Integrated Production and Transportation Scheduling Problem with Multiple Plants, Multiple Vehicles and Perishable Products

Abstract

The integrated production and transportation scheduling problem is one of the interesting topics in the literature. This paper addresses Integrated Production and Transportation Scheduling Problems with Multiple Plants, Multiple Vehicles, and Perishable Products (PTSP-MP-MV). To the best of our knowledge, this problem has not been studied in the literature. In this problem, each plant has a different capacity and a different production rate. There is a single machine and a limited number of homogeneous vehicles in each plant. Each vehicle can be used more than once because of the vehicle capacity and planning horizon restrictions. Only one type of product is produced, and this product has a limited lifespan. The objective of the problem is to minimize the total cost including production, distribution, and vehicle costs. We propose a mixed integer programming (MIP) formulation for the problem and strengthen it with several valid inequalities to improve lower bounds. The performance of the formulation is calculated using a newly generated set of test instances. Computational results show that small-sized instances with 5 and 10 customers can be solved optimally in less than 90 s. Satisfactory results are obtained for the test instances up to 20 customers whose optimality gap values are calculated as 0.54% nearly 1 h. It is also shown that the valid inequalities are improved lower bounds about 3%. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.