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A bi-objective multi-warehouse multi-period order picking system under uncertainty: a benders decomposition approach

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Soft Computing 2025年第4期29卷 2047-2074页

作者： Nikkhoo, Fatemeh Husseinzadeh Kashan, Ali Nikbakhsh, Ehsan Ostadi, Bakhtiar Faculty of Industrial and Systems Engineering Tarbiat Modares University Tehran Iran

In warehouse management order picking is one of the key operations that incur high costs as well as one of the most complex tasks. It comprises the construction of order batches, batch assignment, picker routes, and scheduling of pickers. Therefore, the development of an efficient order picking system and the optimization of these operations have significant effects on the overall efficiency of the warehouse. This paper focuses on studying and modeling the order batching, batch assignment, and picker routing problems in a multi-warehouse, multi-period, multi-picker order picking system. We propose a multi-objective mathematical model for minimizing the delivery times of batches and the total cost of order picking operations. Also, for the first time, a possibilistic approach is applied to overcome uncertain conditions in the order picking problem. Given the complexity of the problem, benders decomposition is implemented to solve the proposed model. The applicability of the proposed method is evaluated through a range of small to large test problems and an actual case study. The results indicate that the proposed exact method is capable of finding high-quality solutions within a reasonable computational time and number of iterations, which serves as evidence of its suitability for large-scale, complex real-world industrial contexts. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

关键词： benders decomposition algorithm Fuzzy possibilistic programming Multi-period Multi-warehouse Order batching Picker routing

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Designing a resilient hydrogen hub under disruption risks and non-stationary demand distribution

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年第8期63卷 2780-2805页

作者： Asghari, Mohammad Afshari, Hamid Jaber, Mohamad Y. Searcy, Cory Dalhousie Univ Dept Ind Engn Sexton Campus108-5269 Morris StrPOB 15000 Halifax NS B3H 4R2 Canada Toronto Metropolitan Univ Dept Mech Ind & Mechatron Engn Toronto ON Canada Amer Univ Beirut Suliman S Olayan Sch Business Beirut Lebanon Univ Brescia Dept Mech & Ind Engn Energy Transit & Sustainable Prod Syst Brescia Italy

Hydrogen is a viable and sustainable energy alternative. It offers a solution to mitigate greenhouse gases and fortify energy security. However, its supply chain faces many uncertainties and challenges, including demand fluctuations and sourcing disruptions. This paper introduces an innovative two-stage stochastic model to plan hydrogen hub procurement, storage, and sales. In the first stage, the model optimises the order quantities by considering real-time inventory levels. This forward-thinking strategy aims to improve operational efficiency and adaptability. In the second stage, the model refines the hub operations by incorporating supplier resilience, exploration of alternative markets, emission considerations from each source, and terminal connection planning. Integrating these elements contributes to a comprehensive framework for robust hydrogen hub scheduling. This paper adopts a benders decomposition algorithm to address the mathematical complexity of the model. This approach is necessary to ensure a smooth and efficient computational process. Empirical testing and validation of the developed model, along with the robustness of the solution methodology, emphasise its effectiveness in handling uncertainties and disruptions. This paper contributes to the existing literature by shedding light on critical facets of disruption management, supplier resilience, and emissions reduction within the hydrogen supply chain design.

关键词： Operation research in energy affordable and clean energy resilient hydrogen hub planning non-stationary demand disruption management benders decomposition algorithm

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Modeling and optimizing an agro-supply chain considering different quality grades and storage systems for fresh products: a benders decomposition solution approach

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2022年第1期44卷 21-50页

作者： Keshavarz-Ghorbani, Fatemeh Pasandideh, Seyed Hamid Reza Kharazmi Univ Fac Engn Dept Ind Engn Tehran Iran

This paper proposes a mathematical model in the context of agro-supply chain management, considering specific characteristics of agro-products to assist purchase, storage, and transportation decisions. In addition, a new method for determining the required quality score of different types of products is proposed based on their loss factors and purchasing costs. The model aims to minimize total cost imposed by purchasing fresh products, opening warehouses, holding inventories, operational activities, and transportation. Two sets of examples, including small and medium-sized problems, are implemented by general algebraic modeling language (GAMS) software to evaluate the model. Then, benders decomposition (BD) algorithm is applied to tackle the complexity of solving large-sized instances. The results of both GAMS and BD are compared in terms of objective function values and computational time to demonstrate the efficiency of the BD algorithm. Finally, the model is applied in a real case study involving an apple supply chain to obtain managerial insights.

