Location and allocation decisions for multi-echelon supply chain network – A multi-objective evolutionary approach

This paper aims at multi-objective optimization of single-product for four-echelon supply chain architecture consisting of suppliers, production plants, distribution centers (DCs) and customer zones (CZs). The key design decisions considered are: the number and location of plants in the system, the flow of raw materials from suppliers to plants, the quantity of products to be shipped from plants to DCs, from DCs to CZs so as to minimize the combined facility location and shipment costs subject to a requirement that maximum customer demands be met. To optimize these two objectives simultaneously, four-echelon network model is mathematically represented considering the associated constraints, capacity, production and shipment costs and solved using swarm intelligence based Multi-objective Hybrid Particle Swarm Optimization (MOHPSO) algorithm. This evolutionary based algorithm incorporates non-dominated sorting algorithm into particle swarm optimization so as to allow this heuristic to optimize two objective functions simultaneously. This can be used as decision support system for location of facilities, allocation of demand points and monitoring of material flow for four-echelon supply chain network.     

An interactive possibilistic programming approach for a multi-objective closed-loop supply chain network under uncertainty

In this article, we first propose a closed-loop supply chain network design that integrates network design decisions in both forward and reverse supply chain networks into a unified structure as well as incorporates the tactical decisions with strategic ones (e.g., facility location and supplier selection) at each period. To do so, various conflicting objectives and constraints are simultaneously taken into account in the presence of some uncertain parameters, such as cost coefficients and customer demands. Then, we propose a novel interactive possibilistic approach based on the well-known STEP method to solve the multi-objective mixed-integer linear programming model. To validate the presented model and solution method, a numerical test is accomplished through the application of the proposed possibilistic-STEM algorithm. The computational results demonstrate suitability of the presented model and solution method.     

整合供应商选择的多层级选址-库存模型

针对多级供应链网络设计中选址和库存一体化决策问题,基于梯级库存策略,建立了整合供应商选择的多层级选址-库存模型。模型以网络中供应商的选择成本、工厂和配送中心的打开成本、层级之间的运输成本、库存成本、采购成本和生产成本之和最小为目标,同时对供应商的选择、工厂和配送中心的选址、配送中心对顾客的分配、层级之间的运输量、工厂和配送中心的订货批量进行决策。为了求解所建立的模型,设计了基于部分编码的粒子群优化算法。20个不同规模的算例测试表明：所建立的模型是有效的,能用于多层级供应链网络的设计;所设计的算法无论是在求解精度,还是在运算速度上都明显优于数学优化软件Lingo 9.0,尤其是当供应链网络中总节点数较大时。     

A particle swarm approach for optimizing a multi-stage closed loop supply chain for the solar cell industry

In order to implement sustainable strategies in a supply chain, enterprises should provide highly favorable and effective solutions for reducing carbon dioxide emissions, which brings out the issues of designing and managing a closed-loop supply chain (CLSC). This paper studies an integrated CLSC network design problem with cost and environmental concerns in the solar energy industry from sustainability perspectives. A multi-objective closed-loop supply chain design (MCSCD) model has been proposed, in consideration of many practical characteristics including flow conservation at each production/recycling unit of forward/reverse logistics (FL/RL), capacity expansion, and recycled components. A deterministic multi-objective mixed integer linear programming (MILP) model capturing the tradeoffs between the total cost and total CO₂ emissions was developed to address the multistage CSLC design problem. Subsequently, a multi-objective PSO (MOPSO) algorithm with crowding distance-based nondominated sorting approach is developed to search the near-optimal solution of the MCSCD model. The computational study shows that the proposed MOPSO algorithm is suitable and effective for solving large-scale complicated CLSC structure than the conventional branch-and-bound optimization approach. Analysis results show that an enterprise needs to apply an adequate recycling strategy or energy saving technology to achieve a better economic effectiveness if the carbon emission regulation is applied. Consequently, the Pareto optimal solution obtained from MOPSO algorithm may give the superior suggestions of CLSC design, such as factory location options, capacity expansion, technology selection, purchasing, and order fulfillment decisions in practice.     

