determination of material flows in a multi-echelon assembly supply chain

this study aims to minimize the total cost of a four-echelon supply chain including suppliers, an assembler, distributers, and retailers. the total cost consists of purchasing raw materials from the suppliers by the assembler, assembling the final product, materials transportation from the suppliers to the assembler, product transportation from the assembler to the distributors, product transportation from the distributors to the retailers, and product holding and stock-out in the distribution centers. to this end, having modeled the problem addressed, a numerical example including ten suppliers, an assembler, three distributors and eight retailers in the chain is solved for four periods of time. then the model is solved by a simulated annealing-based heuristic and lingo. finally, a set of 30 numerical problems of small and large sizes are developed and solved. the results indicate that simulated annealing-based heuristic provides near optimal solutions.