关键词： Agro-supply chain Quality score benders decomposition algorithm Inventory management

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A benders decomposition approach for order acceptance and scheduling problem: a robust optimization approach

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COMPUTATIONAL & APPLIED MATHEMATICS 2017年第4期36卷 1471-1515页

作者： Emami, Saeed Moslehi, Ghasem Sabbagh, Mohammad Isfahan Univ Technol Dept Ind & Syst Engn Esfahan *** Iran

In this paper, we consider a simultaneous order acceptance and scheduling problem in a non-identical parallel machines environment. The orders are defined by their due dates, revenues, tardiness penalties, different processing times on the machines, and sequence-dependent setup times. We present an MILP formulation to maximize the profit. Furthermore, we assume that the revenue from an accepted order and the processing times are uncertain and accordingly, develop the robust counterpart of the proposed MILP model. The problem is computationally intractable;therefore, we develop a benders decomposition approach to solve it. We introduce some valid cuts to accelerate the convergence of the classical benders algorithm and a heuristic method to obtain the feasible solutions. Through numerical experiments on randomly generated large instances with up to 40 orders and 6 machines, we demonstrate that the proposed benders decomposition approach outperforms the MILP model.

关键词： Order acceptance and scheduling Non-identical parallel machines Robust optimization benders decomposition algorithm

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benders decomposition approach with heuristic improvements for the robust foodgrain supply network design problem

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2020年第1期71卷 16-36页

作者： Tanksale, Ajinkya Jha, Jitendra K. Indian Inst Technol Kharagpur Dept Ind & Syst Engn Kharagpur W Bengal India

We investigate the problem of designing a supply chain for foodgrains distribution under uncertainty, which is motivated from the Indian public distribution system (PDS). Initially, a deterministic mixed-integer programming (MIP) model is formulated to determine the strategic decisions of storage and transportation capacity hiring and the tactical decisions of procurement, inventory, and transportation planning to minimise the total cost over a finite planning horizon. The storage capacity hiring decision is characterised by the options of hiring under long-term contract for the entire planning horizon and from spot market for individual period. Next, we extend the model to consider the uncertainties associated with supply, demand and procurement parameters, and propose a scenario-based robust optimisation model to minimum the total relative regret. An MIP-based fix-and-optimise heuristic is proposed to efficiently solve the deterministic equivalent problem of each scenario. To solve the robust model, we implement benders decomposition algorithm (BDA) with several heuristic techniques including warm-start strategy to build an initial feasible solution, trust region for master problem, and logical inequalities to accelerate the performance of the BDA. Finally, the effectiveness of the solution approach is demonstrated through extensive computational experiments using the test instances simulating the Indian PDS.

关键词： Foodgrain supply chain network design robust optimisation benders decomposition algorithm fix-and-optimise

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A heuristic-based benders decomposition for the hybrid relief distribution network minimizing deprivation cost of vulnerable areas

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KYBERNETES 2024年

作者： Rahimi, Sanaz Khalaj Rahmani, Donya KN Toosi Univ Technol Fac Ind Engn Dept Ind Engn Tehran Iran