A biased‐randomized metaheuristic for the capacitated location routing problem

The location routing problem (LRP) involves the three key decision levels in supply chain design, that is, strategic, tactical, and operational levels. It deals with the simultaneous decisions of (a) locating facilities (e.g., depots or warehouses), (b) assigning customers to facilities, and (c) defining routes of vehicles departing from and finishing at each facility to serve the associated customers’ demands. In this paper, a two‐phase metaheuristic procedure is proposed to deal with the capacitated version of the LRP (CLRP). Here, decisions must be made taking into account limited capacities of both facilities and vehicles. In the first phase (selection of promising solutions), we determine the depots to be opened, perform a fast allocation of customers to open depots, and generate a complete CLRP solution using a fast routing heuristic. This phase is executed several times in order to keep the most promising solutions. In the second phase (solution refinement), for each of the selected solutions we apply a perturbation procedure to the customer allocation followed by a more intensive routing heuristic. Computational experiments are carried out using well‐known instances from the literature. Results show that our approach is quite competitive since it offers average gaps below 0.4% with respect to the best‐known solutions (BKSs) for all tested sets in short computational times.     

Joint optimization of production planning and supplier selection incorporating customer flexibility: an improved genetic approach

Efficient and effective production planning and supplier selection are important decisions for manufacturing industries in a highly competitive supply chain, in particular, when customers are willing to accept products with less desirable product attributes (e.g., color, material) for economic reasons. Yet these two decision making problems have traditionally been studied separately due to their inherent complexity. This paper attempts to solve optimally the challenging joint optimization problem of production planning and supplier selection, considering customer flexibility for a manufacturer producing multiple products to satisfy customers’ demands. This integrated problem has been formulated as a new mixed integer programming model. The objective is to maximize the manufacturer’s total profit subject to various operating constraints of the supply chain. Due to the complexity and non-deterministic polynomial-time (NP)-hard nature of the problem, an improved genetic approach is proposed to locate near-optimal solutions. This approach differs from a canonical genetic algorithm in three aspects, i.e., a new selection method to reduce the chance of premature convergence and two problem-specific repair heuristics to guarantee the feasibility of the solutions. The computational results of applying the proposed approach to solve a set of randomly generated test problems clearly demonstrate its excellent performance.     

采用双档案协同进化离散多目标烟花算法的低碳疫苗冷链优化配送

建立低碳疫苗冷链配送问题的约束多目标优化模型,在满足可用车数量、车辆容量约束和时间窗约束的条件下,考虑最小化碳排放的企业运输成本和客户不满意度。提出一种双档案协同进化的离散多目标烟花算法,采用消除车辆数量和容量约束的解码方式,设计了部分映射爆炸算子,设置可行解档案和不可行解档案协同进化,并对不可行解档案实施可行性搜索。实验结果表明,与已有算法相比,所提算法在低碳疫苗冷链配送问题上能高效地搜索到一组收敛精度和分布性能更优的Pareto非支配解。     

Designing an integrated multi-echelon agile supply chain network: a hybrid taguchi-particle swarm optimization approach

The present paper attempts to explore the integration of production, distribution and logistics activities at the strategic decision making level where, the objective is to design a multi-echelon supply chain network considering agility as a key design criterion. The design network conceived here addresses a class of five echelons of supply chains including suppliers, plants, distribution centers, cross-docks and customer zones. The problem has been mathematically formulated as a multi-objective optimization model that aims to minimize the cost (fixed and variable) and maximizes the plant flexibility and volume flexibility. The notion of cross-dock has been introduced as an intermediate level between distribution centers and customer zones to increase the profitability of manufacturing and service industries. In order to solve the underlying problem, a novel algorithm entitled hybrid taguchi-particle swarm optimization (HTPSO) has been proposed that incorporates the characteristics of statistical design of experiments and random search techniques. The main idea is to integrate the fundamentals of taguchi method i.e. orthogonal array and signal to noise ratio (SNR) in the PSO meta-heuristic to minimize the effect of the causes of variations. The proposed model has been authenticated by undertaking problem instances of varying size. Extensive computational experiments are conducted to validate the same and also the efficacy of the proposed HTPSO algorithm. The results obtained reveal that proposed solution methodology is an effective approach to solve the underlying problem.     

