Pricing and strategy selection in a closed-loop supply chain under demand and return rate uncertainty

Closed-loop supply chain (CLSC) decision-making involves many uncertainties, which makes the decision-making process more complex and diversified. This study considered a two-stage CLSC consisting of an original manufacturer and a third-party recycler. Without any government policy support, considering the effects of market demand, product return rate, and consumer perceived value, a CLSC decision model based on market demand with a [0,1] distribution was established. The model analyzes three situations—a manufacturer monopoly, the Cournot duopoly game, and the Stackelberg competition game—and solves them. The optimal values of decision variables such as optimal pricing, market demand, and all parties’ profits in the CLSC are obtained, and a strict mathematical proof is given. Through the model-solving process, the effects of product return rate and consumer perceived value on decision variables are analyzed; then, the profit allocation between the original manufacturer and the third-party recycler under different cooperation modes is analyzed. In addition, the four combinations of competition and cooperation are analyzed based on game theory. The Nash equilibrium solution and Pareto optimal solution of the four modes are analyzed by drawing a bimatrix Nash equilibrium table. The results indicate that the cooperation–cooperation mode is difficult to produce automatically, and government policy guidance and support are often needed to achieve Pareto optimality. Finally, a numerical example is given to validate the proposed model. In this way, the proposed model provides reliable theoretical support for the decision-making of both sides in a CLSC.

     

A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a fuzzy linear programming model for tactical supply chain planning in a multi-echelon, multi-product, multi-level, multi-period supply chain network. In this approach, the demand, process and supply uncertainties are jointly considered. The aim is to centralize multi-node decisions simultaneously to achieve the best use of the available resources along the time horizon so that customer demands are met at a minimum cost. This proposal is tested by using data from a real automobile SC. The fuzzy model provides the decision maker (DM) with alternative decision plans with different degrees of satisfaction.     

A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment

In this study, a fuzzy multi-objective joint replenishment inventory model of deteriorating items is developed. The model maximizes the profit and return on inventory investment (ROII) under fuzzy demand and shortage cost constraint. We propose a novel inverse weight fuzzy non-linear programming (IWFNLP) to formulate the fuzzy model. A soft computing, differential evolution (DE) with/without migration operation, is proposed to solve the problem. The performances of the proposed fuzzy method and the conventional fuzzy additive goal programming (FAGP) are compared. We show that the solution derived from the IWFNLP method satisfies the decision maker’s desirable achievement level of the profit objective, ROII objective and shortage cost constraint goal under the desirable possible level of fuzzy demand. It is an effective decision tool since it can really reflect the relative importance of each fuzzy component.     

Possibilistic linear-programming approach for supply chain networking decisions

Supply chain networking decisions are very important for the medium- and long-term planning success of manufacturing companies. The inputs to supply chain planning models are subject to environmental and system uncertainties. In this paper, a fuzzy set theory-based model is proposed to deal with those uncertainties. For this purpose, a possibilistic linear programming (PLP) model is used to make strategic resource-planning decisions using fuzzy demand forecasts and fuzzy yield rates as well as other inputs such as costs and capacities. The objective of the proposed PLP is to maximize the total profit of the enterprise. The model is applied to Mercedes–Benz Türk, one of the largest bus-manufacturing companies in the world, and conclusions and suggestions for further research are provided.     

An optimization model for traceable closed-loop supply chain networks

In this paper, a new non-linear mixed-integer mathematical programming problem is proposed to model a stochastic multi-product closed-loop supply chain (CLSC). The radio frequency identification (RFID) system is implemented in the supply chain to decrease product losses and the overall lead time of transportation while computing the profit derived from internet and conventional sales. The resulting traceable CLSC improves upon the existing literature by allowing us to: (1) boost the incorporation of traceability assumptions in mathematical programming problems so as to enhance the efficiency and visibility of a supply chain, (2) analyze the strategic effects that different internet sale formats have on customers’ evaluations and acquisition choices, and (3) account for the environmental and socio-economical dimension by explicitly formalizing employment-based incomes as part of the profit function. Two meta-heuristic algorithms are introduced to solve the proposed optimization problem, namely, the greedy randomized adaptive search procedure (GRASP) and particle swarm optimization (PSO). Twelve test problems of different sizes are generated and solved using these algorithms. The computational results show that GRASP outperforms PSO in terms of both profit and CPU time values. Finally, a case study in the network marketing industry is presented and managerial implications outlined to show the validity of the proposed model and shed more light on its practical implications.     

