DEVELOPMENT OF A SOLUTION TECHNIQUE FOR THE FACILITY LOCATION AND STEP-FIXED CHARGE SOLID TRANSPORTATION PROBLEM

Author(s)

Gbeminiyi John Oyewole1*, Adesida Ayorinde2, Osita Anyaeche2

Author affiliation

1Department of Industrial and Systems Engineering, The University of Pretoria, Pretoria 0002, South Africa
2Department of Industrial and Production Engineering, University of Ibadan, Nigeria

Abstract

In this paper, a new variant of the Solid Transportation Problem (STP) that incorporates both facility location and Step-Fixed Charge Solid Transportation Problem (SFCSTP) is presented with applications in logistics. It integrates decisions of diverse planning horizons: operational, tactical and strategic. The problem is termed Step-Fixed Charge Solid Location and Transportation Problem (SFCSLTP). Its objective function behaves like a step- function with breakpoints. The SFCSLTP considers three possible scenarios of breakpoints. The first is termed scenario 1, occurring at the minimum demand point. The second scenario at the maximum demand (scenario 2). The third scenario (scenario3) occurs at a point in between the maximum and minimum demand requirements. Benchmark data obtained from literature was extended for experimentation. The solution to the SFCSLTP was obtained using CPLEX solver. Results from the experimentation with scenarios 1, 2, and 3 respectively confirmed the analytical prediction of a possible decrease in the minimum cost when the breakpoint tends towards the maximum demand point. In addition, experimentation results offer new insights into transportation models where the objective function behaves as step-function, and also about computation efficiency of such models with solvers such as CPLEX. Managers involved with logistic planning will find this model useful.

Keywords

Piecewise-Linear Cost, Location-Fixed Cost, Route-Fixed Cost, Break-Point Scenarios, CPLEX.