Komeil Yousefi - Department of Industrial Engineering, Shomal University, Amol, Iran
Ahmad J Afshari - Department of Industrial Engineering, Shomal University, Amol, Iran
Mostafa Hajiaghaei-Keshteli - Department of Industrial Engineering,University of Science and Technology of Mazandaran, Behshahr, Iran

Proposing discount offers for products prices usuallydirectly influences on the process of distributing and sellingproducts. The fixed charge transportation problem (FCTP)is a deployment of the classical transportation problem inwhich a fixed cost is incurred, independent of the amounttransported, along with a variable cost that is proportionalto the amount shipped. Since the problem is considered asan NP-hard, in this paper we propose a well-knownmetaheuristic to solve the FCTP with discount suppositionon both fixed and variable charges. In addition, two modelswith all-units discount and incremental discount is firstlyproposed in this study to apply the discount mechanism.Also, as the previous researchers mainly used spanningtree-based and priority-based representations, we used bothmethods in metaheuristic and compared the results.Furthermore, we apply the Taguchi experimental designmethod to set the proper values of algorithm in order toimprove its performance. Finally, computational resultsmetaheuristic with different encoding approaches, both interms of the solution quality and computation time, areinvestigated in different problem sizes.

Fixed charge transportation problem; Discount model; Genetic algorithm; Spanning tree; Priority-based; aguchiexperimental design