A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return

A closed-loop supply chain (CLSC) network consists of both forward and reverse supply chains. In this paper, a CLSC network is investigated which includes multiple plants, collection centres, demand markets, and products. To this aim, a mixed-integer linear programming model is proposed that minimizes the total cost. Besides, two test problems are examined. The model is extended to consider environmental factors by weighed sums and ε-constraint methods. In addition, we investigate the impact of demand and return uncertainties on the network configuration by stochastic programming (scenario-based). Computational results show that the model can handle demand and return uncertainties, simultaneously.     

Closed-loop supply chain network design: A financial approach

The more common approaches used in the SCM consider only the physical logistic operations and ignore the financial aspects of the chain. This paper presents a financial approach to model a closed-loop supply chain design in which financial aspects are explicitly considered as exogenous variables. The model decides to determine the strategic decisions as well as the tactical decisions. The main contribution of this paper is to incorporate the financial aspects (i.e. current and fixed assets and liabilities) and a set of budgetary constraints representing balances of cash, debt, securities, payment delays, and discounts in the supply chain planning. Moreover, the financial approach applies the change in equity (instead of the measure of profit/cost in traditional approaches) as the objective function to be optimized in the presented model.To show the advantages of the presented approach, the results attributed to the financial approach and the traditional approach are compared, where the latter firstly decides on operations and fits finances afterwards. The results indicate that the traditional approach leads to lower change in equity compared to the financial approach. This fact illustrates the inadequacy of treating process operations and finances in isolated environments and pursuing as objective myopic performance indicators such as profit or cost. Moreover, a sensitivity analysis of the parameters using ANOVA for different levels of the parameters under different customer order patterns is performed to enhance the managerial insights of the study. The results clearly reveal the better improvement of using the financial approach over the traditional approach, and convince the decision makers to take advantage of the proposed approach.     

A robust optimization approach to wine grape harvesting scheduling

Optimization models are increasingly being used in agricultural planning. However, the inherent uncertainties present in agriculture make it difficult. In recent years, robust optimization has emerged as a methodology that allows dealing with uncertainty in optimization models, even when probabilistic knowledge of the phenomenon is incomplete. In this paper, we consider a wine grape harvesting scheduling optimization problem subject to several uncertainties, such as the actual productivity that can be achieved when harvesting. We study how effective robust optimization is solving this problem in practice. We develop alternative robust models and show results for some test problems obtained from actual wine industry problems.     

Reverse channel decisions for a fuzzy closed-loop supply chain

This article reports the results of a study that explores the decisions of reverse channel choice in a fuzzy closed-loop supply chain. Specifically, a manufacturer produces new products by using original components or by remanufacturing used products and wholesales the new products to the retailer who then sells them to the consumers. The used products are collected by the manufacturer or the retailer or a third party. The primary goal of this paper is to investigate the implications of three different used-product collection modes on the decisions of the manufacturer, the retailer, and the third party, and on their own profits in the expected value model. By using game theory and fuzzy theory, the firms optimal strategies are obtained.     

A two-period game of a closed-loop supply chain

We consider a two-period closed-loop supply chain (CLSC) game where a remanufacturer appropriates of the returns’ residual value and decides whether to exclusively manage the end-of-use product collection or to outsource it to either a retailer or a third-service provider (3P). We determine that the manufacturer outsources the product collection only when an outsourcee performs environmentally and operationally better. On the outsourcees side there is always an economic convenience in managing the product returns process exclusively, independently of returns rewards and operational performance. When outsourcing is convenient, a manufacturer always chooses a retailer if the outsourcees show equal performance. Overall, the manufacturer is more sensitive to environmental performance than to operational perfomance. Finally, there exists only a small region inside which outsouring the collection process contributes to the triple bottom line.     

Designing contracts for a closed-loop supply chain under information asymmetry

This paper studies the problem of designing contracts in a closed-loop supply chain when the cost of collection effort is the retailer’s private information. We investigate four cases: two contracts (a two-part nonlinear contract and a collection effort requirement contract), each under complete information and asymmetric information. We derive the manufacturer’s optimal contracts for all four cases and analyze the impact of information on the equilibrium results of supply chain members.     

Robust environmental closed-loop supply chain design under uncertainty

With the fast developments in product remanufacturing to improve economic and environmental performance, an environmental closed-loop supply (ECLSC) chain is important for enterprises' competitiveness. In this paper, a robust ECLSC network is investigated which includes multiple plants, collection centers, demand zones, and products, and consists of both forward and reverse supply chains. First, a robust multi-objective mixed integer nonlinear programming model is proposed to deal with ECLSC considering two conflicting objectives simultaneously, as well as the uncertain nature of the supply chain. Cost parameters of the supply chain and demand fluctuations are subject to uncertainty. The first objective function aims to minimize the economical cost and the second objective function is to minimize the environmental influence. Then, the proposed model is solved as a single-objective mixed integer programming model applying the LP-metrics method. Finally, numerical example has been presented to test the model. The results indicate that the proposed model is applicable in practice.     

