E-Commerce Middle-Mile Network Design with Delivery Speed Choices and Service Level Constraints
References
- (2008) E-fulfillment and multi-channel distribution: A review. Eur. J. Oper. Res. 187(2):339–356.Crossref, Google Scholar
- (2021) Carbon Efficient Network Design: Evaluating the Trade-offs Between Carbon Emissions, TransportationCost and Delivery Time for a Middle-Mile Distribution Network (MIT PRESS, Cambridge, MA).Google Scholar
- (2015) The recoverable robust facility location problem. Transportation Research Part B: Methodological . 79:93–120. Crossref, Google Scholar
- Amazon Annual Report (2022) Annual reports, proxies and shareholder letters. Accessed January 12, 2024, https://ir.aboutamazon.com/annual-reports-proxies-and-shareholder-letters/default.aspx.Google Scholar
- (2008) Facility location with stochastic demand and constraints on waiting time. Manufacturing Service Oper. Management 10(3):484–505.Link, Google Scholar
- (2023) Middle-mile optimization for next-day delivery. Preprint, submitted October 27, https://arxiv.org/abs/2310.18388.Google Scholar
- (2024) Survey on Lagrangian relaxation for MILP: Importance, challenges, historical review, recent advancements, and opportunities. Ann. Oper. Res. 333(1):29–45.Crossref, Google Scholar
- (2021) Solving the team orienteering problem with nonidentical agents: A Lagrangian approach. Networks 78(4):443–460.Crossref, Google Scholar
- (2006) Combinatorial benders’ cuts for mixed-integer linear programming. Oper. Res. 54(4):756–766.Link, Google Scholar
- (2019) Benders decomposition for very large scale partial set covering and maximal covering location problems. Eur. J. Oper. Res. 275(3):882–896.Crossref, Google Scholar
- (2016) Multi-period capacitated facility location under delayed demand satisfaction. Eur. J. Oper. Res. 255(3):729–746.Crossref, Google Scholar
- (2013) Fixed Charge Facility Location Problems (John Wiley, Hoboken, NJ).Crossref, Google Scholar
- (2009) A branch-and-cut algorithm for integer bilevel linear programs. Chinneck JW , Kristjansson B , Saltzman MJ , eds. Operations Research and Cyber-Infrastructure (Springer, Berlin), 65–78.Crossref, Google Scholar
- (2023) Logistics performance, ratings, and its impact on customer purchasing behavior and sales in e-commerce platforms. Manufacturing Service Oper. Management 25(3):827–845.Link, Google Scholar
- Feng Y, Caldentey R, Xin L, Zhong Y, Wang B, Hu H (2024) Designing sparse graphs for stochastic matching with an application to middle-mile transportation management. Management Sci. 70(12):8988–9013.Google Scholar
- (2019) Fixed-Charge Facility Location Problems (Springer International Publishing, Cham, Switzerland).Crossref, Google Scholar
- (2017) Redesigning benders decomposition for large-scale facility location. Management Sci. 63(7):2146–2162.Link, Google Scholar
- (1985) An applications oriented guide to Lagrangian relaxation. Interfaces (Providence) 15(2):10–21.Link, Google Scholar
- (2004) The Lagrangian relaxation method for solving integer programming problems. Management Sci. 50(12_supplement):1861–1871.Link, Google Scholar
- (2016) A Lagrangian-based branch-and-bound algorithm for the two-level uncapacitated facility location problem with single-assignment constraints. Transportation Sci. 50(4):1286–1299.Link, Google Scholar
- (2023) Lead-Time-Constrained Middle-Mile Consolidation Network Design with Fixed Origins and Destinations. Transportation Res. Part B: Methodological 174:102782.Crossref, Google Scholar
- (2011) Improved convergent heuristics for the 0-1 multidimensional knapsack problem. Ann. Oper. Res . 183:125–142. Crossref, Google Scholar
- (1998) Solving the uncapacitated network design problem by a lagrangean heuristic and branch-and-bound. Oper. Res. 46(2):247–259.Link, Google Scholar
- (2000) A Lagrangian heuristic based branch-and-bound approach for the capacitated network design problem. Oper. Res. 48(3):461–481.Link, Google Scholar
- (1999) An exact algorithm for the capacitated facility location problems with single sourcing. Eur. J. Oper. Res. 113(3):544–559.Crossref, Google Scholar
- Houston Strategy Forum (2021) Part 3—What is middle mile?—Dr. Scott Mason, Amazon—Supply chain. Accessed June 2, 2024, https://www.youtube.com/watch?v=nzxeX7XTIfc.Google Scholar
- (2017) Facility location under service level constraints for heterogeneous customers. Ann. Oper. Res. 253(1):275–305.Crossref, Google Scholar
- (2023) Multiple allocation hub location with service level constraints for two shipment classes. Eur. J. Oper. Res. 309(2):634–655.Crossref, Google Scholar
- (2011) Product differentiation and operations strategy in a capacitated environment. Eur. J. Oper. Res. 210(3):716–728.Crossref, Google Scholar
- (2002) E-business and supply chain management: An overview and framework. Production Oper. Management 11(4):413–423.Crossref, Google Scholar
- (2005) Facility location models for distribution system design. Eur. J. Oper. Res. 162(1):4–29.Crossref, Google Scholar
- (2019) Location Science (Springer, Berlin).Crossref, Google Scholar
