Robust Design of a Closed-loop Supply Chain Network for Uncertain Carbon Regulations and Random Product Flows

This paper addresses a multi-period capacitated closed-loop supply chain (CLSC) network design problem subject to uncertainties in the demands and returns as well as the potential carbon emission regulations. Two promising regulatory policy settings are considered: namely, (a) a carbon cap and trade system, or (b) a tax on the amount of carbon emissions. A traditional CLSC network design model using stochastic programming is extended to integrate robust optimization to account for regulations of the carbon emissions caused by transportation. We propose a hybrid model to account for both regulatory policies and derive tractable robust counterparts under box and ellipsoidal uncertainty sets. Implications for network configuration, product allocation and transportation configuration are obtained via a detailed case study. We also present computational results that illustrate how the problem formulation under an ellipsoidal uncertainty set allows the decision maker to balance the trade-off between robustness and performance. The proposed method yields solutions that provide protection against the worst-case scenario without being too conservative

Uncertainty Models in Reverse Supply Chain: A Review

Reverse logistic has become an important topic for the organization due to growing environmental concern, government regulation, economic value, and sustainable competitiveness. Uncertainty is one of the key factors in the reverse supply chain that must be controlled; thus, the company could optimize the reverse supply chain function. This paper discusses progress in reverse logistic research. A total of 72 published articles were selected, analyzed, categorized and the research gaps were found among them. The study began by analyzed previous research articles in reverse logistic. In this stage, we also collected and reviewed journals discussing about the reverse supply chain. Meanwhile, the result of this stage shows that uncertainty factor has not been reviewed in detail. The most common theme as the background research in reverse logistic is environmental and economic aspect. Uncertainty in Close Loop Supply Chain is the most widely used approach, followed by the usage on reverse logistics, reverse supply chain and reverse Model. The most used approach and method on uncertainty are Mixed Integer Linear Programing, mixed integer nonlinear Programing, Robust Fuzzy Stochastic Programming, and Improved kriging-assisted robust optimization method. Customer demand, total cost, product returns are the most widely researched aspects. This paper may be useful for academicians, researchers and practitioners in learning on reverse logistic and reverse supply chain; therefore, close loop supply chain can be guidance for upcoming researches. Research opportunity based on this research combines total cost, quality return product, truck capacity, delivery route, remanufacturing capacity, and facility location got optimum function in uncertainty. The research method and approach for MINLP, IK-MRO and RSFP provide many opportunities for research. For theme and area in reverse logistic, close loop supply chain is the theme that provides the most research opportunities

Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax

We optimize the design of a closed-loop supply chain network that encompasses flows in both forward and reverse directions and is subject to uncertainty in demands for both new and returned products. The model also accommodates a carbon tax with tax rate uncertainty. The proposed model is a three-stage hybrid robust/stochastic program that combines probabilistic scenarios for the demands and return quantities with uncertainty sets for the carbon tax rates. The first stage decisions are facility investments, the second stage concerns the plan for distributing new and collecting returned products after realization of demands and returns, and the numbers of transportation units of various modes are the third stage decisions. The second- and third-stage decisions may adjust to the realization of the carbon tax rate. For computational tractability, we restrict them to be affine functions of the carbon tax rate. Benders cuts are generated using recent duality developments for robust linear programs. Computational results show that adjusting product flows to the tax rate provides negligible benefit, but the ability to adjust transportation mode capacities can substitute for building additional facilities as a way to respond to carbon tax uncertainty

Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition

Environmental, social and economic concerns motivate the operation of closed- loop supply chain networks (CLSCN) in many industries. We propose a novel profit maximization model for CLSCN design as a mixed-integer linear program in which there is flexibility in covering the proportions of demand satisfied and returns collected based on the firm\u27s policies. Our major contribution is to develop a novel hybrid robust-stochastic programming (HRSP) approach to simultaneously model two different types of uncertainties by including stochastic scenarios for transportation costs and polyhedral uncertainty sets for demands and returns. Transportation cost scenarios are generated using a Latin Hypercube Sampling method and scenario reduction is applied to consolidate them. An accelerated stochastic Benders decomposition algorithm is proposed for solving this model. To speed up the convergence of this algorithm, valid inequalities are introduced to improve the quality of lower bound, and also a Pareto-optimal cut generation scheme is used to strengthen the Benders optimality cuts. Numerical studies are performed to verify our mathematical formulation and also demonstrate the benefits of the HRSP approach. The performance improvements achieved by the valid inequalities and Pareto-optimal cuts are demonstrated in randomly generated instances

