Competitive Supply Chain Network Design Research Articles

A Mixed-Integer Linear Formulation for a Dynamic Modified Stochastic p-Median Problem in a Competitive Supply Chain Network Design

Background: The Dynamic Modified Stochastic p-Median Problem (DMS-p-MP) is an important problem in supply chain network design, as it deals with the optimal location of facilities and the allocation of demand in a dynamic and uncertain environment. Methods: In this research paper, we propose a mixed-integer linear formulation for the DMS-p-MP, which captures the key features of the problem and allows for efficient solution methods. The DMS-p-MP adds two key features to the classical problem: (1) it considers the dynamic nature of the problem, where the demand is uncertain and changes over time, and (2) it allows for the modification of the facility locations over time, subject to a fixed number of modifications. The proposed model uses robust optimization in order to address the uncertainty of demand by allowing for the optimization of solutions that are not overly sensitive to small changes in the data or parameters. To manage the computational challenges presented by large-scale DMS-p-MP networks, a Lagrangian relaxation (LR) algorithm is employed. Results: Our computational study in a real-life case study demonstrates the effectiveness of the proposed formulation in solving the DMS p-Median Problem. The results show that the number of opened and closed buildings remains unchanged as the time horizon increases due to the periodic nature of our demand. Conclusions: This formulation can be applied to real-world problems, providing decision-makers with an effective tool to optimize their supply chain network design in a dynamic and uncertain environment.

A sustainable competitive supply chain network design for a green product under uncertainty: A case study of Iranian leather industry

The leather industry typically generates a large amount of wastewater. Leather production requires large quantities of freshwater and various chemicals are added to the water at every stage of production. The absence of proper regulatory bodies and specialized treatment plants to recycle the wastewater add to the environmental hazards caused by the industry. Due to the problems cited above and the significant cost of safe wastewater disposal, numerous manufacturers illegally discharge their chemically polluted wastewater, causing immeasurable damage to the environment and public health. Governments' failure to adopt suitable taxation and subsidy policies further aggravates the crisis and discourages manufacturers from transitioning toward sustainable production practices. As a result, the majority of manufacturers are on the brink of bankruptcy. In this study, we propose a model for a leather industry supply chain that incorporates the three pillars of sustainability which include economic viability, environmental protection, and social equity. The proposed model features flexible governmental policies and enacts a Stackelberg competition between the producers and retailers under both certain and uncertain conditions in the context of the Iranian leather industry to ensure maximum customer satisfaction. To verify the applicability of the model, it was applied to a real-world case study under uncertainty. In the end, the validity of the model was confirmed when the results were approved by a panel of industry experts.

A Possibilistic Bi-objective Mode l for A Competitive Supply Chain Network Design under Variable Coverage

In this paper, the strategic planning of a supply chain under a static chain-to-chain competition on the plane is addressed. It is assumed that each retailer has a coverage area called the radius of influence. The demand of each demand zone is divided equally between the retailers which can cover that market. However, the demand of distant customers who are not in the retailers’ radius of influence, will be lost. This competition is modelled for a real case application of a super market chain. It is assumed that the chain’s owner wants to expand retail outlets to improve its market share. Since this expansion could affect the current customers of existing retailers, the owner wants to avoid attacking the market share of its current retailers. A bi-objective fuzzy mixed integer nonlinear model is proposed. For solving the model, it is first reformulated to a mixed integer linear program and then an interactive approach is devised to handle the fuzzy bi-objective model. Four expansion strategies are analysed from which useful managerial insights are drawn.

An efficient hybrid genetic algorithm for multi-product competitive supply chain network design with price-dependent demand

According to the recent studies, competition between supply chains (SCs) will play a noticeable part of competition in the future’s market. This study considers a SC vs. SC multi-product competition in the duopolistic markets. Pricing, location, transportation and production decisions are taken in a Stackelbrg game formulated as bi-level model. These supply chains (called leader and follower) are three-stage, multi-product, multi-source, and single-period SCs. Karush-Kuhn-Tucker (KKT) conditions are applied in order to transform the presented bi-level model into a single-level mixed integer nonlinear programming (MINLP). Due to computational complexity of the problem, an efficient Hybrid Genetic Algorithm (HGA) is proposed to solve the large size problems. In order to obtain more robust solutions, Taguchi method is applied to calibrate hybrid meta-heuristic parameters. The efficiency of the proposed HGA is investigated through the comparisons with optimal solutions and also with GA. Managerial insights are proposed alongside with the Sensitivity Analysis for important parameters.

Centralized Supply Chain Network Ddesign: Monopoly, Duopoly, and Ooligopoly Competitions under Uncertainty

This paper presents a competitive supply chain network design problem in which one, two, or three supply chains are planning to enter the price-dependent markets simultaneously in uncertain environments and decide to set the prices and shape their networks. The chains produce competitive products either identical or highly substitutable. Fuzzy multi-level mixed integer programming is used to model the competition modes, and then the models are converted into an integrated bi-level one to be solved, in which the inner part sets the prices in dynamic competition and the outer part shapes the network cooperatively.Finally, a real-world problem is investigatedto illustrate how the bi-level model works and discuss how price, market share, total income, and supply chain network behave with respect to key marketing activities such as advertising, promotions, and brand loyalty.

Dynamic Competitive Supply Chain Network Design with Price Dependent Demand and Huff Utility Function

This paper develops a two-stage model to consider a franchise/franchisee environment in which supply chains are simultaneously entering the untapped market to produce either identical or highly substitutable products and give franchise to franchisees. Customer demand is elastic, price dependent and customer utility function is based on Huff gravity rule model. The supply chains, in the first stage, shape their networks and set the market prices based on dynamic games. The franchisees, in the second stage, specify their attractiveness levels and set the locations of their retailers in simultaneous games. Possibility theory was also applied to cope with uncertainty. Finally, we applied our model to a real world problem, discussed the results, conducted some sensitivity analyses, and gained some managerial insights.

