Multi-stage Supply Chain Network Research Articles

Supply Chain Planning for IC Design House Back-End Production Network With Turnkey Service

Owing to global competition, integrated circuit (IC) design houses are facing challenges in the optimal use of capacity and resources to fulfill customer demands and maximize profit. A hybrid make-to-stock (MTS) and make-to-order (MTO) model is generally used. Wafer procurement is made according to customers’ long-term demand forecast based on MTS. Limited wafer fab resources and back-end capacity are first allocated to on-hand orders and then to forecast demand. In production planning, several factors need to be considered to determine the production quantity and inventory level, such as the material, capacity, substitute, technical constraint, and order tardiness. This study considers a typical multi-stage supply chain network of semiconductor back-end production with turnkey service for IC design houses. The objective is to maximize the total profit with the constraints of equipment capacity, the flexibility of substitutes, and the usage of the turnkey mode. The problem is formulated with a mixed-integer programming model and solved using two novel heuristic algorithms: a product-based decomposition (PD_SCP) with profit-based criteria and a Lagrangian decomposition combined with the product-based decomposition (LD-SCP) method. Using the LD-SCP algorithm takes a long time but results in a great solution. Sensitivity analysis is conducted to investigate the impact of different parameters on production cost and total profit.

An integrated multitiered supply chain network model of competing agricultural firms and processing firms: The case of fresh produce and quality

In this paper, we develop an integrated multitiered competitive agricultural supply chain network model in which agricultural firms and processing firms compete to sell their differentiated products. The focus here is on fresh produce and minimally processed such agricultural products, with quality also captured. The competition among agricultural firms and processing firms is studied through game theory, where the governing Cournot–Nash equilibrium conditions correspond to a variational inequality problem. The algorithm, at each iteration, yields explicit closed form expressions for the agricultural product path flows, the agricultural product shipments from agricultural firms to the processing firms, and the Lagrange multipliers. A numerical study consisting of several supply chain disruption scenarios demonstrates the applicability of our modeling framework.

Continuous-time planning and scheduling of internal closed-loop systems in multi-stage supply chain networks with recycling trade-offs

The article considers supply chain networks of process industries within several days or months. Continuous-time production, distribution, and recycling of goods and their subsequent reintegration into closed loops is analyzed. The aim of the study is to quantify trade-offs resulting from decisions on the usage of recyclable quantities. A mixed-integer linear programming model based on a new network structure with third-party contractors is developed. A numerical study consists of thirty scenarios with randomly generated data. The model allows for generating compromise solutions in acceptable computation times, if limiting the transfer of recyclable goods to disposal results in decreasing network profits.

A coordinated scheduling problem for the supply chain in a flexible job shop machine environment

In this study, a new coordinated scheduling problem is proposed for the multi-stage supply chain network. A multi-product and multi-period supply chain structure has been developed, including a factory, warehouses, and customers. Furthermore, the flexible job shop scheduling problem is integrated into the manufacturing part of the supply chain network to make the structure more comprehensive. In the proposed problem, each product includes a sequence of operations and is processed on a set of multi-functional machines at the factory to produce the final product. Final products are delivered to the warehouses to meet customers’ demands. If the demands of customers are not fulfilled, the shortage in the form of backorder may occur at any period. The problem is expressed as a bi-objective mixed-integer linear programming (MILP) model. The first objective function is to minimize the total supply chain costs. On the other hand, the second objective function aims to minimize the makespan in all periods. A numerical example is presented to evaluate the performance of the proposed MILP model. Five multi-objective decision-making (MODM) methods, namely weighted sum, goal programming, goal attainment, LP metric, and max–min, are used to provide different alternative solutions to the decision-makers. The performance of the methods is evaluated according to both objective function values and CPU time criteria. In order to select the best solution technique, the displaced ideal solution method is applied. The results reveal that the weighted sum method is the best among all MODM methods.

A modified firefly algorithm for optimizing a multi stage supply chain network with stochastic demand and fuzzy production capacity

Production-distribution network (PDN) design is among complex problems with dynamic relationships that cause substantial amount of uncertainty including customers’ demands, production capacity and others. This paper addresses a multi stage production–distribution planning (PDP) problem with multi suppliers, producers, potential entrepots, potential retailers and inland and outland customers under uncertain environment. A mixed integer linear programming (MILP) model is presented to describe the purpose problem for optimizing the integrated total cost of the system. The proposed model considers operational risks involving uncertainties related to producers’ capacity and customers’ demand with applying probability distribution and fuzzy set theory. Commercial software cannot solve large sized instances in a reasonable run time. So, we presented a novel heuristic based on firefly algorithm (FA) called selective firefly algorithm (SFA) to solve the large sized problems. In the proposed SFA, each firefly identifies all fireflies with more brightness and evaluates its brightness change before moving, implicitly. Afterwards, the firefly that makes the best change is selected and initial firefly moves toward the selected firefly. Several numerical examples in both small and large sizes are applied to demonstrate the performance of the proposed heuristic.