PurposeThe study aims to optimize truck routes by minimizing social and economic costs. It introduces a strategy involving diverse drones and their potential for reusing at DNs based on flight range. In HTDRP-DC, trucks can select and transport various drones to LDs to reduce deprivation time. This study estimates the nonlinear deprivation cost function using a linear two-piece-wise function, leading to MILP formulations. A heuristic-based benders decomposition approach is implemented to address medium and large instances. Valid inequalities and a heuristic method enhance convergence boundaries, ensuring an efficient solution ***/methodology/approachResearch has yet to address critical factors in disaster logistics: minimizing the social and economic costs simultaneously and using drones in relief distribution;deprivation as a social cost measures the human suffering from a shortage of relief supplies. The proposed hybrid truck-drone routing problem minimizing deprivation cost (HTDRP-DC) involves distributing relief supplies to dispersed demand nodes with undamaged (LDs) or damaged (DNs) access roads, utilizing multiple trucks and diverse drones. A benders decomposition approach is enhanced by accelerating *** deprivation and economic costs results in selecting optimal routes, effectively reducing the time required to assist affected areas. Additionally, employing various drone types and their reuse in damaged nodes reduces deprivation time and associated deprivation costs. The study employs valid inequalities and the heuristic method to solve the master problem, substantially reducing computational time and iterations compared to GAMS and classical benders decomposition algorithm. The proposed heuristic-based benders decomposition approach is applied to a disaster in Tehran, demonstrating efficient solutions for the HTDRP-DC regarding computational time and convergence ***/valueCurrent research introduces an

关键词： Hybrid truck-drone routing problem benders decomposition algorithm Heuristics algorithm Post-disaster condition Valid inequality Deprivation cost

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A data-driven mathematical model to design a responsive-sustainable pharmaceutical supply chain network: a benders decomposition approach

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ANNALS OF OPERATIONS RESEARCH 2023年 1-42页

作者： Rekabi, Shabnam Goodarzian, Fariba Garjan, Hossein Shokri Zare, Fatemeh Munuzuri, Jesus Ali, Irfan Univ Tehran Coll Engn Sch Ind Engn Tehran Iran Univ Seville Sch Engn Engn Grp Camino Descubrimientos S-N Seville 41092 Spain Babol Noshirvani Univ Technol Dept Ind Engn Babol Iran Amirkabir Univ Technol Dept Ind Engn Tehran Iran Aligarh Muslim Univ Dept Stat & Operat Res Aligarh 202002 India

The pharmaceutical supply chain is unique to other supply chains due to certain characteristics. Medicine is classified as a valuable asset, and any minor disruption in its supply chain can result in significant crises. So, this work develops a novel multi-objective model to configure a responsive sustainable pharmaceutical supply chain network by considering Cap-and-Trade policy, different manufacturing technologies selections, and different transportation modes selections. The model seeks to minimize the overall costs, environmental harms, and travel times for dissatisfied clients, whose requests must be answered by distribution centers constructed in other locations to maximize the chain's responsiveness. This study is highly beneficial in practical applications where finding the optimal location of nodes that satisfy multiple constraints is critical. Moreover, it increases the efficiency of resource allocation, reduces travel time and cost, and determines the optimal flow of products between nodes. Furthermore, time series-based machine learning algorithms are conducted to forecast the demand for medicine to decrease the possibility of a shortage of pharma supply in the supply chain network. By examining several methods, it is revealed that the Prophet model has superior performance to other models. So, this method is utilized to forecast demand. The goal attainment method is first used to solve small problem instances to meet the suggested model. However, this method was inefficient for solving large-sized examples. As a result, Bender's decomposition solution approach is used. The presented decision model's efficacy is evaluated against a real-life case study. Moreover, a sensitivity analysis is done on important parameters to offer insightful managerial information. The sensitivity analysis results show that the third objective function (which represents overall travel times for unmet clients) increases as demand rises. This indicates that unsatisfied demand

关键词： benders decomposition algorithm Cap-and-trade policy Pharmaceutical supply chain Perishability Sustainability Time-series prediction

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Solving the integrated bin allocation and collection routing problem for municipal solid waste: a benders decomposition approach

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ANNALS OF OPERATIONS RESEARCH 2023年第1期322卷 441-465页

作者： Maheo, Arthur Rossit, Diego Gabriel Kilby, Philip Monash Univ Fac IT Melbourne Vic Australia Univ Nacl Sur UNS CONICET Dept Engn INMABB Bahia Blanca Buenos Aires Argentina Australian Natl Univ Canberra ACT Australia

The municipal solid waste system is a complex reverse logistic chain which comprises several optimisation problems. Although these problems are interdependent-i.e., the solution to one of the problems restricts the solution to the other-they are usually solved sequentially in the related literature because each is usually a computationally complex problem. We address two of the tactical planning problems in this chain by means of a benders decomposition approach: determining the location and/or capacity of garbage accumulation points, and the design and schedule of collection routes for vehicles. Our approach manages to solve medium-sized real-world instances in the city of Bahia Blanca, Argentina, showing smaller computing times than solving a full MIP model.

