Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm

Broek, Michiel A. J. uit het; Schrotenboer, Albert H.; Jargalsaikhan, Bolor; Roodbergen, Kees Jan; Coelho, Leandro C.

doi:10.1287/opre.2020.2033

Cited by 9 publications

(5 citation statements)

References 34 publications

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“…Optimal solutions are obtained using the branch-and-cut algorithm (see Section 7). Optimal solutions and LP relaxations are obtained using CPLEX 12.8 and its associated callbacks coded in C++, based on the library provided by Uit het Broek et al (2020).…”

Section: Resultsmentioning

confidence: 99%

“…The literature includes several optimal algorithms for the mTSP (Gavish and Srikanth 1986, Gromicho, Paixão, and Branco 1992, Laporte and Norbert 1980, Svestka and Huckfeldt 1973, Uit het Broek et al 2020) and multiple mathematical formulations (see Sarin et al (2014) for a comparison of 32 formulations.) There are some heuristic solutions for the mTSP, mainly based on partitioning a TSP tour into m subtours (Russell 1977, Potvin, Lapalme, and Rousseau 1989, Frederickson, Hecht, and Kim 1978.…”

Section: Literature Reviewmentioning

confidence: 99%

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A Special Case of the Multiple Traveling Salesmen Problem in End-of-Aisle Picking Systems

Baardman

Roodbergen²,

Carlo

et al. 2021

Transportation Science

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This study focuses on the problem of sequencing requests for an end-of-aisle automated storage and retrieval system in which each retrieved load must be returned to its earlier storage location after a worker has picked some products from the load. At the picking station, a buffer is maintained to absorb any fluctuations in speed between the worker and the storage/retrieval machine. We show that, under conditions, the problem of optimally sequencing the requests in this system with a buffer size of m loads forms a special case of the multiple traveling salesmen problem in which each salesman visits the same number of cities. Several interesting structural properties for the problem are mathematically shown. In addition, a branch-and-cut method and heuristics are proposed. Experimental results show that the proposed simulated annealing-based heuristic performs well in all circumstances and significantly outperforms benchmark heuristics. For instances with negligible picking times for the worker, we show that this heuristic provides solutions that are, on average, within 1.8% from the optimal value.

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Section: Resultsmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

A Special Case of the Multiple Traveling Salesmen Problem in End-of-Aisle Picking Systems

Baardman

Roodbergen²,

Carlo

et al. 2021

Transportation Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…A new set of PE constraints for asymmetric multidepot routing problems has been recently proposed by uit het Broek et al (2021). These inequalities are based on D + k and D − k constraints for the asymmetric traveling salesperson problem (Grötschel and Padberg 1985) and are inherently asymmetric, which is why we do not consider them in the remainder of this article.…”

Section: Depot-consistency Constraintsmentioning

confidence: 99%

“…Recent generic branch-price-and-cut based solution frameworks for vehicle routing problems (Baldacci andMingozzi 2009, Pessoa et al 2020) have also been applied to the MDCVRP and significantly increased the size of instances that can be solved. A parallel stream of papers focuses on the study of inequalities that prevent vehicles from ending their trip at a depot different from their initial one (Belenguer et al 2011;Benavent and Martínez 2013;Santos 2017, 2020;uit het Broek et al 2021). Ensuring the latter aspect is the main additional challenge imposed by multi-depot routing problems compared with their single-depot counterparts.…”

Section: Introductionmentioning

confidence: 99%

Multi-Depot Routing with Split Deliveries: Models and a Branch-and-Cut Algorithm

Gouveia

Leitner

Ruthmair

2023

Transportation Science

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We study the multi-depot split-delivery vehicle routing problem (MDSDVRP) that combines the advantages and potential cost savings of multiple depots and split deliveries and develop the first exact algorithm for this problem. We propose an integer programming formulation using a small number of decision variables and several sets of valid inequalities. These inequalities focus on ensuring the vehicles’ capacity limits and that vehicles return to their initial depot. As we show that the new constraints do not guarantee these aspects, our branch-and-cut framework also includes an efficient feasibility check for candidate solutions and explicit feasibility cuts. The algorithm that also uses a comparably simple, yet effective heuristic to compute high-quality initial solutions is tested on the MDSDVRP and two well-known special cases, the split-delivery vehicle routing problem (SDVRP) and the multi-depot traveling salesman problem (MDTSP). The results show that the new inequalities tighten the linear programming relaxation, increase the performance of the branch-and-cut algorithm, and reduce the number of required feasibility cuts. We report the first proven optimal results for the MDSDVRP and show that our algorithm significantly outperforms the state-of-the-art for the MDTSP while being competitive on the SDVRP. For the latter, 20 instances are solved for the first time, and new best primal and dual bounds are found for others.

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“…Scholars have conducted extensive research on it from different perspectives since the first proposition of this issue was put by Dantizg and Rams in 1959. 1 These scholars are Gutierrez et al, 2 Errico et al, 3 Xuping et al, 4 Yaming et al, 5 Sacramento et al, 6 Belgin et al, 7 Fink et al, 8 Li et al, 9 Xue et al, 10 Timo, 11 Wang et al, 12 Hoogeboom et al 13 Rostami et al, 14 Uit het Broek et al, 15 Hoogeboom et al, 13 Dumez et al, 16 Zhang et al, 17 Pessoa et al, 18 and so on. However, most of these studies consider how to reduce the total cost of distribution from the view of economy.…”

Section: Introductionmentioning

confidence: 99%

Optimization of the Milk-run route for inbound logistics of auto parts under low-carbon economy

Quan

Qiu-hua

et al. 2021

Journal of Algorithms & Computational Technology

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Greenhouse gas emissions have brought serious negative impacts on human beings and organisms, so energy saving and emission reduction have been recognized by more and more people. Traditional Milk-run model seldom considers the factors of energy saving and emission reduction, and its routing optimization cannot meet the current needs of low-carbon economic development. On the basis of traditional Vehicle Routing Problem research, considering the fixed cost, time penalty cost, energy consumption cost and carbon emission cost of vehicles, the Milk-run model of distribution routing considering carbon emissions under time window constraints is studied. Then the improved ant colony algorithm is used to solve the constructed model. Finally, the order and related data of a company are used to verify the validity and practicality of the model and algorithm. Compared to the scanning method, the results show that not only the total journey distance has been shortened but also the total cost and cost of carbon emissions have been reduced. The optimization of distribution routing considering carbon emissions can reduce the distribution cost of logistics enterprises, respond to the call of low-carbon development in China and help to achieve a win-win situation of social and economic benefits.

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Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm

Cited by 9 publications

References 34 publications

A Special Case of the Multiple Traveling Salesmen Problem in End-of-Aisle Picking Systems

A Special Case of the Multiple Traveling Salesmen Problem in End-of-Aisle Picking Systems

Multi-Depot Routing with Split Deliveries: Models and a Branch-and-Cut Algorithm

Optimization of the Milk-run route for inbound logistics of auto parts under low-carbon economy

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