Production routing for perishable products

This paper introduces the production routing problem for perishable products with fixed shelf life and gradual decay, where the age of products impacts the price that can be obtained when satisfying customer demands. In this problem, a single supplier is responsible for the production and distribution of perishable products to a set of customers. Fixed setup and variable production costs occur at the supplier location when production takes place, and routing costs are charged for the distribution activities. Additionally, inventory holding costs are incurred at both the production facility and the customer locations. Transshipments between customer locations are allowed on the basis of a unit transshipment cost. The objective is to maximise the total profit given by the sales revenue minus the sum of production, routing, inventory and transshipment costs. The problem is formulated as a mixed integer linear program and solved using a branch-and-cut and a hybrid, iterated local search-based heuristic. Based on the results of the computational experiments, we analyse the impact of perishability on the structure of the solutions. We explore perishability in the form of both product shelf life and decay, observing that larger decay rates lead to a reduction in total profit, as a result of both a decrease in revenues and an increase in the total cost. We further analyse the impact of different decay rates on the cost structure of the problem and the significance of transshipments for the management of perishability across the system. Finally, we adapt our hybrid method to solve the standard production routing problem. Comparison of our results with state-of-the-art solution methods on benchmark instances from the literature shows that our heuristic provides good quality solutions that are competitive with the scientific literature.