A loss-averse ordering strategy with a piecewise-formed reference point

We study a loss-averse (LA) retailer with a quantity-oriented reference point (RP) in a piecewise form in a random market. The proposed RP is characterized by a two-fold convex combination of three elements (profits in three environments) at low reference levels, and a standard convex combination of two elements (profits in two environments) at high reference levels. We aim to use prospect theory with the above piecewise-formed RP to characterize the LA retailer’s optimal procurement strategy in maximizing her expected profit, and describe the effect on the procurement strategy from some parameters. We prove that there exists a procurement strategy inducing the LA retailer to make her optimal ordering decision given a random market with a general distribution. We analyze the respective effect of LA degree and reference level on retailer’s optimal procurement strategy, and obtain some intuitive insights, such as, a LA retailer always orders less than a loss-neutral one; increasing LA degree leads to more cautious ordering behavior; a lower RP level leads retailer to over-order, and a higher RP leads to under-order. Moreover, we find that the joint effect from LA degree and RP level on the optimal order quantity is mutually reinforcing. This joint effect also presents results consistent with people’s cognition, that is, the optimal order quantity of a LA retailer with RP is more likely to be lower than a classical retailer, compared to a risk-neutral retailer with RP. We finally provide the sensitivity analysis of parameters on the optimal order strategy.