Solving vehicle routing problems with stochastic and correlated travel times and makespan objectives

Bakach, Iurii; Campbell, Ann Melissa; Ehmke, Jan Fabian; Urban, Timothy L.

doi:10.1016/j.ejtl.2021.100029

Cited by 7 publications

(2 citation statements)

References 58 publications

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“…Each leg of the journey is subject to correlated temporal uncertainty as a result of weather factors such as wind speed and direction. In vehicle routing problems correlation has been shown to exist in travel times (Bakach et al 2021), with coefficients as high as 0.75 (Park and Rilett 1999).…”

Section: Introductionmentioning

confidence: 99%

A Column Generation Approach to Correlated Simple Temporal Networks

Murray

Arulselvan

Cashmore

et al. 2023

ICAPS

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Probabilistic Simple Temporal Networks (PSTN) represent scheduling problems under temporal uncertainty. Strong controllability (SC) of PSTNs involves finding a schedule to a PSTN that maximises the probability that all constraints are satisfied (robustness). Previous approaches to this problem assume independence of probabilistic durations, and approximate the risk by bounding it above using Boole’s inequality. This gives no guarantee of finding the schedule optimising robustness, and fails to consider correlations between probabilistic durations that frequently arise in practical applications. In this paper, we formally define the Correlated Simple Temporal Network (Corr-STN) which generalises the PSTN by removing the restriction of independence. We show that the problem of Corr-STN SC is convex for a large class of multivariate (log-concave) distributions. We then introduce an algorithm capable of finding optimal SC schedules to Corr-STNs, using the column generation method. Finally, we validate our approach on a number of Corr-STNs and find that our method offers more robust solutions when compared with prior approaches.

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Section: Introductionmentioning

confidence: 99%

A Column Generation Approach to Correlated Simple Temporal Networks

Murray

Arulselvan

Cashmore

et al. 2023

ICAPS

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“…Those parameters are assumed to follow a normal distribution and the realisations of that assumption have a good outcome. In the routing problem, normal distribution is widely used to estimate the travel time or travel cost(Li, Tian & Leung, 2010;Shen, Xu, Wu & Ni, 2019;Bakach, Campbell, Ehmke & Urban, 2021…”

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confidence: 99%

A simulation-based optimisation for the stochastic green capacitated p-median problem

Imran

Utomo

Ramadhan

et al. 2022

JIEM

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Purpose: This paper aims to propose a new model called the stochastic green capacitated p-median problem with a simulation-based optimisation approach. An integer linear programming mathematical model is built considering the total emission produced by vehicles and the uncertain parameters including the travel cost for a vehicle to travel from a particular facility to a customer and the amount of CO2 emissions produced. We also develop a simulation-based optimisation algorithm for solving the problem.Design/methodology/approach: The authors proposed new algorithms to solve the problem. The proposed algorithm is a hybridisation of Monte Carlo simulation and a Variable Neighbourhood Search matheuristic. The proposed model and method are evaluated using instances that are available in the literature.Findings: Based on the results produced by the computational experiments, the developed approach can obtain interesting results. The obtained results display that the proposed method can solve the problems within a short computational time and the solutions produced have good quality (small deviations).Originality/value: To the best of our knowledge, there is no paper in the previous literature investigating the simulation-based optimisation for the stochastic green capacitated p-median problem. There are two main contributions in this paper. First, to build a new model for the capacitated p-median problem taking into account the environmental impact. Second, to design a simulation-based optimisation approach to solve the stochastic green capacitated p-median problem incorporating VNS-based matheuristic and Monte Carlo simulation.

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