Heuristics for unequal weight delivery problems with a fixed error guarantee

Altınkemer, Kemal; Gavish, Bezalel

doi:10.1016/0167-6377(87)90012-5

Cited by 71 publications

(65 citation statements)

References 12 publications

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“…The main result of this section is the lower bound given in Theorem 1 which improves the lower bound given by Haimovich and Rinnooy Kan [13]. In the next sections, we make use of this bound to improve the approximation ratio of the algorithms for SDVRP and CVRP by Altinkemer and Gavish [3] and [2] respectively.…”

Section: Lower Bounds On the Optimal Cost Of The Vrpmentioning

confidence: 79%

“…2. We improve the approximation results of Altinkemer and Gavish [3,2] for the VRP with triangle inequality, with and without split deliveries. This improvement, though slight, does resolve a long standing open question of whether any improvement was possible.…”

Section: Capacitated Routing Problemsmentioning

confidence: 85%

“…Based on this bound, they derived approximation results. Subsequent papers (e.g., Altinkemer and Gavish [3,2], Li and Simchi-Levi [15]) rely on this bound to improve or generalize approximation results for the VRP. The primary contributions of this paper are as follows:…”

Section: Capacitated Routing Problemsmentioning

confidence: 95%

“…When the nodes are points on the plane and the travel cost is the Euclidean distance, α can be 1 + for any > 0 (see Arora [4] or Mitchell [16]). When customers have unequal demand and split deliveries are not allowed (CVRP), the unequal-weight iterated tour partitioning (UITP) heuristic by Altinkemer and Gavish [2] is a 2 + (1 − 2 Q )α approximation algorithm assuming that Q is even and an α-optimal traveling salesman tour is part of the input. The survey by Haimovich and Rinnooy Kan [14] analyzes these algorithms from a worst case and from a probabilistic perspective.…”

Section: Capacitated Routing Problemsmentioning

confidence: 99%

See 3 more Smart Citations

Improved bounds for vehicle routing solutions

Bompadre

Dror

Orlin

2006

Discrete Optimization

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Section: Lower Bounds On the Optimal Cost Of The Vrpmentioning

confidence: 79%

Section: Capacitated Routing Problemsmentioning

confidence: 85%

Section: Capacitated Routing Problemsmentioning

confidence: 95%

Section: Capacitated Routing Problemsmentioning

confidence: 99%

See 2 more Smart Citations

Improved bounds for vehicle routing solutions

Bompadre

Dror

Orlin

2006

Discrete Optimization

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“…If we assume that each DC may be visited only once, then S 2 can be solved in strongly polynomial time by a straight forward extension from the known Optimal Partitioning Procedure (Beasley, 1983;Altinkemer and Gavish, 1987;Li and Simchi-Levi, 1990). For the completeness of the paper, we present this Extended Optimal Partitioning (EOP) procedure as follows:…”

Section: DCmentioning

confidence: 99%

On the integrated production, inventory, and distribution routing problem

Liu²,

et al. 2006

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Abstract. The integrated production, inventory and distribution routing problem (PDRP) isconcerned with coordinating the production, inventory and delivery operations to meet customer demand with an objective to minimize the cost. The particular PDRP that we consider in this study also involves heterogeneous transporters with non-instantaneous traveling times and many customer demand centers each with its own inventory capacities. Optimally solving such an integrated problem is in general not easy due to its combinatorial nature, especially when transporter routing is involved.In this paper, we propose a two-phase solution approach to this problem. Phase I solves a mixed integer programming model which includes all the constraints in the original model except the transporter routings are restricted to direct shipment between facilities and customer demand centers. The resulting optimal solution to the Phase I problem is always feasible to the original model. Phase II solves an associated consolidation problem to handle the potential inefficiency of direct shipment. The delivery consolidation problem is formulated as a capacitated transportation problem with additional constraints and is solved by an efficient heuristic routing algorithm. The main advantage of this proposed approach, over the classical decoupled approach, is its ability to simultaneously optimize the production, inventory and transportation operations (subject to restricted routing/direct shipments) without the needs for aggregating the demand and relaxing the constraints on transportation capacities. We evaluate the performance of this proposed two-phase approach and report its application to a real-life supply network which motivated this study.

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Split delivery routing

Dror

Trudeau

1990

Naval Research Logistics

237

124

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This article examines a relaxed version of the generic vehicle routing problem. In this version, a delivery to a demand point can be split between any number of vehicles. In spite of this relaxation the problem remains computationally hard. Since only small instances of the vehicle routing problem are known to be solved using exact methods, the vehicle route construction for this problem version is approached using heuristic rules. The main contribution of this article to the existing body of literature on vehicle routing issues in (a) is presenting a new vehicle routing problem amenable to practical applications, and (b) demonstrating the potential for cost savings over similar "traditional" vehicle routing when implementing the model and solutions presented here. The solution scheme allowing for split deliveries is compared with a solution in which no split deliveries are allowed. The comparison is conducted on six sets of 30 problems each for problems of size 75, 115, and 150 demand points (all together 540 problems). For very small demands (up to 10% of vehicle's capacity) no significant difference in solutions is evident for both solution schemes. For the other five problem sets for which point demand exceeds 10% of vehicle's capacity, very significant cost savings are realized when allowing split deliveries. The savings are significant both in the total distance and the number of vehicles required. The vehicles' routes constructed by our procedure tend to cover cohesive geographical zones and retain some properties of optimal solutions.

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Heuristics for unequal weight delivery problems with a fixed error guarantee

Cited by 71 publications

References 12 publications

Improved bounds for vehicle routing solutions

Improved bounds for vehicle routing solutions

On the integrated production, inventory, and distribution routing problem

Split delivery routing

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