All-or-Nothing Generalized Assignment with Application to Scheduling Advertising Campaigns

Adany, Ron; Feldman, Moran; Haramaty, Elad; Khandekar, Rohit; Schieber, Baruch; Schwartz, Roy; Shachnai, Hadas; Tamir, Tami

doi:10.1007/978-3-642-36694-9_2

Cited by 7 publications

(20 citation statements)

References 12 publications

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“…On the other hand, Jansen et al [9] also showed that unless the Exponential Time Hypothesis fails, there is no approximation scheme which has a running time of 2 o(1/ ) + n O (1) for the multiple knapsack problem even if there are only two knapsacks (of the unit capacity). Thus, allowing the number of knapsacks m to be part of the input as well as allowing each knapsack to have a distinct capacity does not essentially make the problem harder in the sense that the 2…”

Section: O(logmentioning

confidence: 99%

“…We hope the study in this line will help reveal the impact of these parameters. Our problem is closely related to the all-or-nothing generalized assignment problem (AGAP) [1]. The AGAP problem also asks for a most profitable packing of n groups of items into m identical knapsacks, where the profit of a group is defined to be the total profit of items in the group, and is achieved only if every item of this group is packed.…”

Section: O(logmentioning

confidence: 99%

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Packing Groups of Items into Multiple Knapsacks

Chen

Zhang

2018

ACM Trans. Algorithms

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We consider a natural generalization of the classical multiple knapsack problem in which instead of packing single items we are packing groups of items. In this problem, we have multiple knapsacks and a set of items which are partitioned into groups. Each item has an individual weight, while the profit is associated with groups rather than items. The profit of a group can be attained if and only if every item of this group is packed. Such a general model finds applications in various practical problems, e.g., delivering bundles of goods. The tractability of this problem relies heavily on how large a group could be. Deciding if a group of items of total weight 2 could be packed into two knapsacks of unit capacity is already NP-hard and it thus rules out a constantapproximation algorithm for this problem in general. We then focus on the parameterized version where the total weight of items in each group is bounded by a factor δ of the total capacity of all knapsacks. Both approximation and inapproximability results with respect to δ are derived. We also show that, depending on whether the number of knapsacks is a constant or part of the input, the approximation ratio for the problem, as a function on δ, changes substantially, which has a clear difference from the classical multiple knapsack problem.

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Section: O(logmentioning

confidence: 99%

Section: O(logmentioning

confidence: 99%

Packing Groups of Items into Multiple Knapsacks

Chen

Zhang

2018

ACM Trans. Algorithms

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“…Our approach provides a simpler alternative MOIP formulation that can be used to generate provably Pareto‐optimal solutions for small‐ to medium‐sized problems, and possibly large‐scale problems that can be decomposed into smaller subproblems. However, we also hope that our formulation can be used as a basis for alternative heuristics, possibly with provable performance guarantees similar to approximation algorithms (e.g., see Williamson and Shmoys, ; Adany et al., ), that can be used for large‐scale problems.…”

Section: Multiobjective Optimization Formulations In Tv Advertisingmentioning

confidence: 99%

A multiobjective approach for maximizing the reach or GRP of different brands in TV advertising

Evangelista

Regis

2017

Int Trans Operational Res

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This paper focuses on a multiobjective optimization problem in TV advertising from an advertising agency's perspective, which involves deciding on which commercial breaks to air the ads of various brands to jointly maximize reach or gross rating point (GRP) for the different brands subject to budget constraints, brand competition constraints, and other scheduling constraints. We present a multiobjective integer programming formulation of this problem and develop and implement algorithms for generating provably Pareto‐optimal solutions. We also develop reduction and visualization procedures to aid a decision maker in choosing suitable subsets of the Pareto‐optimal solutions obtained. Numerical experiments on five TV advertising problems involving 20–40 objective functions and thousands of decision variables and constraints demonstrate the effectiveness of the proposed formulation and solution methods in generating Pareto‐optimal objective vectors that reflect brand priorities and that are well distributed along the Pareto front.

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“…For a special case of GMKP, when all knapsack capacities are equal and the heaviest group weighs at most 2/3 of the total capacity, parameterized-approximation algorithms were proposed by Chen and Zhang [2018]. Adany et al [2016] proposed a PTAS for a generalized assignment problem with grouped items that has additional constraints: there is a limit on the number of items per group, and knapsacks can accommodate at most one item from each group. The algorithms proposed by Chen and Zhang [2018] and Adany et al [2016] guarantee feasiblity while sacrificing rewards; the algorithms proposed in this paper sacrifice feasibility (bounded by a maximum exceeded knapsack capacity) while generating solutions achieving the optimal reward (in relation to the original GMKP).…”

Section: Introductionmentioning

confidence: 99%

Bi-Criteria Multiple Knapsack Problem with Grouped Items

Castillo-Zunino¹,

Keskinocak²

2020

Preprint

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The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities. Either all items in a group are assigned or none at all. We propose algorithms which guarantee that rewards are not less than the optimal solution, with a bound on exceeded knapsack capacities. To obtain capacityfeasible solutions, we propose a binary-search heuristic combined with these algorithms. We test the performance of the algorithms and heuristics in an extensive set of experiments on randomly generated instances and show they are efficient and effective, i.e., they run reasonably fast and generate good quality solutions.

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All-or-Nothing Generalized Assignment with Application to Scheduling Advertising Campaigns

Cited by 7 publications

References 12 publications

Packing Groups of Items into Multiple Knapsacks

Packing Groups of Items into Multiple Knapsacks

A multiobjective approach for maximizing the reach or GRP of different brands in TV advertising

Bi-Criteria Multiple Knapsack Problem with Grouped Items

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