Solving Multi-Step Fixed Charge Transportation Problem
| Author(s) | : | Mahmoud M. El-Sherbiny, Ibrahim A. Aljasser, Bokkasam Sasidhar |
| Institution | : | Quantitative Analysis Department, College of Business Administration, King Saud University, Riyadh, Saudi Arabia |
| Published In | : | Vol. 8, Issue 10 — October 2021 |
| Page No. | : | 15-27 |
| Domain | : | Engineering |
| Type | : | Research Paper |
| ISSN (Online) | : | 2348-4470 |
| ISSN (Print) | : | 2348-6406 |
Fixed charge transportation problem (FCTP), which can be considered as adistribution problem, is considered to be an NP-hard problem. One of its versions is the Step Fixedcharge transportation problem (SFCTP) where the cost of shipping through every route that is used inthe solution consists of a variable cost plus a fixed cost. New versions of SFCTP in the form of MultiStep Fixed Charge Transportation Problem (MSFCTP) and also Flat Multi Step Fixed ChargeTransportation Problem (FMSFCTP) - one of the special versions of MSFCTP are proposed. InFMSFCTP the problem of minimizing transportation cost is considered in situations where anopening cost is incurred for every route used in the solution and increases proportionately withshipped quantity. The special version of FMSFCTP considers the opening cost to remain flat up to acertain quantity and increases in multiples of this flat cost. This cost structure invokes the ceilingfunction and causes the value of the objective function to behave like a step function. Themathematical models of MSFCTP and FMSFCTP, together with a heuristic algorithm for solvingFMSFCTP are described and presented in this paper. Two problems have been solved to evaluate anddemonstrate the performance of the proposed algorithm.
Mahmoud M. El-Sherbiny, Ibrahim A. Aljasser, Bokkasam Sasidhar, “Solving Multi-Step Fixed Charge Transportation Problem”, International Journal of Advance Engineering and Research Development (IJAERD), Vol. 8, Issue 10, pp. 15-27, October 2021.
