A note on determining operating strategies for probabilistic vehicle routing

Yee, J.R.; Golden, Bruce L.

doi:10.1002/nav.3800270114

Cited by 26 publications

(14 citation statements)

References 2 publications

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“…Bastian and Rinnooy Kan 1992 show that with one vehicle and independent identically distributed loads, SVRP could be reduced to the time-dependent traveling salesman problem (TDTSP) (Garfinkel 1985). Work in this direction was also done in papers such as Tillman 1969, Dror and Trudeau 1986, Yee and Golden 1980, Bertsimas 1992, and Dror et al 1989. Researchers have further considered the case in which travel times between jobs are random.…”

Section: Introductionmentioning

confidence: 99%

Real-Time Multivehicle Truckload Pickup and Delivery Problems

Yang

Jaillet

Mahmassani

2004

Transportation Science

246

163

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In this paper we formally introduce a generic real-time multi-vehicle truckload pick-up and delivery problem. The problem includes the consideration of various costs associated with trucks' empty travel distances, jobs' delayed completion times, and job rejections. Although very simple, the problem captures most features of the operational problem of a real-world trucking fleet that dynamically moves truckloads between different sites according to customer requests that arrive continuously over time.We propose a mixed integer programming formulation for the off-line version of the problem. We then consider and compare five rolling horizon strategies for the real-time version. Two of the policies are based on a repeated reoptimization of various instances of the off-line problem, while the others use simpler local (heuristic) rules. One of the re-optimization strategies is new while the other strategies have recently been tested for similar real-time fleet management problems.The comparison of the policies is done under a general simulation framework. The analysis is systematic and consider varying traffic intensities, varying degrees of advance information, and varying degrees of flexibility for job rejection decisions. The new re-optimization policy is shown to systematically outperform the others under all these conditions.

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Section: Introductionmentioning

confidence: 99%

Real-Time Multivehicle Truckload Pickup and Delivery Problems

Yang

Jaillet

Mahmassani

2004

Transportation Science

246

163

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“…The simple detour-to-depot policy, first stated in Dror et al (1989), allows replenishment only when the remaining quantity in the vehicle is not sufficient to serve the current customer, an event known as stockout, or route failure. On the other hand, the optimal policy prescribes replenishments in an optimal way, and can be computed with the stochastic dynamic programming algorithm from Yee and Golden (1980). In optimal restocking, preventive replenishment can be performed to avoid route failures on customers located far from the depot.…”

Section: Related Literaturementioning

confidence: 99%

“…We assume the restocking decisions are made optimally. Therefore, the expected cost of a route can be calculated with the stochastic dynamic programming algorithm from Yee and Golden (1980). The version of the algorithm we present below allows unbounded demands, i.e., for some customer v i and some d > Q, it is possible that p Di (d) > 0.…”

Section: Extended Formulationmentioning

confidence: 99%

“…Therefore, after every visit a decision has to be made: whether or not to replenish before visiting the next customer in the route. It is well-known that, given an a priori route, optimal restocking decisions can be computed with a stochastic dynamic programming algorithm (Yee and Golden 1980). We consider the VRPSD under optimal restocking, which calls for the identification of a set of a priori routes visiting all customers with minimum total expected cost, considering that restocking decisions are always optimal.…”

Section: Introductionmentioning

confidence: 99%

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New Exact Algorithm and Solution Properties for the Vehicle Routing Problem with Stochastic Demands

Florio,

Hartl,

Minner

2018

Preprint

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This paper considers the vehicle routing problem with stochastic demands (VRPSD) under optimal restocking. We develop an exact algorithm that is effective for solving instances with many vehicles and few customers per route. In our experiments, we show that in these instances solving the stochastic problem is most relevant (i.e., the potential gains over the deterministic equivalent solution are highest). The proposed branch-price-and-cut algorithm relies on an efficient labeling procedure, exact and heuristic dominance rules, and completion bounds to price profitable columns. Instances with up to 76 nodes could be solved in less than 5 hours, and instances with up to 148 nodes could be solved in long-runs of the algorithm. The experiments also allowed new findings on the problem. Solving the stochastic problem leads to solutions up to 10% superior to the deterministic equivalent solution. When the number of routes is not fixed, the optimal solutions under detour-to-depot and optimal restocking are nearly equivalent. Opening new routes is a good strategy to reduce restocking costs, and in many cases results in solutions with less transportation costs. For the first time, scenarios where the expected demand in a route is allowed to exceed the capacity of the vehicle were also tested, and the results indicate that superior solutions with lower cost and fewer routes exist.

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“…Typically, these rules prescribe replenishment trips to the depot, and in these cases the recourse corresponds to a restocking policy. Traditional restocking policies include the detour-to-depot, or classical, policy (Dror et al 1989), and the optimal restocking policy (Yee & Golden 1980).…”

Section: Introductionmentioning

confidence: 99%

Vehicle Routing with Stochastic Demands and Partial Reoptimization

Florio,

Feillet,

Poggi

et al. 2022

Preprint

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We consider the vehicle routing problem with stochastic demands (VRPSD), a problem in which customer demands are known in distribution at the route planning stage and revealed during route execution upon arrival at each customer. A long-standing open question on the VRPSD concerns the benefits of allowing, during route execution, partial reordering of the planned customer visits. Given the practical importance of this question and the growing interest on the VRPSD under optimal restocking, we study the VRPSD under a recourse policy known as the switch policy. The switch policy is a canonical reoptimization policy that permits only pairs of successive customers to be reordered. We consider this policy jointly with optimal preventive restocking and introduce a branch-cut-and-price algorithm to compute optimal a priori routing plans in this context. At its core, this algorithm features pricing routines where value functions represent the expected cost-to-go along planned routes for all possible states and reordering decisions. To ensure pricing tractability, we adopt a strategy that combines elementary pricing with completion bounds of varying complexity, and solve the pricing problem without relying on dominance rules. Our numerical experiments demonstrate the effectiveness of the algorithm for solving instances with up to 50 customers. Notably, they also give us new insights into the value of reoptimization. The switch policy enables significant cost savings over optimal restocking when the planned routes come from an algorithm built on a deterministic approximation of the data, an important scenario given the difficulty of finding optimal VRPSD solutions. The benefits are smaller when comparing optimal a priori VRPSD solutions obtained for both recourse policies.As it appears, further cost savings may require joint reordering and reassignment of customer visits among vehicles when the context permits.

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A note on determining operating strategies for probabilistic vehicle routing

Cited by 26 publications

References 2 publications

Real-Time Multivehicle Truckload Pickup and Delivery Problems

Real-Time Multivehicle Truckload Pickup and Delivery Problems

New Exact Algorithm and Solution Properties for the Vehicle Routing Problem with Stochastic Demands

Vehicle Routing with Stochastic Demands and Partial Reoptimization

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