Managing returnable transport items in a vendor managed inventory system

This paper addresses a closed-loop inventory routing problem with demand uncertainty, which manages the delivery operations to customers and pick-up operations of empty returnable transport items (RTIs) from customers. The problem involves decisions regarding forward and backward vehicle routes, the delivery and collection quantities, the amount of production in terms of the number of filled RTIs, and the number of RTIs produced/ bought by the vendor during the defined planning horizon. The problem considers the holding costs, fixed cost of operating vehicles, fuel consumption cost, producing/buying costs, cleaning costs of RTIs, and loading and unloading costs. We formulate the problem as a mixed integer linear programming model and propose a Relax and Fix based solution approach to solve large instances. We conduct extensive analyses on a case study derived from a fruit and vegetable distribution network and several hypothetical instances. Our analyses investigate the effects of several problem parameter changes (i.e., average collection rate, customer service level, cost of buying crate and handling cost) on the total logistics cost. Additional numerical analyses are performed to demonstrate the usage of the model for evaluating the cost of being more green and environmental-friendly. Moreover, experiments on relatively large-scaled problems allow us to demonstrate the potential benefits of the proposed heuristic