effect, the study introduces the well-known loss aversion function and obtains the optimal purchasing policy to maximize a loss-averse buyer’s expected utility in a multi-sourcing. To maximize expected utility, it is proven that a loss-averse buyer who becomes more loss-averse should purchase fewer items in the long-term contract. Moreover, under the optimal purchasing policy that maximizes expected utility, a loss-averse buyer’s expected profit is decreasing when the loss aversion coefficient is increasing. If a loss-averse buyer intends to get a bigger expected profit, he/she should be less loss-averse and select an optimal purchasing policy with a smaller loss aversion coefficient.