بهینه سازی کلونی مورچه چند هدفه: یک روش فرا اکتشافی برای تامین طراحی زنجیره ای

This paper proposes a new approach to determining the Supply Chain (SC) design for a family of products comprising complex hierarchies of subassemblies and components. For a supply chain, there may be multiple suppliers that could supply the same components as well as optional manufacturing plants that could assemble the subassemblies and the products. Each of these options is differentiated by a lead-time and cost. Given all the possible options, the supply chain design problem is to select the options that minimise the total supply chain cost while keeping the total lead-times within required delivery due dates. This work proposes an algorithm based on Pareto Ant Colony Optimisation as an effective meta-heuristic method for solving multi-objective supply chain design problems. An experimental example and a number of variations of the example are used to test the algorithm and the results reported using a number of comparative metrics. Parameters affecting the performance of the algorithm are investigated.

Today’s rapidly changing business environment requires corporations to continuously evaluate and configure their Supply Chains (SCs) to provide customers with high quality products/services at the lowest possible cost and within the shortest possible time (Zhang and Sharifi, 2007 and Zhang, 2010). A supply chain is a network of optional resources through which materials (raw materials, work in progress, and finished products) flow along one direction while information (demand data, due date, delivery, and assembly cost and time) along both directions in order to satisfy demands for products from customers. The process of finding the best flow patterns (i.e., choices of resources) for a family of products is known as the optimisation of supply chain design (Goetschalckx et al., 2002). The determination of a flow pattern for every product in a family requires the selection of a supplier (or suppliers) for every component used by the product mix, the selection of a manufacturing plant (or plants) for assembling every sub- or final assembly in the product mix, and the choice of transport options for delivering every product to customers. For a typical supply chain, there often exist many suppliers that could supply the same components, multiple optional manufacturing plants that could assemble each sub-assembly or product, and alternative transport options that could be used for every product–destination combination. These resource options are differentiated by the lead-time and cost associated with each option. Optimising supply chain design requires the selection of resource options across the supply chain to minimise the total cost for the supply chain while keeping total lead-times as short as possible (or within what customers are prepared to accept). This is a non-trivial task due to the complexity involved in optimising two different, often contradicting, objectives (cost and time) simultaneously. The involvements of multiple products of complex hierarchy, sharing common components and sub-assemblies, and the existence of a large number of resource options across a supply chain, add further complexity to the problem. In the literature, there are basically two ways in which two or more objectives could be dealt with simultaneously. The first involves transforming the multi-objective problem into a single-objective problem that aggregates all the objectives through a procedure called weighted sum in which every objective is multiplied by a weighting factor and the objective function is calculated as the sum of the weighted objectives (Corner and Buchanan, 1995). This requires a-priori knowledge of the relative importance of different criteria (objectives) which is not always available. An alternative method is to accept several criteria (objectives) simultaneously and determine a non-dominated set. This set is a collection of alternative solutions that represent potential trade-offs among objectives. The advantage is to allow the decision-maker to choose between trade-offs based on situations. This paper proposes a heuristic algorithm based on Pareto Ant Colony Optimisation for multi-objective supply chain design problem. With this algorithm, the supply chain design problem is formulated into an Ant Colony Optimisation problem, and a number of colonies of ants are used in a sequence to explore the solution space and search for successively better non-dominated set of supply chain designs. An experimental example and a number of variants are used to test the algorithm and illustrate the benefits of utilising multiple pheromone matrices and multiple ant colonies in multi-objective supply chain design problems. This paper is organised as follows. In Section 2, the literature related to the supply chain design problem is reviewed. In Section 3, the theory of Pareto Ant Colony Optimisation (P-ACO) is explained. Section 4 describes the problem representation and solution methodology for finding supply chain designs by P-ACO. In order to test the proposed method an experimental application is introduced and results of tests reported in Section 5. The paper is concluded in Section 6.

The use of methodologies based on social insects as heuristic methods for combinatorial optimisation problems has tremendous potential. In this paper, the multi-objective supply chain design problem has been formulated to a Pareto Ant Colony heuristic problem in which two objectives, total cost and total time, are involved. Two ways in which the pheromone in the ant colony is represented and updated, referred to as SPM and MPM, are proposed. In SPM, a single pheromone matrix is used and the increment to pheromone is made as a function of both cost and time objectives. In MPM, the pheromone matrix is split into two matrices, one corresponding to cost and another to time objective. The update of pheromone is based on cost and time performances separately. Our tests show that the final solutions found using SPM or MPM methods are similar, given the same number of colonies and the same number of ants in each colony, with the results from MPM being slightly better. SPM seems to converge more rapidly in the early stage of the searching process but is slow in fine tuning the solutions, compared to MPM. There does appear to be an advantage to be gained by using MPM. The performance of the algorithm is related to the settings of a number of control parameters, but there are pointers as to how their values should be set. The work suggests that it is possible to design supply chain structures across a family of products, considering both total cost and time objectives, by using Pareto ACO meta-heuristics. Future work is directed towards considering the existence of inventories in parts of the supply chains and uncertainties in resource lead-times.