A new approach in graph- based integrated production and distribution scheduling for perishable products

This study is concerned with how the quality of perishable products can be improved by shortening the time interval between production and distribution. As special types of food such as dairy products decay fast, the integration of production and distribution scheduling (IPDS) is investigated. An integrated scheduling of both processes improves the performance and costs because the separated scheduling of these processes without considering mutual requirements leads to non-optimal solutions. An optimal solution to IPDS requires simultaneously solving of the production scheduling and vehicle routing problems. This article deals with a variation of IPDS that contains a short shelf-life product; hence, there is no inventory of the product in the process. Once an amount of products is produced, they must be transported with non-negligible transportation time directly to various customer locations. The objective is to determine the minimum cost of the makespan and number of vehicles required to complete the distribution of the products to satisfy the demand of a given set of customers over a wide geographic region. The overall problem consists of permutation flow shop scheduling with machines, jobs and vehicles with different speeds and transportation capacities which transport jobs from the manufacturing company to customers distributed in various zones by determining the vehicle routes and number of vehicles. After developing an Integer Linear Programming (ILP) model of the problem, because it is NP-hard, a new graph-based heuristic method is proposed to efficiently solve the problem.