Proposing a non-linear mathematical model for order splitting in a supply chain with perishable products: solving by genetic algorithm.

• Author: Seyedhosseini, Seyed-Mohammad
• Position: Report

1. INTRODUCTION & LITERATURE REVIEW

   In competitive world today, establishing and maintaining agile supply chains through optimal allocations among different members of each echelon play vital roles in making enterprises viable and lucrative. Studying the literature review related to the past decade shows that there is an increasing interest in manufacturing resource allocation for supply chain optimization by solving a decision-making problems through artificial intelligence-based heuristics including genetic algorithm (GA), multi-agent, simulated annealing, taboo search, and ant colony optimization. Moreover, the GA has gained more and more popularity in the resolution of manufacturing resource allocation problem as it provides an optimal solution to the complicated or NP-hard problems. Moon, et al. (2006) proposed an adaptive GA for advanced planning in manufacturing supply chain development by analyzing alternative manufacturing resources and sequences to determine the schedules and operation sequences that minimize the make span. In a two-echelon single-vendor multiple-buyers supply chain model under vendor managed inventory (VMI) mode of operation, Nachiappan and Jawahar (2007) formulated a non-linear integer-programming problem and proposed a GA based heuristic to find the optimal sales quantity for each buyer. Shu-Hsien Liao, et al. (2011) dealt with an integrated location-inventory distribution network problem in a supply chain. They presented a Multi-Objective Location-Inventory Problem (MOLIP) model and investigated the possibility of a multi-objective evolutionary algorithm based on the non-dominated sorting genetic algorithm for solving MOLIP. Paul Brijesh (2011), considered a static divergent two-stage supply chain with one distributor and many retailers. He focused on determining the best installation inventory control. Also, on account of the computational complexity involved in optimally solving problems over a large finite time horizon, a GA based heuristic methodology presented. Moreover, investigating the conducted research shows that very little of research has been done in the area of integrated production and distribution planning for perishable products. For instance, Bhattacharjee and Ramesh (2000) developed an optimization model which maximizes profits by optimized quantities of products allocated in different periods with different prices and relevant operational costs (holding and ordering costs). They considered single product with a fixed perishing life that there wasn't any direct relation between the variation of product prices and their lifetime. Later, Jian Lia, et al. (2007) developed an economic-order-quantity model (EOQ)-based models with perishable items to evaluate the impact of a form postponement strategy on the retailer in a supply chain. Their theoretical analysis and computational results showed that a postponement strategy for perishable items can give a lower total average cost under certain circumstances. Prakash L. Abad (2008) considered the pricing and lot-sizing problem for a product subject to general rate of deterioration and partial backordering. He used impatience functions to model backlogging of demand and provided provide an iterative procedure for solving the overall problem. The purpose of this paper, unlike the other research, is to propose an efficient mathematical planning model for effective order splitting in a supply chain with perishable products. Also, a utility function indicating the preference of customers between price and lifetime of various products is determined. Moreover, there is a direct relationship between the selling price and the remained lifetime of perishable products. The objective is to find the optimal order quantities in multi-period situation while maximizing the whole profit. Under these conditions, the problem is first formulated as a non-linear integer-programming (NIP) model and then a genetic algorithm (GA) is proposed to solve it.

2. PROBLEM DESCRIPTION

   This paper deals with supply chain planning from the perspective of proposing a non-linear mathematical model while there are perishable products and multi-period. In this model, it is considered that supply chain has three echelons containing multi-suppliers, a variety of products, multi- buyer and various customers. In order to develop a mathematical model for the considered problem, the following assumptions and notation are taken into account.1) Each buyer can procure all kinds of products for customers.2) Each customer can order a variety of products to the various buyers. 3) In each period, each buyer receives the...