Logic cuts for multilevel generalized assignment problems

Osorio, Maria A.; Laguna, Manuel

doi:10.1016/s0377-2217(02)00576-3

Cited by 28 publications

(20 citation statements)

References 15 publications

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“…A branch and cut algorithm was able to solve only small instances [29]. The most recent results were obtained in [30] by the branch-and-price (B&P) algorithm on instances with up to 80 machines, 400 task and 5 levels.…”

Section: Multilevel Generalized Assignment Problemmentioning

confidence: 99%

An implementation of exact knapsack separation

2015

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Cutting planes have been used with great success for solving mixed integer programs. In recent decades, many contributions have led to successive improvements in branch-and-cut methods which incorporate cutting planes in branch and bound algorithm. Using advances that have taken place over the years on 0-1 knapsack problem, we investigate an efficient approach for 0-1 programs with knapsack constraints as local structure. Our approach is based on an efficient implementation of knapsack separation problem which consists of the four phases: preprocessing, row generation, controlling numerical errors and sequential lifting. This approach can be used independently to improve formulations with cutting planes generated or incorporated in branch and cut to solve a problem. We show that this approach allows us to efficiently solve large-scale instances of generalized assignment problem, multilevel generalized assignment problem, capacitated p-median problem and capacitated network location problem to optimality.Keywords Knapsack problem · Cutting plane · Exact separation · Generalized assignment problem · Multilevel generalized assignment problem · Capacitated p-median problem · Capacitated network location problem B Igor Vasilyev

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Section: Multilevel Generalized Assignment Problemmentioning

confidence: 99%

An implementation of exact knapsack separation

2015

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“…Step 2 J = {1, 2, 4, 5, 6,7,8,9,11,12,13,14,15,16,17,18,19 Step 1 This solution is feasible, and all tasks are allocated to a single period, or consecutive periods. Therefore proceed to Step 6.…”

Section: Examplementioning

confidence: 99%

“…These papers are indicative that research into both exact and heuristic methods for GAP is still active. Recent papers by Osorio and Laguna [11] and Yagiura et al [12] indicate that there is also active research into some extensions of GAP. GAPS2 has been less extensively studied.…”

mentioning

confidence: 99%

An LP-based heuristic procedure for the generalized assignment problem with special ordered sets

French¹,

Wilson²

2007

Computers & Operations Research

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“…The algorithm combines different approaches to solve the generalised assignment and the knapsack problems following Albareda-Sambola, Van Der Vlerk [52], Li and Curry [53], Osorio and Laguna [54] and Martello and Toth [55], but also implements some findings indicated by Ross and Soland [56] and Fisher, Jaikumar [57]. In the constant search for optimal solutions to the GAP, the use of heuristics is most important, as shown in the works by Cattrysse and Van Wassenhove [58], Cattrysse, Salomon [59], Amini and Racer [60] and Lorena and Narciso [61], where it has accelerated the search for solutions to the optimisation problem.…”

mentioning

confidence: 99%

“…By developing the HC route assignment algorithm presented herein, we built on the results of Ribeiro and Pradin [62], who relied on a two-phase method: firstly, selecting and assigning similar HC assistance tasks (Phase 1); secondly, establishing a new division and reallocation to minimise possible inefficiency (Phase 2), similarly to the work presented by Hiermann and Prandtstetter [31]. Here the idea of Osorio and Laguna [54] was also implemented into the algorithm, with multiple resources or agents' different levels of efficiency after considering the assignment. The procedure and solution to assign loads (the HC services offered by the nurses) and orders to means of transport is discussed below.…”

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confidence: 99%

Sustainable Urban Homecare Delivery with Different Means of Transport

et al. 2018

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Abstract:Due to the increasing number of requests for homecare services, care institutions struggle to perform in urban traffic, which eventually makes travel times longer and less predictable and, therefore, leads to a declining service quality. Homecare delivery scheduling and planning tools must lead to efficient reliable routes that allow the nursing crew to make the least efforts and use the fewest institutional resources, and that consider urban sustainability goals. For the case study, a European city was selected with 58,000 people of whom 73 patients received long-term care at homes provided by 11 homecare nurses. While maximising patient satisfaction, a homecare planning algorithm considered many means of transport and minimised travel times. The study reduced the total nurses' working hours/day by a bus and walking combination, and by comparing if nurses ride e-bikes, which respectively reduced~35-44% of the total time that nurses spent travelling. This result is applicable to an urban environment where the public transport network is sufficient and biking is allowed on a reasonable number of roads. Better homecare management can support the efficient use of resources of health care institutions, high-quality home care and aspirations towards livable communities and sustainable development.

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Logic cuts for multilevel generalized assignment problems

Cited by 28 publications

References 15 publications

An implementation of exact knapsack separation

An implementation of exact knapsack separation

An LP-based heuristic procedure for the generalized assignment problem with special ordered sets

Sustainable Urban Homecare Delivery with Different Means of Transport

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