Multi-objective biogeography-based optimization for supply chain network design under uncertainty

This paper proposes a new two-stage optimization method for multi-objective supply chain network design (MO-SCND) problem with uncertain transportation costs and uncertain customer demands. On the basis of risk-neutral and risk-averse criteria, we develop two objectives for our SCND problem. We introduce two solution concepts for the proposed MO-SCND problem, and use them to define the multi-objective value of fuzzy solution (MOVFS). The value of the MOVFS measures the importance of uncertainties included in the model, and helps us to understand the necessity of solving the two-stage multi-objective optimization model. When the uncertain transportation costs and customer demands have joined continuous possibility distributions, we employ an approximation approach (AA) to compute the values of two objective functions. Using the AA, the original optimization problem becomes an approximating mixed-integer multi-objective programming model. To solve the hard approximating optimization problem, we design an improved multi-objective biogeography-based optimization (MO-BBO) algorithm integrated with LINGO software. We also compare the improved MO-BBO algorithm with the multi-objective genetic algorithm (MO-GA). Finally, a realistic dairy company example is provided to demonstrate that the improved MO-BBO algorithm achieves the better performance than MO-GA in terms of solution quality.     

A novel nondominated sorting simplified swarm optimization for multi-stage capacitated facility location problems with multiple quantitative and qualitative objectives

Capacitated facility location problems (CFLPs) arise in the practical application of many supply chain networks that select a set of suppliers, plants, distribution centers, and customers. In general, the goal of CFLPs is to consider multiple critical performances that involve quantitative and qualitative factors, such as cost, transportation time, inventory, profit, and customer satisfaction, to obtain various perspectives from decision makers in most real-world applications. CFLP becomes increasingly complex and challenging when decision makers simultaneously consider both factors; however, offering comprehensive decisions is important. In this study, a novel solution based on simplified swarm optimization (SSO) and a nondominated sorting technique is proposed to provide Pareto-optimal solutions for enhancing search efficiency and solution quality. To yield feasible solutions, three repairer mechanisms, namely, random repair, cost-based, and utility-based mechanisms, are proposed to enhance the search efficiency and diversity of each population. A fuzzy analytic hierarchy process is used to calculate the weight of qualitative objectives. To evaluate the efficiency and effectiveness of the proposed algorithm, extensive experiments are conducted on benchmark and newly generated instances of the four stages of CFLPs. Then, results are compared with those of the nondominated sorting genetic algorithm-II, multi-objective SSO, and multi-objective particle swarm optimization reported from the literature. The computational results demonstrate that the proposed algorithm is highly competitive and performs well in terms of solution quality and computational time. The Pareto set in the investigated type of facility location problems leads to solutions that may better support decision-making.     

A bi-objective optimization of supply chain design and distribution operations using non-dominated sorting algorithm: A case study

This paper considers simultaneous optimization of strategic design and distribution decisions for three-echelon supply chain architecture consisting of following three players; suppliers, production plants, and distribution centers (DCs). The key design decisions considered are: the number and location of plants in the system, the flow of raw materials from suppliers to plants, the quantity of products to be shipped from plants to distribution centers, so as to minimize the combined facility location, production, inventory, and shipment costs and maximize fill rate. To achieve this, three-echelon network model is mathematically represented and solved using swarm intelligence based Multi-objective Hybrid Particle Swarm Optimization algorithm (MOHPSO). This heuristic incorporates non-dominated sorting (NDS) procedure to achieve bi-objective optimization of two conflicting objectives. The applicability of proposed optimization algorithm was then tested by applying it to standard test problems found in literature. On achieving comparable results, the approach was applied to actual data of a pump manufacturing industry. The results show that the proposed solution approach performs efficiently.     

基于改进智能水滴算法的多目标供应链最优模型

为了最大限度地降低制造型供应链的销售成本并缩短供货时间,提出了一种基于改进智能水滴算法的多目标供应链优化模型。该模型通过在选项选择期间同时考虑成本和时间来提高供应链效率,并能够将制造型供应链中的销售成本和交货时间最小化。通过使用帕累托最优准则对传统的智能水滴算法进行修改,从而得到一个帕累托集,以实现两个目标的最小化。通过3个实例对所提算法进行了测试,并采用世代距离和超区域比指标将其与蚁群优化算法进行了比较。实验结果显示,所提方法的性能更优,生成的解集更接近真实帕累托集,能够覆盖更大的解区域面积,且计算效率较高。     