Multi-stage stochastic and robust optimization for closed-loop supply chain design

This dissertation focuses on formulating and solving multi-stage decision problems in uncertain environments using stochastic programming and robust optimization approaches. These approaches are applied to the design of closed-loop supply chain (CLSC) networks, which integrate both traditional flow and the reverse flow of products. The uncertainties associated with this application include forward demands, the quantity and quality of used products to be collected, and the carbon tax rate. The design decisions include long-term facility configurations as well as short-term contracts for transportation capacities by various modes that differ according to their variable costs, fixed costs, and emission rates. This dissertation consists of three papers. The first paper develops a multi-stage stochastic program for a CLSC network design problem with demands and quality of return uncertainties. The second paper focuses on robust optimization; particularly, the question of whether an adjustable robust counterpart (ARC) produces less conservative solutions than the robust counterpart (RC). Using the results of the second paper, a three-stage hybrid robust/stochastic program is proposed in the third paper, in which an ARC is formulated for a mixed integer linear programming model of the CLSC network design problem. In the first paper, a multi-stage stochastic program is proposed for the CLSC network design problem where facility locations are decided in the first stage and in subsequent stages, the capacities of transportation of different modes are contracted under uncertainty about the amounts of new and return products to transport among facilities. We explore the impact of the uncertain quality of returned products as well as uncertain demands with dependencies between periods. We investigate the stability of the solution obtained from scenario trees of varying granularity using a moment matching method for demands and distribution approximation for the quality of returns. Multi-stage solutions are evaluated in out-of-sample tests using simulated historical data and also compared with two-stage model. We observe an instance of overfitting, in which a scenario tree including more outcomes at each stage produces a dramatically different solution that has slightly higher average cost, compared to the solution from a less granular tree, when evaluated against the underlying simulated historical data. We also show that when the scenarios include demand dependencies, the solution performs better in out-of-sample simulation. In the second paper, the ARC of an uncertain linear program extends the RC by allowing some decision variables to adjust to the realizations of some uncertain parameters. The ARC may produce a less conservative solution than the RC does but cases are known in which it does not. While the literature documents some examples of cost savings provided by adjustability (particularly affine adjustability), it is not straightforward to determine in advance whether they will materialize. We establish conditions under which adjustability may lower the optimal cost with a numerical condition that can be checked in small representative instances. The provided conditions include the presence of at least two binding constraints at optimality of the RC formulation, and an adjustable variable that appears in both constraints with implicit bounds from above and below provided by different extreme values in the uncertainty set. The third paper concerns a CLSC network that is subject to uncertainty in demands for both new and returned products. The model structure also accommodates uncertainty in the carbon tax rate. The proposed model combines probabilistic scenarios for the demands and return quantities with an uncertainty set for the carbon tax rate. We constructed a three-stage hybrid robust/stochastic program in which the first stage decisions are long-term facility configurations, the second stage concerns the plan for distributing new and collecting returned products after realization of demands and returns but before realization of the carbon tax rate, and the numbers of transportation units of various modes, as the third stage decisions, are adjustable to the realization of the carbon tax level. For computational tractability, we restrict the transportation capacities to be affine functions of the carbon tax rates. By utilizing our findings in the second paper, we found conditions under which the ARC produces a less conservative solution. To solve the affinely adjustable version, Benders cuts are generated using recent duality developments for robust linear programs. Computational results show that the ability to adjust transportation mode capacities can substitute for building additional facilities as a way to respond to carbon tax uncertainty. The number of opened facilities in ARC solutions are decreased under uncertainty in demands and returns. The results confirm the reduction of total expected cost in the worst case of the carbon tax rate by increasing utilization of transportation modes with higher capacity per unit and lower emission rate

