Accelerated Benders Decomposition Algorithm Research Articles

A benders-local branching algorithm for second-generation biodiesel supply chain network design under epistemic uncertainty

This paper proposes a possibilistic programming model in order to design a second-generation biodiesel supply chain network under epistemic uncertainty of input data. The developed model minimizes the total cost of the supply chain from supply centers to the biodiesel and glycerin consumer centers. Waste cooking oil and Jatropha plants, as non-edible feedstocks, are considered for biodiesel production. To cope with the epistemic uncertainty of the parameters, a credibility-based possibilistic programming approach is employed to convert the original possibilistic programming model into a crisp counterpart. An accelerated benders decomposition algorithm using efficient acceleration mechanisms is devised to deal with the computational complexity of solving the proposed model in an efficient manner. The performance of the proposed possibilistic programming model and the efficiency of the developed accelerated benders decomposition algorithm are validated by performing a computational analysis using a real case study in Iran.

Integrated design of emergency shelter and medical networks considering diurnal population shifts in urban areas

This article addresses an emergency shelter and medical network design problem by integrating evacuation and medical service activities and considering diurnal population shifts to respond to large-scale natural disasters in urban areas. A multi-objective mixed-integer programming model that incorporates the characteristics of diurnal population shifts is developed to determine the configuration of the integrated emergency shelter and medical network. An accelerated Benders decomposition algorithm is then devised to solve large-scale problems in reasonable time. A realistic case study on the Xuhui District of Shanghai City in China and extensive numerical experiments are presented to demonstrate the effectiveness of the proposed model and solution method. Computational results suggest that more emergency shelters and emergency medical centers should be established when accounting for diurnal population shifts than when diurnal population shifts are not considered. The accelerated Benders decomposition algorithm is significantly more time efficient as compared with the CPLEX solver.

Subloop-based reversal of port rotation directions for container liner shipping network alteration

Container liner shipping network alteration is a practical manner of shipping network design, which aims to make minor modifications to ameliorate the existing network. In a generic liner shipping network with butterfly ports, each ship route is separated into a set of subloops on the basis of its structure and internal butterfly ports. Reversing the subloop directions has an impact on the network-wide cost including inventory cost, transshipment cost, and slot-purchasing cost. This paper proposes a new destination-based nonlinear model for the subloop-based reversal of port rotation directions with the objective of minimizing the overall network-wide cost. We prove that the addressed problem is NP-hard. Next, the model is transformed to an equivalent mixed-integer linear programming model. Based on the structure of the reformulated model, we develop a Benders decomposition (BD) algorithm and a metaheuristic method to solve practical-size instances. Three acceleration strategies are incorporated into the BD algorithm, which are adding Pareto-optimal cuts, updating big-M coefficients and generating combinatorial Benders cuts. Case studies based on three small examples and an Asia-Europe-Oceania liner shipping network with a total of 46 ports are conducted. Results show that the problem could be efficiently solved by the accelerated BD algorithm and the optimization of subloop directions is conducive to decreasing the network-wide cost especially the inventory cost.

An accelerated Benders decomposition algorithm for reliable facility location problems in multi-echelon networks

Abstract In this paper, we present an accelerated Benders decomposition algorithm for solving the multi-echelon reliable capacitated facility location problem (ME-RCFLP). The objective is a tradeoff between system reliability, and total investment and operational costs while the facilities can be “hardened” (Increase their capacity and decrease their probability of full and partial failure) with more cost. We allow the facilities to have different partial and full failure rates, and more than one facility may be assigned to a client (partial assignment). A new scenario-based formulation is proposed for the problem to effectively cover the outcomes of uncertainty and it is used to introduce an efficient Benders decomposition algorithms as well as a sample average approximation algorithm (SAA) for solving the ME-RCFLP. Computational results show the validity of the proposed model and the efficiency of the proposed solution methods in solving the problem.

Large-scale reverse supply chain network design: An accelerated Benders decomposition algorithm

Abstract Reverse logistics (RL) is a term that captures any process that involves the movement of goods or services from their destination back to their source. RL is increasingly gaining recognition as an essential component in the design process of supply chains. In this paper, we formulate a mixed-integer linear programming (MILP) model that aims to determine the optimal locations and capacities of various nodes such as inspection centers and remanufacturing facilities and to help decision makers find optimal transportation decisions and to determine the number and type of transportation units required in the network. We develop an exact method to solve large-scale real-sized instances of this problem. We initially attempt to solve the problem using the traditional Benders Decomposition (BD) technique which fails to solve the problem in reasonable computational times. We improve the traditional BD technique by adding several accelerating methods such as trust-region, logistics constraints, Pareto-optimal cuts, restructuring of the problem, and continuous relaxation of the integer variables to increase the convergence rate and to reduce the total number of cuts required in the master problem. In almost all the instances, we were able to reach optimal solutions. For the remaining instances, we succeed in solving the largest problem with an optimality gap of 0.5% and within a reasonable running time. The paper highlights and evaluates the performance and effectiveness of the different acceleration techniques of our improved BD algorithm along with the computational results.