A stochastic programming approach for supply chain network design under uncertainty

This paper proposes a stochastic programming model and solution algorithm for solving supply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only address a modest number of scenarios for the uncertain problem parameters. Our solution methodology integrates a recently proposed sampling strategy, the sample average approximation (SAA) scheme, with an accelerated Benders decomposition algorithm to quickly compute high quality solutions to large-scale stochastic supply chain design problems with a huge (potentially infinite) number of scenarios. A computational study involving two real supply chain networks are presented to highlight the significance of the stochastic model as well as the efficiency of the proposed solution strategy.     

Capacitated dynamic lot sizing problems in closed-loop supply chain

In this paper, we address the capacitated dynamic lot sizing problem arising in closed-loop supply chain where returned products are collected from customers. These returned products can either be disposed or be remanufactured to be sold as new ones again; hence the market demands can be satisfied by either newly produced products or remanufactured ones. The capacities of production, disposal and remanufacturing are limited, and backlogging is not allowed. A general model of this problem is formulated, and several useful properties of the problem are characterized when cost functions are concave. Moreover, this problem is analyzed and solved to optimality using dynamic programming algorithms under different scenarios. It is shown that the problem with only disposal or remanufacturing can be converted into a traditional capacitated lot sizing problem and be solved by a polynomial algorithm if the capacities are constant. A pseudo-polynomial algorithm is proposed for the problem with both capacitated disposal and remanufacturing. The problem with capacitated production and remanufacturing and the problem with uncapacitated production and capacitated remanufacturing are also analyzed and solved. Through numerical experiments we show that the proposed algorithms perform well when solving problems of practical sizes. From the experimental results also indicates that it is worthwhile to expand the remanufacturing capacity only when returned products exist in a relatively long planning horizon, and production capacities have little effect on the remanufacturing plan when the demand is mainly satisfied by the production.     

Integrated production planning and order acceptance under uncertainty: A robust optimization approach

The aim of this paper is to formulate a model that integrates production planning and order acceptance decisions while taking into account demand uncertainty and capturing the effects of congestion. Orders/customers are classified into classes based on their marginal revenue and their level of variability in order quantity (demand variance). The proposed integrated model provides the flexibility to decide on the fraction of demand to be satisfied from each customer class, giving the planner the choice of selecting among the highly profitable yet risky orders or less profitable but possibly more stable orders. Furthermore, when the production stage exceeds a critical utilization level, it suffers the consequences of congestion via elongated lead-times which results in backorders and erodes the firm’s revenue. Through order acceptance decisions, the planner can maintain a reasonable level of utilization and hence avoid increasing delays in production lead times. A robust optimization (RO) approach is adapted to model demand uncertainty and non-linear clearing functions characterize the relationship between throughput and workload to reflect the effects of congestion on production lead times. Illustrative simulation and numerical experiments show characteristics of the integrated model, the effects of congestion and variability, and the value of integrating production planning and order acceptance decisions.     

Environmental supply chain network design using multi-objective fuzzy mathematical programming

The concern about environmental impact of business activities has spurred an interest in designing environmentally conscious supply chains. This paper proposes a multi-objective fuzzy mathematical programming model for designing an environmental supply chain under inherent uncertainty of input data in such problem. The proposed model is able to consider the minimization of multiple environmental impacts beside the traditional cost minimization objective to make a fair balance between them. A life cycle assessment-based (LCA-based) method is applied to assess and quantify the environmental impact of different options for supply chain network configuration. Also, to solve the proposed multi-objective fuzzy optimization model, an interactive fuzzy solution approach is developed. A real industrial case is used to demonstrate the significance and applicability of the developed fuzzy optimization model as well as the usefulness of the proposed solution approach.     

A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling

Due to the implementation of government legislation, social responsibility, environmental concern, economic benefits and customer awareness the industries are under a great pressure not only to provide environmentally friendly products but also to take back the product after its use. The issue in reverse logistics is to take back the used products, either under warranty or at the end of use or at the end of lease, so that the products or its parts are appropriately disposed, recycled, reused or remanufactured. In order to overcome this issue, it is necessary to setup a logistics network for arising goods flow from end users to manufacturers. In this study, the optimum usage of secondary lead recovered from the spent lead–acid batteries for producing new battery is presented. The disposal in surface or sewage water or land of liquid content of the lead–acid batteries is strictly restricted. Because of the need for environmental protection and the lack of considerable lead resources, the spent batteries treatment and lead recovery are becoming crucial now-a-days. The objective of this paper is to develop a multi echelon, multi period, multi product closed loop supply chain network model for product returns and the decisions are made regarding material procurement, production, distribution, recycling and disposal. The proposed heuristics based genetic algorithm (GA) is applied as a solution methodology to solve mixed integer linear programming model (MILP). Finally the computational results obtained through GA are compared with the solutions obtained by GAMS optimization software. The solution reveals that the proposed methodology performs very well in terms of both quality of solutions obtained and computational time.     

