Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns

Tatarakis, Antonios; Minis, Ioannis

doi:10.1016/j.ejor.2008.07.006

Cited by 31 publications

(19 citation statements)

References 17 publications

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“…. , N − 1} a similar threshold-type structural result as the one presented in Tatarakis and Minis [15] for any positive integer K and (ii) to prove for each customer j ∈ {1, . .…”

Section: Introductionmentioning

confidence: 77%

Single Vehicle Routing Problems With a Predefined Customer Order, Unified Load and Stochastic Discrete Demands

Pandelis

Karamatsoukis

Kyriakidis

2012

Prob. Eng. Inf. Sci.

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We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers that are served according to a particular order. It is assumed that the demands of the customers for each product are discrete random variables, and the total demand of each customer for all products cannot exceed the vehicle capacity. The joint probability mass function of the demands of each customer is known. It is assumed that all products are stored together in the vehicle's single compartment. The policy that serves all customers with the minimum total expected cost is found by implementing a suitable dynamic programming algorithm. We prove that this policy has a specific threshold-type structure. Furthermore, we study a corresponding infinite-time horizon problem in which the service of the customers is not completed when the last customer has been serviced but it continues periodically with the same customer order. The demands of each customer for the products have the same distributions at different periods. The discounted cost optimal policy and the average-cost optimal policy have the same structure as the optimal policy in the finite-horizon problem. Numerical results are given that illustrate the structural results.

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“…. , N − 1} a similar threshold-type structural result as the one presented in Tatarakis and Minis [15] for any positive integer K and (ii) to prove for each customer j ∈ {1, . .…”

Section: Introductionmentioning

confidence: 77%

Single Vehicle Routing Problems With a Predefined Customer Order, Unified Load and Stochastic Discrete Demands

Pandelis

Karamatsoukis

Kyriakidis

2012

Prob. Eng. Inf. Sci.

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“…The restocking policies of Pandelis et al (2012) and Tatarakis and Minis (2009) are a relaxation of the a priori policies we consider, which do not permit preemptive capacity replenishment prior to route failures. In contrast to the work of Pandelis et al (2012) and Tatarakis and Minis (2009), which assumes a fixed delivery sequence, we search the space of a priori delivery sequences seeking lower-cost a priori policies.…”

Section: Related Literaturementioning

confidence: 99%

“…Demonstrating a threshold-type structure on the optimal policy for any integer number of vehicle compartments, Pandelis et al (2012) generalize the work of Tatarakis and Minis (2009), which applies to only two compartments. The restocking policies of Pandelis et al (2012) and Tatarakis and Minis (2009) are a relaxation of the a priori policies we consider, which do not permit preemptive capacity replenishment prior to route failures. In contrast to the work of Pandelis et al (2012) and Tatarakis and Minis (2009), which assumes a fixed delivery sequence, we search the space of a priori delivery sequences seeking lower-cost a priori policies.…”

Section: Related Literaturementioning

confidence: 99%

A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands

Goodson

2015

European Journal of Operational Research

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“…Tatarakis and Minis [66] proposed two dynamic programming models to compute the Downloaded 12/15/14 to 132.236.27.111. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php expected cost of a fixed route for the multiple product VRPSD.…”

Section: Stochastic Demandsmentioning

confidence: 99%

Chapter 8: Stochastic Vehicle Routing Problems

Gendreau¹,

Jabali²,

Rei³

2014

Vehicle Routing

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Vehicle routing problems (VRPs) have been the subject of numerous research studies since Dantzig and Ramser [16] first presented this general class of optimization problems in a practical setting. Since then, the operations research community has devoted collectively a large effort towards efficiently solving these problems, developing both exact and heuristic methods; see Laporte [40]. The majority of these studies have been conducted under the assumption that all the information necessary to formulate the problems is known and readily available (i.e., one is in a deterministic setting). In practical applications, this assumption is usually not verified given the presence of uncertainty affecting the parameters of the problem. Uncertainty may come from different sources, both from expected variations and unexpected events. Such variations can affect various aspects of the problem under study (e.g., stochastic parameters, which entail additional feasibility requirements and extra costs). This is particularly true in the case of VRP models, which are used both at the tactical level and at the operational level to plan and control logistical operations. In this case, uncertainty is present given the time lag separating the moments where routes are planned and executed, considering the informational flow that defines the problem. For example, if customer demands are uncertain and only revealed when customers are visited, a planned route performed by a vehicle on a given day may turn out to be infeasible if the total observed demand for the customers scheduled on the route exceeds the capacity of the vehicle. When such a situation occurs, additional costs often involving additional decisions must be taken to produce a feasible solution. The need to account for such extra costs when solving VRPs entails developing models that explicitly factor in all relevant uncertainty features of the problem.Therefore, in recent years, there has been a steadily growing interest in both formulating and solving Stochastic Vehicle Routing Problems (SVRPs); see the surveys of Gendreau, Laporte, and Séguin [25] and Cordeau et al. [15]. This interest has been further

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Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns

Cited by 31 publications

References 17 publications

Single Vehicle Routing Problems With a Predefined Customer Order, Unified Load and Stochastic Discrete Demands

Single Vehicle Routing Problems With a Predefined Customer Order, Unified Load and Stochastic Discrete Demands

A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands

Chapter 8: Stochastic Vehicle Routing Problems

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