Development of a Mathematical Model for Solving the Multi-Objective Multi-Item Transportation Problem using Linear Programming

The multi-objective multi-item transportation problem is a challenging issue in the context of supply chain management which deals with optimizing several conflicting objectives, considering the allocation of different products departing from many source nodes to multiple demand destinations. In this paper we propose a systematic mathematical approach based on linear programming to solve this challenging optimization problem. Based on these assumptions the study designs a multi-objective linear programming (MOLP) model with cost, delivery time and environment as the main objectives. The model is developed under clear-cut restrictions that consider supply avai lability, demand requirements, vehicle capacity and multi-product allocation rules. A practical example is considered with real operational data of a regional distribution network for optimal transportation planning and WinQSB software is used to find the best routes. Results show that the proposed model can effectively compromise conflicting multi-objectives, reducing total cost by 18.5%, delivery time by 12.3% and CO2 emissions by 15.2%. The research uses the weighted sum-constraint method for Pareto optimization based decisiontrade-offs, and results into a full tradeoffs analysis and possible transportation planning solutions to decision-making people.