An iterative approach for a bi-level competitive supply chain network design problem under foresight competition and variable coverage

This paper develops a bi-level program for a chain-to-chain competition under foresight competition and variable coverage. Customers patronize those retailers who are within their radius of influence. The demand of customers who are not in the catchment area of any retailer, are lost. An iterative global search method is proposed that incorporates the possible reaction of the follower in the leader’s problem as new constraints (i.e. cuts) in each iteration. Several numerical experiments are conducted whose results demonstrate ignoring the foresight competition would lead to loss of market share and profitability of the new entrant’s supply chain.

A variational inequality formulation for designing a multi-echelon, multi-product supply chain network in a competitive environment

In a competitive environment, supply chains are competing with each other to gain the market share and competition is a critical factor influencing the supply chain network structure. The current paper presents a variational inequality formulation and provides the results for a competitive supply chain network design model. The new-entrant supply chain competes against an existing one in a non-cooperative behavior. The networks include raw material suppliers, manufacturers, retailers, and the same demand markets. The manufacturers produce multiple products with deterministic, price-dependent demand. The goal is to maximize the future revenue of both chains. The problem is modeled by mathematical programming and the governing Nash equilibrium conditions are derived. Then, a finite-dimensional variational inequality formulation is presented to solve the equilibrium problem. Qualitative properties of the equilibrium pattern are provided to establish existence and uniqueness results under reasonable conditions. The modified projection algorithm is used to solve the variational inequality problem. A numerical example is presented in order to show the efficiency of the proposed model and to investigate the behavior of the model under different conditions.

Decentralized supply chain network design: monopoly, duopoly and oligopoly competitions under uncertainty

This paper presents the competitive supply chain network design problem in which n decentralized supply chains simultaneously enter the market with no existing rival chain, shape their networks and set wholesale and retail prices in competitive mode. The customer demand is elastic and price dependent, customer utility function is based on the Hoteling model and the chains produce identical or highly substitutable products. We construct a solution algorithm based on bi-level programming and possibility theory. In the proposed bi-level model, the inner part sets the prices based on simultaneous extra- and Stackleberg intra- chains competitions, and the outer part shapes the networks in cooperative competitions. Finally, we use a real-word study to discuss the effect of the different structures of the competitors on the equilibrium solution. Moreover, sensitivity analyses are conducted and managerial insights are offered.

Simultaneous Decentralized Competitive Supply Chain Network Design under Oligopoly Competition

This paper discusses a problem in which decentralized supply chains enter the market simultaneously with no existing rival chains, shape the supply chains’ networks, and set wholesale and retail prices in a noncooperative manner. All the chains produce either identical or highly substitutable products. Customer demand is elastic and price-dependent. A three-step algorithm is proposed to solve this problem. Step one considers the supply chains’ potential network structures. Step two is based on a finite-dimensional variational inequality formulation and is solved by a modified projection method to determine equilibrium prices. Step three selects the equilibrium locations to shape the chains’ equilibrium network structure with the help of the Wilson algorithm. Finally, this approach is applied to a real-world scenario, and the results are discussed. Moreover, sensitivity analyses are conducted.

Simultaneous competitive supply chain network design with continuous attractiveness variables

A two-stage algorithm is developed for the competitive supply chain network design problem in which two competitors simultaneously enter the market with no existing rival chain, shape their networks, and set attractiveness of their opened distribution centres to maximize their profits. The customer behaviour is based on the Huff gravity-based rule.The proposed algorithm is constructed based on the Lemke and Howson algorithm and variational inequality formulation with the help of bi-level programming, the modified projection method, and the possibility theory. We derive the equilibrium condition and establish the finite dimensional variational inequality formulation, and provide properties of the equilibrium patterns in terms of the results of existence and uniqueness. Finally, we generate some instances and use a real world study to discuss the effect of the different structures of the competitors, namely centralized, decentralized, cooperative, or unknown modes, on the equilibrium solution.

Designing an integrated multi-echelon supply chain network with competition

This paper develops a model for competitive supply chain network design which investigates competition between new and existing chains where demand is deterministic and price-dependent. The network consists of raw material suppliers, manufacturers, retailers, and demand market. The supply chains compete in a non-cooperative manner and manufacturers produce homogeneous products. The objective is to maximise the future profits of both chains. First, the problem is formulated by mathematical programming and Lagrangian theory is used for adding the constraints to the objective function. Then, the equilibrium conditions are derived and the problem is formulated as a finite-dimensional variational inequality model. Qualitative properties of the equilibrium pattern are derived to establish existence and uniqueness results under reasonable conditions. The modified projection method is used to solve the variational inequality problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed model and analyse the results under different conditions.

Supply chain network design under profit maximization and oligopolistic competition

In this paper, we model the supply chain network design problem with oligopolistic firms who are involved in the competitive production, storage, and distribution of a homogeneous product to multiple demand markets. The profit-maximizing firms select both the capacities associated with the various supply chain network activities as well as the product quantities. We formulate the governing Nash–Cournot equilibrium conditions as a variational inequality problem and identify several special cases of the model, notably, a generalization of a spatial oligopoly and a classical oligopoly problem to include design capacity variables. The proposed computational approach, which is based on projected dynamical systems, fully exploits the network structure of the problems and yields closed form solutions at each iteration. In order to illustrate the modeling framework and the algorithm, we also provide solutions to a spectrum of numerical supply chain network oligopoly design examples. This paper makes a contribution to game theoretic modeling of competitive supply chain network design problems in an oligopolistic setting.