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.     

Revised multi-choice goal programming for multi-period,multi-stage inventory controlled supply chain model with popup stores in Guerrilla marketing

In this paper, we consider a supply chain network design problem with popup stores which can be opened for a few weeks or months before closing seasonally in a marketplace. The proposed model is multi-period and multi-stage with multi-choice goals under inventory management constraints and formulated by 0–1 mixed integer linear programming. The design tasks of the problem involve the choice of the popup stores to be opened and the distribution network design to satisfy the demand with three multi-choice goals. The first goal is minimization of the sum of transportation costs in all stages; the second is to minimization of set up costs of popup stores; and the third goal is minimization of inventory holding and backordering costs. Revised multi-choice goal programming approach is applied to solve this mixed integer linear programming model. Also, we provide a real-world industrial case to demonstrate how the proposed model works.     

An inexact-stochastic dual water supply programming model

This paper introduces an inexact-stochastic dual water supply programming (ISDWSP) model based on analysis of the inexact characteristics in demand and supply subsystems of dual water supply system and their dynamic interactions. The model is based on an inexact chance-constrained programming (ICCP) method allowing both distribution information in B (right parameter in the model constrain) and uncertainties in A (left parameter in the model constrain) and C (parameter in the model function) with objective of maximizing economic return, and constrained to available water resource, economical, environmental and social constrains. The decision-making variables of ISDWSP model are water demanded amount by different sectors and waterworks building scale. In the solution process, the ISDWSP is transformed into two deterministic sub-models, which correspond to the upper and lower bounds of the objective function, and the reasonable interval solution set in the given decision space can be obtained by solving the two sub-models. Thus, decision alternatives can be obtained by adjusting decision variable values within their solution intervals and will be useful for decision makers to choose the projected applicable conditions considering tradeoffs between eco-environmental and economic objectives. The model is also applied in a new developing zone of North China with the results of the case study providing reasonable solutions for dynamic planning of different source water (DSW) allocation in a regional system. Finally, waterworks building plan is generated based on the projected applicable conditions.     

Integrating link-based discrete credit charging scheme into discrete network design problem

In this paper, we present an optimization model for integrating link-based discrete credit charging scheme into the discrete network design problem, to improve the transport performance from the perspectives of both transport network planning and travel demand management. The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users. The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem. The network user at the lower level tries to minimize his/her own generalized travel cost (including both the travel time and the value of the credit charged for using the link) by choosing his/her route. While the transport authority at the upper level tries to find the optimal number of lanes and credit charging level with their locations to minimize the total system travel time (or maximize the transportation system performance). A genetic algorithm is used to solve the proposed mixed-integer nonlinear bilevel programming problem. Numerical experiments show the efficiency of the proposed model for traffic congestion mitigation, reveal that interaction effects across the tradable credit scheme and the discrete network design problem which amplify their individual effects. Moreover, the integrated model can achieve better performance than the sequential decision problems.     

Robust optimal dynamic production/pricing policies in a closed-loop system

Hybrid manufacturing/remanufacturing systems play a key role in implementing closed-loop production systems which have been considered due to increasingly environmental concerns and latent profit of used products. Manufacturing and remanufacturing rates, selling price of new products, and acquisition price of used products are the most critical variables to optimize in such hybrid systems. In this paper, we develop a dynamic production/pricing problem, in which decisions should be made in each period confronting with uncertain demand and return. The manufacturer is able to control the demand and return by adjusting selling price and acquisition price respectively, also she can stock inventories of used and new products to deal with uncertainties. Modeling a nominal profit maximization problem, we go through robust optimization approach to reformulate it for the uncertain case. Final robust optimization model is obtained as a quadratic programming model over discrete periods which can be solved by optimization packages of QP. A numerical example is defined and sensitivity analysis is performed on both basic parameters and parameters associated with uncertainty to create managerial views.