Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

Kou, Shuhan; Golden, Bruce L.; Poikonen, Stefan

doi:10.1111/itor.13260

Cited by 3 publications

(1 citation statement)

References 23 publications

(50 reference statements)

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“…The VRP, first introduced by Dantzig and Ramser (1959), has been extended to abundant variants due to enormous different practical distribution scenarios (Kou et al., 2023). In recent years, exact algorithms for the VRP have received a good amount of research attention and are able to solve the instances with up to 200 customers, such as the branch‐and‐cut algorithms and branch‐and‐price algorithms (Baldacci et al., 2011; Pecin et al., 2017; Costa et al., 2019).…”

Section: Introductionmentioning

confidence: 99%

A branch‐and‐price‐based heuristic for the vehicle routing problem with two‐dimensional loading constraints and time windows

Ji,

Zhou,

Zhang

et al. 2023

Int Trans Operational Res

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Addressed in this study is a vehicle routing problem with two‐dimensional loading constraints and time windows (2L‐CVRPTW), aiming to minimize the transportation cost while satisfying the two‐dimensional loading and routing constraints with time windows. To solve this problem, for the first time a mixed‐integer linear programming model is formulated with considering practical last‐in‐first‐out loading constraints, and a branch‐and‐price‐based (BP‐based) heuristic is proposed based on a set partitioning formulation. In the heuristic, a modified labeling algorithm is proposed for the complex pricing problem, which is a relaxation of the elementary shortest path problem with resource constraints and two‐dimensional loading constraints. Therein, an effective Tabu‐maximum open space packing heuristic is proposed to verify the feasibility of the two‐dimensional packing problem of each route generated by the labeling algorithm. In addition, effective accelerating and branching strategies are introduced to improve the solving efficiency of the heuristic. To evaluate the effectiveness and the advantages of the proposed heuristic, extensive computational experiments are performed based on the generated instances. The computational results show that the proposed BP‐based heuristic can effectively solve the 2L‐CVRPTW, in which the optimal solutions can be achieved much faster than CPLEX in small‐scale problems. Relationships between the transportation cost and the characteristics of the instances are analyzed. The stability of the algorithm and the effectiveness of the accelerating strategies are verified and discussed.

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Section: Introductionmentioning

confidence: 99%

A branch‐and‐price‐based heuristic for the vehicle routing problem with two‐dimensional loading constraints and time windows

Ji,

Zhou,

Zhang

et al. 2023

Int Trans Operational Res

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An improved model for estimating optimal VRP solution values

Kou,

Golden,

Bertazzi

2023

Optim Lett

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Analysis of Real-Time Order Fulfillment Policies: When to Dispatch a Batch?

Gautam,

Geunes

2023

Service Science

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This paper considers orders that arrive one-by-one over time to a fulfillment center. Each order requests a product with some degree of customization that needs to be delivered expeditiously to a nearby location using a delivery vehicle. However, each vehicle can batch multiple orders together for delivery within a single trip. The benefits of batching include more efficient capacity utilization, lower total vehicle ownership requirements, and reduced environmental impact. The main drawback of batching is the consequent reduced average quality of service due to associated delivery delays when waiting for additional orders to arrive and executing a delivery route. To address this trade-off, we consider a set of threshold policies for batching and dispatching groups of orders, and characterize the associated long-run average cost per unit time for each policy that explicitly accounts for the customer’s total order lead time, including the time between order dispatch and delivery to the customer which, in turn, depends on route sequencing policies. For the threshold policies, our state variable may not only include the number of outstanding orders, but may also incorporate information on order arrival times and delivery locations. We model the stochastic dynamics of the system and obtain the long-run average cost per unit time, which we compute using a renewal-reward approach. We also consider different delivery sequencing approaches, including first-come, first-served and shortest traveling salesperson. In addition, we evaluate the effectiveness of accounting for all order information in the decision-making process, as opposed to just the number of outstanding orders or the time in the system for each order. Our analysis shows that a generalized class of cost- and quantity-based threshold policies often outperforms existing policies in the literature with the additional benefits of being robust to overestimates of the optimal cost threshold value and achieving strong delay cost performance. History: This paper has been accepted for the Service Science/Stochastic Systems Joint Special Issue. Supplemental Material: The online appendix is available at https://doi.org/10.1287/serv.2022.0042 .

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Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

Cited by 3 publications

References 23 publications

A branch‐and‐price‐based heuristic for the vehicle routing problem with two‐dimensional loading constraints and time windows

A branch‐and‐price‐based heuristic for the vehicle routing problem with two‐dimensional loading constraints and time windows

An improved model for estimating optimal VRP solution values

Analysis of Real-Time Order Fulfillment Policies: When to Dispatch a Batch?

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