Network Design Model to Integrate Shelter Assignment with Contraflow Operations in Emergency Evacuation Planning

In traditional emergency evacuation planning, shelter assignment and contraflow operations are determined sequentially. In this paper, we show that these two types of network design should be considered simultaneously to achieve a better evacuation performance. A mixed integer linear program is proposed, in which an earliest arrival flow model is employed to describe the underlying system optimum evacuation traffic flow pattern. The embedded earliest arrival flow model, built upon a node-link network representation, helps to maintain a small problem size. To address the computational difficulty, an accelerated Benders decomposition algorithm is developed to leverage the separable structure of the proposed model. Numerical experiments are used to investigate the effectiveness of the proposed model and solution algorithm. The results illustrate that the integrated consideration of shelter assignment and contraflow operations in evacuation planning facilitates the effective usage of the evacuation network capacity to further reduce the total system travel time in emergency evacuation.

The design of a reliable and robust hierarchical health service network using an accelerated Benders decomposition algorithm

This paper proposes a novel reliable hierarchical location-allocation model addressing a real-world health service network design problem. The model considers several key issues regarding health service network designs such as hierarchical structure of networks characterised by a two-level multi-flow hierarchy with service referral, uncertainty associated with demand, service and geographical accessibility, prioritizing patients based on their urgency and adopting different service strategies to serve them, service quality reflected in the patients’ expected waiting time by considering the priority queuing system, and risk of unexpected disruptive events. To deal with different sources of uncertainty in the concerned problem, a robust scenario-based stochastic programming approach is employed. To solve the proposed model, a Benders decomposition algorithm enhanced by several accelerating methods is developed. A practical case study is presented to illustrate the applicability of the proposed model as well as the effectiveness of the designed solution procedure.

Designing a Reliable and Dynamic Multimodal Transportation Network for Biofuel Supply Chains

This paper presents a cost-efficient and reliable supply chain network design model for biomass to be delivered to biofuel plants. Biomass is bulky, so transportation modes such as rail and barge can be used to deliver this product. For this reason, this study focuses on multimodal supply chain designs for biofuel. Biomass supply is highly seasonal, but the high production seasons for biomass in the Southeast United States often coincide with or are followed by hurricanes, and drought seasons, both of which impact transportation. The dynamic multimodel transportation network design model this paper presents enables this supply chain to cope with biomass supply fluctuations and to hedge against natural disasters. The mixed-integer nonlinear programming model proposed is an 𝒩𝒫-hard problem, and we develop an accelerated Benders decomposition algorithm and a hybrid rolling horizon algorithm to solve this problem. We tested the performance of the algorithm on a case study using data from the Southeast United States. The numerical experiments show that this proposed algorithm can solve large-scale problem instances to a near optimal solution in a reasonable time. Numerical analyses indicate that, under normal conditions, the minimum cost model outperforms the reliable models. However, under disaster scenarios, the minimum cost model is 2.65% to 9.20% more expensive than the reliable and static model and 6.28% to 17.73% more expensive than the reliable and dynamic model. Thus, the reliable and dynamic multimodal network design decisions can aid biofuel supply chain management decisions, especially when considering the potential impacts of natural disasters.

A Benders based rolling horizon algorithm for a dynamic facility location problem

This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location. To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem. Computational results indicate that the hybrid Benders based rolling horizon algorithm consistently offers high quality feasible solutions in a much shorter computational time period than the stand-alone rolling horizon and accelerated Benders decomposition algorithms in the experimental range.

Analyzing the impact of intermodal-related risk to the design and management of biofuel supply chain

This study presents a mathematical model that designs a reliable multi-modal transportation network for a biofuel supply chain system, where intermodal hubs are subject to site-dependent probabilistic disruptions. The disruption probabilities of intermodal hubs are estimated by using a probabilistic model which is developed using real world data. We developed an accelerated Benders decomposition algorithm to solve this challenging NP-hard problem. Numerical analysis show that the model selects to use intermodal hubs located in areas with low disruption probabilities. In case of a disaster, the reliable solution results in 6.21% savings over the minimum cost solution.

An accelerated Benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain

This paper proposes a multi-objective possibilistic programming model to design a sustainable medical supply chain network under uncertainty considering conflicting economic, environmental and social objectives. Effective social and environmental life cycle assessment-based methods are incorporated in the model to estimate the relevant environmental and social impacts. An accelerated Benders decomposition algorithm utilizing three efficient acceleration mechanisms is devised to cope with computational complexity of solving the proposed model. Computational analysis is also provided by using a medical industrial case study to present the significance of the proposed model as well as the efficiency of the accelerated Benders decomposition algorithm.

The workload balancing problem at aircargo terminals

We consider a large air cargo handling facility composed of two identical cargo terminals. In order to improve the operational efficiency, the workload must be balanced between the terminals. Thus, we must assign each airline served by the facility to one of the terminals such that (ideally): (1) each terminal has the same total workload, and (2) the workload at each terminal is distributed evenly along the timeline. Complicating the problem is that cargo loads are difficult to predict (stochastic). We develop a stochastic mixed integer linear program model in which a weighted sum of the balance measures is minimized. We employ sample average approximation for the stochastic program and develop an accelerated Benders decomposition algorithm to reduce the computational time. The proposed model can also be applied to partially reassign the airlines for the operational schedule changes. The computational results show that a small number of reassignments are often sufficient to rebalance the workload. The simulation results based on data from a large international airport show that the proposed algorithms efficiently balance the workload and the cargo service time is consistently reduced.

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.

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.