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

Essays on product return management and closed loop-supply chain network design

This dissertation focuses on managerial and operational challenges associated with product return management and CLSC network design. The possibility of product return plays an important role in consumer\u27s purchase decisions. It also motivates firms to extend their forward-only supply chain network structures to a Closed-Loop Supply Chain (CLSC) network and handle both forward and reverse flows of products. While the configuration of the CLSC network is a complex problem comprised of the determination of the optimal locations and capacities of factories, warehouses and collection centers, this problem becomes even more complex under the potential regulations on carbon emissions. This dissertation follows a three-paper format. With a focus on product return management, the first paper studies the roles that pricing and return policy play in the product exchange process for refurbished products. We first apply netnography to study consumer attitudes, general opinions and experiences concerning refurbished electronics purchases, and then propose an analytical model that considers customers\u27 purchasing and return behavior as a result of the firm\u27s decisions regarding the pricing and return policy for refurbished products. The numerical results suggest that sellers should deliberately consider the market segmentation conditions, consumer valuation, and cost factors when choosing the appropriate price and return policy for refurbished products. The second and third paper focus on different aspects of CLSC network design. The second paper investigates a problem to design facility configurations that are robust to variations in possible carbon regulations and their cost and constraint implications. We establish a two-stage, multi-period stochastic programming model to include uncertain demand and return quantities and then extended it to incorporate the uncertainties in carbon regulation policy by the robust optimization method. We propose a hybrid model to account for either carbon tax or cap-and-trade regulatory policies and derive tractable robust counterparts under box and ellipsoidal uncertainty sets. Implications for network configuration, product allocation and transportation configuration are derived. We also present computational results that illustrate how the problem formulation under an ellipsoidal uncertainty set allows the decision maker to balance the trade-off between robustness and performance. The third paper formulates and solves an integrated model for product return management and CLSC network design considering uncertain carbon cost. We build a robust optimization model to address the carbon cost uncertainty, and develop a piecewise linear approximation for the nonlinear profit as a function of the refund. The results of the robust model are compared with those of deterministic models where no or only nominal carbon cost is considered. Extensive parametric analyses illustrate the impact of the cost, revenue and consumer profile parameters on the optimal refund, profit and network topology

Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition

Environmental, social and economic concerns motivate the operation of closed-loop supply chain networks (CLSCN) in many industries. We propose a novel profit maximization model for CLSCN design as a mixed-integer linear program in which there is flexibility in covering the proportions of demand satisfied and returns collected based on the firm\u27s policies. Our major contribution is to develop a novel hybrid robust-stochastic programming (HRSP) approach to simultaneously model two different types of uncertainties by including stochastic scenarios for transportation costs and polyhedral uncertainty sets for demands and returns. Transportation cost scenarios are generated using a Latin Hypercube Sampling method and scenario reduction is applied to consolidate them. An accelerated stochastic Benders decomposition algorithm is proposed for solving this model. To speed up the convergence of this algorithm, valid inequalities are introduced to improve the lower bound quality, and also a Pareto-optimal cut generation scheme is used to strengthen the Benders optimality cuts. Numerical studies are performed to verify our mathematical formulation and also demonstrate the benefits of the HRSP approach. The performance improvements achieved by the valid inequalities and Pareto-optimal cuts are demonstrated in randomly generated instances

Facility Location for a Closed-Loop Distribution Network: a Hybrid Approach

Purpose The purpose of this paper is to find a sustainable facility location solution for a closed-loop distribution network in the uncertain environment created by of high levels of product returns from online retailing coupled with growing pressure to reduce carbon emissions. Design/methodology/approach A case study approach attempts to optimize the distribution centre (DC) location decision for single and double hub scenarios. A hybrid approach combining centre of gravity and mixed integer programming is established for the un-capacitated multiple allocation facility location problem. Empirical data from a major national UK retail distributor network is used to validate the model. Findings The paper develops a contemporary model that can take into account multiple factors (e.g. operational and transportation costs and supply chain (SC) risks) while improving performance on environmental sustainability. Practical implications Based on varying product return rates, SC managers can decide whether to choose a single or a double hub solution to meet their needs. The study recommends a two hub facility location approach to mitigate emergent SC risks and disruptions. Originality/value A two-stage hybrid approach outlines a unique technique to generate candidate locations under twenty-first century conditions for new DCs. </jats:sec