A multi-stage supply chain network design problem with in-house production and partial product outsourcing

We propose a mixed-integer linear programming model for a novel multi-stage supply chain network design problem. Our model integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, and the distribution of multiple products through the network. The aim is to identify the network configuration with the least total cost subject to side constraints related to resource availability, technological conditions, and customer service level requirements. In addition to in-house manufacturing, end products may also be purchased from external sources and consolidated in warehouses. Therefore, our model identifies the best mix between in-house production and product outsourcing. To measure the impact of this strategy, we further present two additional formulations for alternative network design approaches that do not include partial product outsourcing. Several classes of valid inequalities tailored to the problems at hand are also proposed. We test our models on randomly generated instances and analyze the trade-offs achieved by integrating partial outsourcing into the design of a supply chain network against a pure in-house manufacturing strategy, and the extent to which it may not be economically attractive to provide full demand coverage.

The sustainable supply chain network competition with environmental tax policies

This paper captures different environmental tax policies in a multi-tiered supply chain network competition context. We derive the governing equilibrium conditions for the noncooperative game theory models for each firm and provide the equivalent variational inequality formulations. The numerical examples investigate the impacts of emission tax policies and product differentiation on the competing firms, and compare the effects of different environmental policies (flat emission tax rates, progressive emission taxes, and the government command-and-control regulations with emission standards) on equilibrium product demands, prices, total emissions, and overall profits. The computational results indicate that the implementation of environmental tax policies along with an increase in consumers’ environmental concerns can not only motivate the firms to perform sustainable operations, but also reduce the total carbon footprint. Furthermore, the low-cost progressive emission tax policies can be as effective as the high flat emission tax rate in terms of reduction in carbon footprint. Therefore, the model developed in this paper can be used by the policymakers and the firms to evaluate the effects of different environmental tax policies in a supply chain competition context.

An Optimized Supply Chain Network Model Based on Modified Genetic Algorithm

For complex multi-source, multi-product, multi-stage Supply chain network (SCN) design problem, we propose an optimization supply chain network model. We consider cash conversion cycle as an objective to this model and utilize a modified genetic algorithm to solve the problem. To describe the structure of supply chain network, we propose a new encoding method and a genetic algorithm with modified genetic operators. We use the Pareto approach to obtain the set of Pareto-optimal solutions. In order to evaluate the performance of the modified genetic algorithm and validate the model, we conduct comparisons with standard genetic algorithm and the simulated annealing genetic algorithm. Experimental results show that the modified genetic algorithm achieved better CPU time and the accuracy of the Pareto-optimal solutions than the alternative algorithms and the model was effective.

Multi-stage supply chain network solution methods: hybrid metaheuristics and performance measurement

ABSTRACTWe study a three-stage supply chain network (SCN) design problem for a single-product system. The SCN is composed of suppliers that provide raw materials for the plants, plants that produce and send the finished products to distribution centres (DCs), and DCs that transport finished products to the customers. The use of different conveyances and step-fixed costs improves the applicability and the results but increases the complexity, generating an NP-hard problem. The overall objective of the problem is to minimise the total cost, which is composed of the opening and transportation costs in all three stages. Two hybrid metaheuristics – genetic algorithm–variable neighbourhood search (GA-VNS) and variable neighbourhood search–simulated annealing (VNS-SA) – are proposed to solve this NP-hard problem. In addition to the novelty of the proposed algorithms, we develop an innovative priority-based decoding method to design chromosomes and solutions related to the nature of the problem. A robust parameter and operator setting is implemented using the Taguchi experimental design method with several random test problems. The performance of these algorithms is evaluated and compared for different problem sizes. The experimental results indicate that the GA-VNS is robust and superior to the other competing methods.