- (2018) Consumer-driven e-commerce: A literature review, design framework, and research agenda on last-mile logistics models. Internat. J. Physical Distribution Logist. Management 48(3):308–332.Crossref, Google Scholar
- (2021) Branch-and-cut approach based on generalized benders decomposition for facility location with limited choice rule. Eur. J. Oper. Res. 293(1):109–119.Crossref, Google Scholar
- (2023) Last-mile strategies for urban freight delivery: A systematic review. Transportation Res. Rec. 2677(1):1141–1156.Crossref, Google Scholar
- (1981) Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Oper. Res. 29(3):464–484.Link, Google Scholar
- (2021) Location problems in supply chain design: Concave costs, probabilistic service levels, and omnichannel distribution. PhD thesis, Concordia University, Montreal, Quebec, CA.Google Scholar
- (2022) Two-level capacitated discrete location with concave costs. Transportation Sci. 56(6):1703–1722.Link, Google Scholar
- (1998) Probabilistic, maximal covering location—Allocation models for congested systems. J. Regulatory Sci. 38(3):401–424.Crossref, Google Scholar
- (2002) Location–allocation of multiple-server service centers with constrained queues or waiting times. Ann. Oper. Res. 111(1-4):35–50. Crossref, Google Scholar
- (1990) Knapsack Problems: Algorithms and Computer Implementations (John Wiley, Hoboken, NJ).Google Scholar
- (1999) Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type. Eur. J. Oper. Res. 115(2):285–299.Crossref, Google Scholar
- (2009) Facility location and supply chain management–A review. Eur. J. Oper. Res. 196(2):401–412.Crossref, Google Scholar
- (2019) Walmart targets automated ‘middle-mile’ delivery to cut shipping costs. Accessed January 25, 2024, https://www.ttnews.com/articles/walmart-targets-automated-middle-mile-delivery-cut-shipping-costs.Google Scholar
- (1998) Strategic facility location: A review. Eur. J. Oper. Res. 111(3):423–447.Crossref, Google Scholar
- (2019) Designing e-commerce supply chains: A stochastic facility: Location approach. Internat. Trans. Oper. Res. 26(2):507–528.Crossref, Google Scholar
- (2018) Disaggregated Benders decomposition and branch-and-cut for solving the budget-constrained dynamic uncapacitated facility location and network design problem. Eur. J. Oper. Res. 270(1):78–88.Crossref, Google Scholar
- (2020) Exact and Heuristic Approaches to Middle and Last Mile Logistics (University of Washington, Seattle, WA). Google Scholar
- (2017) The Benders decomposition algorithm: A literature review. Eur. J. Oper. Res. 259(3):801–817.Crossref, Google Scholar
- (2021) The net environmental impact of online shopping, beyond the substitution bias. J. Transportation Geography . 93:103058 Crossref, Google Scholar
- (2024) Efficient solution approaches for the bi-criteria p-hub median and dispersion problem. Eur. J. Oper. Res. 314(1):79–93.Crossref, Google Scholar
- (2020) The distribution network of Amazon and the footprint of freight digitalization. J. Transportation Geography 88:102825.Crossref, Google Scholar
- (2024) Last mile facilities. Rodrigue JP, ed. The Geography of Transport Systems (Routledge, New York), 337–354.Crossref, Google Scholar
- (2012) Speed-up Benders decomposition using maximum density cut (MDC) generation. Ann. Oper. Res. 210(1):101–123.Crossref, Google Scholar
- (2022) Facility location in logistics and transportation: An enduring relationship. Transportation Res. Part E: Logist. Transportation Rev . 166:102903 Crossref, Google Scholar
- SellersCommerce (2024) Ecommerce statistics: Online shopping trends and data. Accessed May 29, 2025, https://www.sellerscommerce.com/blog/ecommerce-statistics/.Google Scholar
- (2015) Electronic supply chains: Status & perspective. Computers & Indust. Eng . 88:536–556. Crossref, Google Scholar
- Statista (2023) Expected delivery time of online purchases in the U.S.: 2021. Accessed February 14, 2024, https://www.statista.com/statistics/1271829/expected-delivery-time-online-purchases-united-states/#statisticContainer.Google Scholar
- Statista (2024) Global retail e-commerce sales 2014-2027. Accessed May 29, 2025, https://www.statista.com/statistics/379046/worldwide-retail-e-commerce-sales/.Google Scholar
- (2018) Hub network design and discrete location: Economies of scale, reliability and service level considerations. PhD thesis, Concordia University, Montreal, Quebec, CA.Google Scholar
- (2012) An improved benders decomposition algorithm for the logistics facility location problem with capacity expansions. Ann. Oper. Res. 210(1):165–190.Crossref, Google Scholar
- (2021) Alternate solution approaches for competitive hub location problems. Eur. J. Oper. Res. 290(1):68–80.Crossref, Google Scholar
- (2007) Integrated production-inventory-distribution system design with risk pooling: Model formulation and heuristic solution. Transportation Sci. 41(3):392–408.Link, Google Scholar
- (2006) Capacitated facility location problem with general setup cost. Comput. Oper. Res. 33(5):1226–1241.Crossref, Google Scholar
- (2021) An exact algorithm for large-scale non-convex quadratic facility location. Preprint, submitted July 20, https://arxiv.org/abs/2107.09746.Google Scholar

