Bi-objective Optimization for Joint Production Scheduling and Distribution Problem with Sustainability

Abstract

This paper considers joint production and distribution planning problem with environmental factors. While the production phase of the problem consists of job shop production environment running under Just-In-Time (JIT) philosophy, the distribution phase involves a heterogeneous fleet of vehicles with regards to capacity and fuel consumption rate. Therefore, we tackle two well-known problems in Operations Research terminology which are called machine scheduling and vehicle routing problems. The joint problem is formulated as a bi-objective structure, the first of which is to minimize the maximum tardiness, the second of which aims to minimize the total amount of CO2 emitted by the vehicles. Orders are required to be consolidated to reduce the traveling time, distance, or cost. An increase in the vehicle capacity results in a higher possibility of consolidation, but in this case, the amount of CO2 emission that the vehicle emits into the air will also increase. Having shown that two objectives are conflicting in an illustrative example, we formulate the problem as amixed integer programming (MIP) formulation and use an Augmented Epsilon Constraint Method (AUGMECON) for solving the bi-objective model. On randomly generated test instances, the applicability of the MIP model through the use of AUGMECON is reported.