关键词： Municipal solid waste Reverse supply chain Integrated allocation-routing problem benders decomposition algorithm Valid inequalities Mixed integer programming

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Sustainable supplier selection and order allocation: A novel multi-objective programming model with a hybrid solution approach

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 129卷 192-209页

作者： Moheb-Alizadeh, Hadi Handfield, Robert North Carolina State Univ Grad Program Operat Res Raleigh NC 27695 USA North Carolina State Univ Dept Business Management Coll Management Raleigh NC 27695 USA

Sustainable supplier selection is the process of identifying the appropriate supply partners of an organization with the most beneficial monetary value, while diminishing the various effects of its operations on society and environment. Therefore, it plays a significant role in moving an organization toward sustainable development. Alongside sustainable supplier selection, assigning proper quantity of orders to suppliers satisfying sustainability criteria is another activity that should be simultaneously carried out in order to develop a comprehensive tool in sustainable supplier management. Meanwhile, the issue of sustainable supplier selection and order allocation has attracted limited attention in the literature. The present paper aims at developing an inclusive multi-objective mixed integer linear programming model, which accounts for multiple periods, multiple products and multimodal transportation, to evaluate suppliers and allocate order quantities. Furthermore, the developed model that includes all sustainability aspects also takes both shortage and discount conditions into account. A hybrid three-step solution methodology is then presented, using which the original multi-objective problem is firstly converted to a single objective model by epsilon-constraint method. In the second step, the current single objective programming model is solved using the benders decomposition algorithm that in turn is accelerated by a variety of algorithmic enhancements. Finally, among all the Pareto optimal solutions of the original multi-objective programming problem, the preferable solution is intelligently selected based on the DEA super efficiency score of all purchasing firms as a decision support tool. The applicability of the proposed approach is illustrated by a real-world case study in automotive industry.

关键词： Supplier selection Order allocation Sustainability epsilon-constraint method benders decomposition algorithm Data envelopment analysis

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Adjustable robust balanced hub location problem with uncertain transportation cost

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COMPUTATIONAL & APPLIED MATHEMATICS 2021年第1期40卷 1-28页

作者： Rahmati, Reza Neghabi, Hossein Ferdowsi Univ Mashhad Dept Ind Engn Mashhad Razavi Khorasan Iran

In this paper, an adjustable robust optimization with a polyhedral uncertainty set is used to deal with uncertain transportation cost in an uncapacitated multiple allocation balanced hub location problem. Adjustable robust optimization is modeled as two-stage or multi-stage problems in which decisions are determined in two or multi-separated stages. In two-stage robust optimization, first, the location of hubs is determined in the absence of uncertain parameters;then, the second-stage decision determined flows path in the presence of uncertainty. Two new mathematical models are proposed for this problem with mixed-integer linear and non-linear structures. benders decomposition algorithm with stronger cut (Pareto-optimal cut) is used to solve proposed models. Adjustable robust models and accelerated benders decomposition algorithms are analyzed using well-known AP data set with different levels of uncertainty. Also, a size reduction method is introduced to solve medium and large instances with good solution quality and shorter computation time. The numerical experiment shows the superiority of the Pareto-optimal cut benders decomposition algorithm comparing with a classic one. Also, the mixed-integer non-linear model has better results in CPU time and the gap in comparison with the linear integer one. Flow balancing affects hub configuration with a decreasing number of hub facilities. Also by increasing the uncertainty budget, more hubs are established and with increasing discount factor, number of hub facilities are decreased.

关键词： Balanced hub location benders decomposition algorithm Adjustable robust optimization Uncertain transportation cost Pareto-optimal cut

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