Lagrangian heuristic for a class of the generalized assignment problems

Litvinchev, Igor; Mata, M.; Rangel, Socorro; Saucedo, Jania

doi:10.1016/j.camwa.2010.03.070

Cited by 22 publications

(6 citation statements)

References 12 publications

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“…An interesting direction for the future research is estimating the loss of optimality arising due to clustering [55,56]. Considering pickup and delivery problem as a part of an integrated supply chain system is also an interesting and challenging problem [57].…”

Section: Discussionmentioning

confidence: 99%

Solution Strategy for One-to-One Pickup and Delivery Problem Using the Cyclic Transfer Approach

Dupas¹,

Grebennik²,

Litvinchev³

et al. 2018

EAI Endorsed Transactions on Energy Web

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One-to-one Pickup and Delivery Problem (PDP) with loading constraints is studied. Mathematical model is presented using combinatorial configurations approach for pickup and delivery and the phi-function technique for loading constraints. Two-stage solution strategy is used. The first stage has two levels: a) clustering the set of pickup and delivery points regarding to the set of vehicles and b) solving the PDP problem with 3D loading constraints for each vehicle within the appropriate cluster. The second stage improves the solution found at the previous stage and is based on the cyclic transfer approach and cyclic permutations. Computational results are presented to support efficiency of the approach.

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Section: Discussionmentioning

confidence: 99%

Solution Strategy for One-to-One Pickup and Delivery Problem Using the Cyclic Transfer Approach

Dupas¹,

Grebennik²,

Litvinchev³

et al. 2018

EAI Endorsed Transactions on Energy Web

View full text Add to dashboard Cite

show abstract

“…Litvinchev et al used a Lagrangian heuristic for solving the many-to-many assignment problem [11]. This work is important because it allowed for agent and task capacity limits which are necessary for the military fleet assignment problem solved in this work.…”

Section: Literature Reviewmentioning

confidence: 99%

Retirement optimization through aircraft transfers and employment

Newcamp

Verhagen

Santos

et al. 2019

Journal of Air Transport Management

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Military aircraft retirements are an afterthought for many lifecycle planners. More active management of end-of-life fleets can yield increased confidence in fleet capability and retirement timelines. This work aimed to provide fleet managers with a tool to manage aircraft retirement forecasts. It solved an equivalent flight hour minimization problem using a mixed-integer linear programming model for a military aircraft fleet having a network with basing and mission type constraints. The model minimized differences in remaining equivalent flight hours for individual aircraft in future years, thereby allowing a fleet manager to alter the timeline for retirement of individual aircraft. The United States Air Force A-10 Thunderbolt II aircraft was selected as a case study while disruptions such as deployments were modeled to show the methodology's robustness. This work proved that a fleet of aircraft with dissimilar utilization histories and varying amounts of remaining useful lifetime could be actively managed to change the time at which individual aircraft were ready for retirement. The benefit to fleet managers is the ability to extract additional lifetime out of their aircraft prior to retirement.

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“…Since the GAP problem is an NPhard problem, it is quite common to use heuristic algorithms that gives the near optimal solution in a short time [11]. In the studies using heuristic algorithms, tabu search algorithm [12][13][14], genetic algorithm [15], bees algorithm [16], a heuristic based on Lagrangian relaxation [17,18], LP-based heuristic [19], a hybrid heuristic based on scatter search [20], improved differential evolution algorithm [21], a parallel genetic algorithm [22] and simulated annealing algorithm [14] were used. Degroote et al [23], poposed a methodology for selection the most suitable algorithm for GAP.…”

Section: Introductionmentioning

confidence: 99%

A multi-start iterated tabu search algorithm for the multi-resource agent bottleneck generalized assignment problem

Bektur¹

2019

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this study, a multi-resource agent bottleneck generalized assignment problem (MRBGAP) is addressed. In the bottleneck generalized assignment problem (BGAP), more than one job can be assigned to an agent, and the objective function is to minimize the maximum load over all agents. In this problem, multiple resources are considered and the capacity of the agents is dependent on these resources and it has minimum two indices. In addition, agent qualifications are taken into account. In other words, not every job can be assignable to every agent. The problem is defined by considering the problem of assigning jobs to employees in a firm. BGAP has been shown to be NP- hard. Consequently, a multi-start iterated tabu search (MITS) algorithm has been proposed for the solution of large-scale problems. The results of the proposed algorithm are compared by the results of the tabu search (TS) algorithm and mixed integer linear programming (MILP) model.

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Lagrangian heuristic for a class of the generalized assignment problems

Cited by 22 publications

References 12 publications

Solution Strategy for One-to-One Pickup and Delivery Problem Using the Cyclic Transfer Approach

Solution Strategy for One-to-One Pickup and Delivery Problem Using the Cyclic Transfer Approach

Retirement optimization through aircraft transfers and employment

A multi-start iterated tabu search algorithm for the multi-resource agent bottleneck generalized assignment problem

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