Hybrid Genetic Algorithm and Invasive Weed Optimization via Priority Based Encoding for Location-Allocation Decisions in a Three-Stage Supply Chain

In this paper, location–allocation problem of a three-stage supply chain network, including suppliers, plants, distribution centers (DCs) and customers is investigated. With respect to the total cost, the aim is determining opened plants and DCs and designing transportation trees between the facilities. Considering the capacity of suppliers, plants and DCs are limited and there is a limitation on the maximum number of opened plants and DCs, a mixed-integer linear programming (MILP) model of the problem is presented. Since multi-stage supply chain networks have been recognized as NP-hard problems, applying priority-based encoding and a four-step backward decoding procedure, a meta-heuristic algorithm, namely GAIWO, based on the best features of genetic algorithm (GA) and invasive weed optimization (IWO) is designed to solve the problem. In small size problems, the efficiency of the GAIWO is checked by solutions of GAMS software. For larger size problems, the performance of the proposed approach is compared with four evolutionary algorithms in both aspects of the structure of the GAIWO and the efficiency of the proposed encoding–decoding procedure. Besides usual evaluation criteria, Wilcoxon test and a chess rating system are used for evaluating and ranking the algorithms. The results show higher efficiency of the proposed approach.

A comparative study on the application of evolutionary algorithms to multi-objective, multi-stage supply chain network design

This paper deals with a multi-objective, multi-stage supply chain network formulation and application of various evolutionary algorithms like particle swarm optimisation (PSO) and genetic algorithm (GA) to solve the formulated problem. As we all know, in recent days, the supply chain network tends to be very complex with lots of suppliers and customers in the value chain. The aim of this paper is to establish a way to optimise a complex multi-stage supply chain network by minimising both costs and lead time under some given constraints while applying both PSO and GA techniques to find out the best solutions available by comparing them. The algorithm techniques were modified to obtain the desired solutions while keeping the entire parameters standard. A numerical real-life example was introduced to check the validity of our assumptions and effectiveness of the techniques used in the paper. Mainly, the Pareto optimal solutions were compared.

A comparative study on the application of evolutionary algorithms to multi-objective, multi-stage supply chain network design

A comparative study on the application of evolutionary algorithms to multi-objective, multi-stage supply chain network design

Two-Stage Supply Chain Network Design Problem with Interval Data

Supply chain is usually represented by a network (which is called supply chain network) that contains some nodes. In a supply chain network these nodes are suppliers, plants, distribution centers and customers which are some facilities connected by some arcs to each other. The arcs connect the nodes in the direction of their production flow, meaning that each arc shows a route between the facilities for transporting the products. A multi-stage supply chain network (MSCN) is defined as a sequence of multiple supply chain network stages. This paper addresses a typical supply chain network problem which is based on a two-stage single-product system under uncertain conditions such that both cost and constraint parameters are interval numbers. The combination of these uncertain parameters are considered in this typical problem for the first time. In this case, two different order relations (the order relations ≤UC and ≤HW) for interval numbers are considered. Then, two solution procedures are developed in order relations for the interval two-stage supply chain network design problem. The efficiency of the proposed method is illustrated by a numerical example where it is proved that the relation ≤HW shows better performance than the relation ≤UC.

A general multitiered supply chain network model of quality competition with suppliers

In this paper, we develop a general multitiered supply chain network equilibrium model consisting of competing suppliers and competing firms who purchase components for the assembly of their final branded products and, if capacity permits, and it enhances profits, produce their own components. The competitive behavior of each tier of decision-makers is described along with their strategic variables, which include quality of the components and, in the case of the firms, the quality of the assembly process itself. The governing equilibrium conditions of the supply chain network are formulated as a variational inequality and qualitative properties are presented. The algorithm, accompanied with convergence results, is then applied to numerical supply chain network examples, along with sensitivity analysis in which the impacts of capacity disruptions and complete supplier elimination are investigated.

A General Multitiered Supply Chain Network Model of Quality Competition with Suppliers

In this paper, we develop a general multitiered supply chain network equilibrium model consisting of competing suppliers and competing firms who purchase components for the assembly of their final branded products and, if capacity permits, and it enhances profits, produce their own components. The competitive behavior of each tier of decision-makers is described along with their strategic variables, which include quality of the components and, in the case of the firms, the quality of the assembly process itself. The governing equilibrium conditions of the supply chain network are formulated as a variational inequality and qualitative properties are presented. The algorithm, accompanied with convergence results, is then applied to numerical supply chain network examples, along with sensitivity analysis in which the impacts of capacity disruptions and complete supplier elimination are investigated.