Multi-objective optimization for sustainable supply chain network design considering multiple distribution channels

The emergence of Omni-channel has affected the practical design of the supply chain network (SCN) with the purpose of providing better products and services for customers. In contrast to the conventional SCN, a new strategic model for designing SCN with multiple distribution channels (MDCSCN) is introduced in this research. The MDCSCN model benefits customers by providing direct products and services from available facilities instead of the conventional flow of products and services. Sustainable objectives, i.e., reducing economic cost, enlarging customer coverage and weakening environmental influences, are involved in designing the MDCSN. A modified multi-objective artificial bee colony (MOABC) algorithm is introduced to solve the MDCSCN model, which integrates the priority-based encoding mechanism, the Pareto optimality and the swarm intelligence of the bee colony. The effect of the MDCSCN model are examined and validated through numerical experiment. The MDCSCN model is innovative and pioneering as it meets the latest requirements and outperforms the conventional SCN. More importantly, it builds the foundation for an intelligent customer order assignment system. The effectiveness and efficiency of the MOABC algorithm is evaluated in comparison with the other popular multi-objective meta-heuristic algorithm with promising results.     

A bi-objective integrated procurement,production, and distribution problem of a multi-echelon supply chain network design: A new tuned MOEA

Efficient management of supply chain (SC) requires systematic considerations of miscellaneous issues in its comprehensive version. In this paper, a multi-periodic structure is developed for a supply chain network design (SCND) involving suppliers, factories, distribution centers (DCs), and retailers. The nature of the logistic decisions is tactical that encompasses procurement of raw materials from suppliers, production of finished product at factories, distribution of finished product to retailers via DCs, and the storage of raw materials and end product at factories and DCs. Besides, to make the structure more comprehensive, a flow-shop scheduling model in manufacturing part of the SC is integrated in order to obtain optimal delivery time of the product that consists of the makespan and the ship time of the product to DCs via factories. Moreover, to make the model more realistic, shortage in the form of backorder can occur in each period. The two objectives are minimizing the total SC costs as well as minimizing the average tardiness of product to DCs. The obtained model is a bi-objective mixed-integer non-linear programming (MINLP) model that is shown to belong to NP-Hard class of the optimization problems. Thus, a novel algorithm, called multi-objective biogeography based optimization (MOBBO) with tuned parameters is presented to find a near-optimum solution. As there is no benchmark available in the literature, the parameter-tuned multi-objective simulated annealing algorithm (MOSA) and the popular non-dominated sorting genetic algorithm (NSGA-II) are developed to validate the results obtained and to evaluate the performance of MOBBO using randomly generated test instances.     

Optimization of Order Fulfillment in Distribution Network Problems

This paper focuses on optimization of order due date fulfillment reliability in multi-echelon distribution network problems with uncertainties present in the production lead time, transportation lead time, and due date of orders. Reliability regarding order due date fulfillment is critical in customer service, and customer retention. However, this reliability can be seriously influenced by supply chain uncertainties, which may induce tardiness in various stages throughout the supply chain. Supply chain uncertainty is inevitable, since most input values are predicted from historical data, and unexpected events may happen. Hence, a multi-criterion genetic integrative optimization methodology is developed for solving this problem. The proposed algorithm integrates genetic algorithms with analytic hierarchy process to enable multi-criterion optimization, and probabilistic analysis to capture uncertainties. The optimization involves determination of demand allocations in the network, transportation modes between facilities, and production scheduling in manufacturing plants. A hypothetical three-echelon distribution network is studied, and the computation results demonstrated the reliability of the proposed algorithms. Received: October 2004 / Accepted: September 2005     

Robust supply chain design under uncertain demand in agile manufacturing

This paper considers a supply chain design problem for a new market opportunity with uncertain demand in an agile manufacturing setting. We consider the integrated optimization of logistics and production costs associated with the supply chain members. These problems routinely occur in a wide variety of industries including semiconductor manufacturing, multi-tier automotive supply chains, and consumer appliances to name a few. There are two types of decision variables: binary variables for selection of companies to form the supply chain and continuous variables associated with production planning. A scenario approach is used to handle the uncertainty of demand. The formulation is a robust optimization model with three components in the objective function: expected total costs, cost variability due to demand uncertainty, and expected penalty for demand unmet at the end of the planning horizon. The increase of computational time with the numbers of echelons and members per echelon necessitates a heuristic. A heuristic based on a k-shortest path algorithm is developed by using a surrogate distance to denote the effectiveness of each member in the supply chain. The heuristic can find an optimal solution very quickly in some small- and medium-size cases. For large problems, a “good” solution with a small gap relative to our lower bound is obtained in a short computational time.     

