Integrated production inventory routing planning with time windows for perishable food

This paper investigates an integrated production inventory routing problem with time windows where a central depot is responsible for supplying single type of perishable food to multiple retailers within the planned time horizon. A mixed integer linear programming (MILP) model aiming at maximizing the total profit is formulated with explicitly tracing the food quality. To strengthen the formulation, a series of valid inequalities are introduced. Randomly generated instances with up to 40 retailers and 3 time periods are used to verify the effectiveness and the complexity of the proposed model, which is solved by the linear programming solver CPLEX. The computational results show that the proposed model is able to provide integrated plan for the decision makers, and instances with 20 retailers and 3 time periods are optimally solved with 102.97s on average. The results also indicate that the introduced valid inequalities are useful in helping CPLEX generate better upper bounds (maximization problem) for 20 out of 23 instances that are not optimally solved within the time limit.