Supply chain performance assessment and supplier and component importance identification in a general competitive multitiered supply chain network model

In this paper, we develop a multitiered competitive supply chain network game theory model, which includes the supplier tier. The firms are differentiated by brands and can produce their own components, as reflected by their capacities, and/or obtain components from one or more suppliers, who also are capacitated. The firms compete in a Cournot---Nash fashion, whereas the suppliers compete a la Bertrand since firms are sensitive to prices. All decision-makers seek to maximize their profits with consumers reflecting their preferences through the demand price functions associated with the demand markets for the firms' products. We construct supply chain network performance measures for the full supply chain and the individual firm levels that assess the efficiency of the supply chain or firm, respectively, and also allow for the identification and ranking of the importance of suppliers as well as the components of suppliers with respect to the full supply chain or individual firm. The framework is illustrated through a series of numerical supply chain network examples.

Supply Chain Performance Assessment and Supplier and Component Importance Identification in a General Competitive Multitiered Supply Chain Network Model

In this paper, we develop a multitiered competitive supply chain network game theory model, which includes the supplier tier. The firms are differentiated by brands and can produce their own components, as reflected by their capacities, and/or obtain components from one or more suppliers, who also are capacitated. The firms compete in a Cournot-Nash fashion, whereas the suppliers compete a la Bertrand since firms are sensitive to prices. All decision-makers seek to maximize their profits with consumers reflecting their preferences through the demand price functions associated with the demand markets for the firms' products. We construct supply chain network performance measures for the full supply chain and the individual firm levels that assess the efficiency of the supply chain or firm, respectively, and also allow for the identification and ranking of the importance of suppliers as well as the components of suppliers with respect to the full supply chain or individual firm. The framework is illustrated through a series of numerical supply chain network examples.

Multistage production distribution under uncertain demands with integrated discrete particle swarm optimization and extended priority-based hybrid genetic algorithm

Production distribution systems are increasingly crucial because of shortened product life cycles, increasing competition, and uncertainty introduced by globalization. Production distribution involves a multistage supply chain network that consists of factories, distribution centers, retailers, and various customers. Customer demands fluctuate and are unpredictable, thereby causing an imprecise customer quantity demand in each period in the production distribution model, and increasing inventory and related costs. Most studies have addressed the production distribution problem with certain demands or a single period. To fill the gap, this study aims to integrate the extended priority-based discrete particle swarm optimization and novel extended priority-based hybrid genetic algorithm for solving flexible multistage production distribution under uncertain demands in multiple periods. In particular, triangular fuzzy demands are considered for minimizing the total cost, including transportation costs, inventory costs, shortage costs, and ordering costs, in the multistage and multi-time-period supply chain. For validation, we designed numerical experiments to compare the proposed approaches with LINGO computational software (for small problems) and conventional genetic algorithms (for normal problems) in real settings. The experimental results demonstrated practical viability of the proposed approaches.

Efficient heuristics for cost optimisation in multi stage supply chain network with a fixed transportation charge

This paper addresses multi stage supply chain network (MSCN) problem associated with fixed cost. The MSCN problem involves the selection of suppliers, locating manufacturing plants and distribution centres and determining the optimum/best strategy for distributing the products from the plants to the distribution centres and from the distribution centres to the customers. The objective is to select the optimum numbers, locations and capacities of plants and distribution centres to open so that all customer demand is satisfied at minimum cost. The problem chosen goes beyond the traditional mathematical programming and it becomes a non-polynomial (NP) hard while considering the fixed costs. We develop a mixed integer programming model and provide an efficient heuristic solution procedure for this distribution system problem. Several numerical experimental results are presented and compared with the approximate and lower bound solutions to show the effectiveness of the proposed method. The comparison reveals that the proposed heuristics generates better solution than the approximation method and closer to lower bound solutions.

Particle swarm optimisation for multi stage supply chain network associated with fixed charges

This paper develops a particle swarm optimisation (PSO) algorithm for the multi stage supply chain network problem associated with the fixed charges. In many distribution problems, the transportation cost consists of fixed costs, that are independent of the quantities transported and variable costs, which are proportional to the quantities transported. The objective of this paper is to select the optimum set of suppliers, plants, distribution centres (DCs) to be opened and determine the quantities to be supplied to satisfy the customer demand with minimum total distribution cost. The problem chosen goes beyond the traditional mathematical programming and it becomes a non-polynomial (NP) hard while considering the fixed costs. The performance of PSO is compared in terms of total distribution cost with spanning tree-based genetic algorithm (st-GA), improved Prufer number encoding-based genetic algorithm (IPEGA) and with LINGO. Computational results showed that the proposed PSO is capable of producing good quality solutions.