A continuous analysis framework for the solution of location–allocation problems with dense demand

Location–allocation problems arise in several contexts, including supply chain and data mining. In its most common interpretation, the basic problem consists of optimally locating facilities and allocating customers to facilities so as to minimize the total cost. The standard approach to solving location–allocation problems is to model alternative location sites and customers as discrete entities. Many problem instances in practice involve dense demand data and uncertainties about the cost and locations of the potential sites. The use of discrete models is often inappropriate in such cases. This paper presents an alternative methodology where the market demand is modeled as a continuous density function and the resulting formulation is solved by means of calculus techniques. The methodology prioritizes the allocation decisions rather than location decisions, which is the common practice in the location literature. The solution algorithm proposed in this framework is a local search heuristic (steepest-descent algorithm) and is applicable to problems where the allocation decisions are in the form of polygons, e.g., with Euclidean distances. Extensive computational experiments confirm the efficiency of the proposed methodology.     

An integrated model for facility location and technology acquisition

This paper presents an analytical approach for simultaneous optimization of the facility location, capacity acquisition and technology selection decisions. The proposed approach can be useful when there is considerable interaction between these structural decisions, e.g., in global manufacturing companies. In these cases, a sequential optimization approach is bound to produce sub-optimal facility designs, and hence an integrated model is needed. We present a formal definition of the facility location and technology acquisition problem, and provide a basic model. We describe the analytical properties of the model, which led to the development of a solution procedure. We report on a set of experiments, and conclude that the computational performance of the proposed algorithm is quite satisfactory.     

A multi-objective meta-heuristic approach for the design and planning of green supply chains - MBSA

Supply Chains are complex networks that demand for decision supporting tools that can help the involved decision making process. Following this need the present paper studies the supply chain design and planning problem and proposes an optimization model to support the associated decisions. The proposed model is a Mixed Integer Linear Multi-objective Programming model, which is solved through a Simulated Annealing based multi-objective meta-heuristics algorithm – MBSA. The proposed algorithm defines the location and capacities of the supply chain entities (factories, warehouses and distribution centers) chooses the technologies to be installed in each production facility and defines the inventory profiles and material flows during the planning time horizon. Profit maximization and environmental impacts minimization are considered. The algorithm, MBSA, explores the feasible solution space using a new Local Search strategy with a Multi-Start mechanism. The performance of the proposed methodology is compared with an exact approach supported by a Pareto Frontier and as main conclusions it can be stated that the proposed algorithm proves to be very efficient when solving this type of complex problems. Several Key Performance Indicators are developed to validate the algorithm robustiveness and, in addition, the proposed approach is validated through the solution of several instances.     

Integrated production and delivery with single machine and multiple vehicles

This paper considers a class of multi-objective production–distribution scheduling problem with a single machine and multiple vehicles. The objective is to minimize the vehicle delivery cost and the total customer waiting time. It is assumed that the manufacturer’s production department has a single machine to process orders. The distribution department has multiple vehicles to deliver multiple orders to multiple customers after the orders have been processed. Since each delivery involves multiple customers, it involves a vehicle routing problem. Most previous research work attempts at tackling this problem focus on single-objective optimization system. This paper builds a multi-objective mathematical model for the problem. Through deep analysis, this paper proposes that for each non-dominated solution in the Pareto solution set, the orders in the same delivery batch are processed contiguously and their processing order is immaterial. Thus we can view the orders in the same delivery batch as a block. The blocks should be processed in ascending order of the values of their average workload. All the analysis results are embedded into a non-dominated genetic algorithm with the elite strategy (PD-NSGA-II). The performance of the algorithm is tested through random data. It is shown that the proposed algorithm can offer high-quality solutions in reasonable time.