Research on game model and complexity of retailer collecting and selling in closed-loop supply chain

A closed-loop supply chain is a complex system in which node enterprises play important roles and exert great influence. Firstly, this paper established a collecting price game model for a close-loop supply chain system with a manufacturer and a retailer who have different rationalities. It assumed that the node enterprises took the marginal utility maximization as the basis of decision-making. Secondly, through numerical simulation, we analyzed complex dynamic phenomena such as the bifurcation, chaos and continuous power spectrum and so on. Thirdly, we analyzed the influences of the system parameters; this further explained the complex nonlinear dynamics behavior from the perspective of economics. The results have significant theoretical and practical application value.     

Integrated supply chain planning under uncertainty using an improved stochastic approach

This paper proposes an integrated model and a modified solution method for solving supply chain network design problems under uncertainty. The stochastic supply chain network design model is provided as a two-stage stochastic program where the two stages in the decision-making process correspond to the strategic and tactical decisions. The uncertainties are mostly found in the tactical stage because most tactical parameters are not fully known when the strategic decisions have to be made. The main uncertain parameters are the operational costs, the customer demand and capacity of the facilities. In the improved solution method, the sample average approximation technique is integrated with the accelerated Benders’ decomposition approach to improvement of the mixed integer linear programming solution phase. The surrogate constraints method will be utilized to acceleration of the decomposition algorithm. A computational study on randomly generated data sets is presented to highlight the efficiency of the proposed solution method. The computational results show that the modified sample average approximation method effectively expedites the computational procedure in comparison with the original approach.     

A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Application of fuzzy optimization to a supply chain network design: A case study of an edible vegetable oils manufacturer

This study applies fuzzy sets to integrate the supply chain network of an edible vegetable oils manufacturer. The proposed fuzzy multi-objective linear programming model attempts to simultaneously minimize the total transportation costs. The first part of the total transportation costs is between suppliers and silos; and rest one is between manufacturer and warehouses. The approach incorporates all operating realities and actual flow patterns at production/distribution network with reference to demands of warehouses, capacities of tin and pet packaging lines. The model has been formulated as a multi objective linear programming model where data are modeled by triangular fuzzy numbers. Finally, the developed fuzzy model is applied for the case study, compiled the results and discussed.     

Complexity analysis of dynamic noncooperative game models for closed-loop supply chain with product recovery

In this paper, we consider a closed-loop supply chain (CLSC) with product recovery, which is composed of one manufacturer and one retailer. The retailer is in charge of recollecting and the manufacturer is responsible for product recovery. The system can be regarded as a coupling dynamics of the forward and reverse supply chain. Under different decision criteria, two noncooperative game models: Stackelberg game model and peer-to-peer game model are developed. The dynamic phenomena, such as the bifurcation, chaos and sensitivity to initial values are analyzed through bifurcation diagrams and the largest Lyapunov exponent (LLE). The influences of decision parameters on the complex nonlinear dynamics behaviors of the two models are further analyzed by comparing parameter basin plots, and the results show that with the improvement of retailer’s competitive position, the CLSC system will be more easier to enter into chaos.     

Development of a new approach for deterministic supply chain network design

This paper proposes a mixed integer linear programming model and solution algorithm for solving supply chain network design problems in deterministic, multi-commodity, single-period contexts. The strategic level of supply chain planning and tactical level planning of supply chain are aggregated to propose an integrated model. The model integrates location and capacity choices for suppliers, plants and warehouses selection, product range assignment and production flows. The open-or-close decisions for the facilities are binary decision variables and the production and transportation flow decisions are continuous decision variables. Consequently, this problem is a binary mixed integer linear programming problem. In this paper, a modified version of Benders’ decomposition is proposed to solve the model. The most difficulty associated with the Benders’ decomposition is the solution of master problem, as in many real-life problems the model will be NP-hard and very time consuming. In the proposed procedure, the master problem will be developed using the surrogate constraints. We show that the main constraints of the master problem can be replaced by the strongest surrogate constraint. The generated problem with the strongest surrogate constraint is a valid relaxation of the main problem. Furthermore, a near-optimal initial solution is generated for a reduction in the number of iterations.     

Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case

We have developed a stochastic mathematical formulation for designing a network of multi-product supply chains comprising several capacitated production facilities, distribution centres and retailers in markets under uncertainty. This model considers demand-side and supply-side uncertainties simultaneously, which makes it more realistic in comparison to models in the existing literature. In this model, we consider a discrete set as potential locations of distribution centres and retailing outlets and investigate the impact of strategic facility location decisions on the operational inventory and shipment decisions of the supply chain. We use a path-based formulation that helps us to consider supply-side uncertainties that are possible disruptions in manufacturers, distribution centres and their connecting links. The resultant model, which incorporates the cut-set concept in reliability theory and also the robust optimisation concept, is a mixed integer nonlinear problem. To solve the model to attain global optimality, we have created a transformation based on the piecewise linearisation method. Finally, we illustrate the model outputs and discuss the results through several numerical examples, including a real-life case study from the agri-food industry.     

An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty

In this work the design of a reverse distribution network is studied. Most of the proposed models on the subject are case based and, for that reason, they lack generality. In this paper we try to overcome this limitation and a generalized model is proposed. It contemplates the design of a generic reverse logistics network where capacity limits, multi-product management and uncertainty on product demands and returns are considered. A mixed integer formulation is developed which is solved using standard B&B techniques. The model is applied to an illustrative case.