Coordinating transportation and pricing policies for perishable products

We study the joint pricing and transportation problem in a perishable product supply chain where products with different levels of quality are substitutable depending on the pricing policy and the customers' quality sensitivity. We propose two frameworks to study this problem under sequential and integrated systems. Pricing and transportation decisions are made separately and then coordinated through an iterative process in the sequential model, but jointly optimized in the integrated system. The integration of transportation and pricing leads to a challenging mixed-integer quadratic programming (MIQP) formulation which is intractable for the current state-of-the-art commercial solvers. We exploit the special structure of this formulation and develop a Benders type decomposition method with a transportation master problem and a collection of pricing subproblems. To evaluate the proposed models and algorithms, we perform numerical experiments on an illustrative case study. We show that the performance of the sequential model is noticeably inferior to the integrated optimization model on two key metrics: profit and product waste. We observe, counter-intuitively, that the presence of customers with lower quality sensitivity who tolerate imperfect products increases the waste to sales ratio. Moreover, due to the interrelationship between pricing and transportation policies, the waste to sales ratio is not monotone in the cost of the freshness keeping efforts. Finally, we show the practical efficiency of our proposed decomposition-based algorithm in solving the MIQP compared to the state-of-the-art solver.