Optimal sourcing decisions considering quantity constraints under rank-dependent utility theory

To improve profits, retailers can order products from two suppliers: one cheap supplier with a long lead time and one quick-response supplier with a high cost. Business practices and empirical investigations have shown that retailers’ actual ordering decisions often deviate from expected utility due to behavioural factors. This paper investigates a sourcing problem for a retailer from two manufacturers with different lead times and costs under quantity constraints considering rank-dependent utility theory (RDEU). RDEU involves behavioural factors, including loss aversion, reference profit and weighting of probabilities. For this problem, we build a two-stage ordering model and derive the optimal ordering decisions before and during the selling season by using convex optimisation methods. We characterise the optimal ordering decisions of the retailer under RDEU considering different quantity constraints. We compare the results with those under the expected utility theory (EUT). We analyse the effects of behavioural factors on the retailer's ordering decisions. It is found that when the selling price is larger, a retailer will always order more from the manufacturers before the selling season under EUT but may order less under RDEU when facing demand uncertainty and quantity constraints during the selling season. Additionally, when the selling price is high, the loss-averse retailer should order more than the risk-neutral retailer to avoid inventory shortage. A higher degree of loss averseness will induce the retailer to delay placing orders to gain more demand information and reduce the possibility of stock out or overstock.