Exact and heuristic algorithms for the interval min-max regret generalized assignment problem

Abstract

We consider a generalization of the 0-1 knapsack problem in which the profit of each item can take any value in a range characterized by a minimum and a maximum possible profit. A set of specific profits is called a scenario. Each feasible solution associated with a scenario has a regret, given by the difference between the optimal solution value for such scenario and the value of the considered solution. The interval min-max regret knapsack problem (MRKP) is then to find a feasible solution such that the maximum regret over all scenarios is minimized. The problem is extremely challenging both from a theoretical and a practical point of view. Its decision version is complete for the complexity class Σ p 2 hence it is most probably not in N P. In addition, even computing the regret of a solution with respect to a scenario requires the solution of an N P-hard problem. We examine the behavior of classical combinatorial optimization approaches when adapted to the solution of the MRKP. We introduce an iterated local search approach and a Lagrangian-based branch-and-cut algorithm, and evaluate their performance through extensive computational experiments.

The Assignment Problem in Human Resource Project Management under Uncertainty

“…(4) Note that the AP algorithm under uncertainty is not the first AP procedure referring to scenarios. Numerous papers have been devoted to the min-max assignment problem and the min-max regret assignment problem (e.g., Aissi et al 2005;Deineko and Woeginger 2006;Wu et al 2018), where the scenarios are also applied. However, the assumptions and methodology adopted in those papers differ significantly from the idea presented in this article.…”

“…Furthermore, it does not require any information on likelihood, which is desired in the case of projects with a high degree of novelty and a fast-evolving environment. As a matter of fact, SP has already been combined with AP in situations where the decision-maker is a strong pessimist (e.g., Aissi et al 2005;Deineko and Woeginger 2006;Wu et al 2018). In this paper, instead of probability calculus, we intend to make use of optimism/pessimism coefficients.…”

A New Model for Reassignment of Tasks to Available Employees in Iraq’s Firms

“…In this way, they suggested a new branch-and-bound algorithm to solve the quadratic integer GAP. See other models of GAP in [14][15][16]. e model proposed in this paper is a combination of some previously discussed GAPs, and it is not similar to the other models.…”

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

“…Studies in the literature can be categorized as studies that proposes exact algorithms and heuristic algorithms. In the studies that propose exact algorithms, the branch-bound algorithm ( [4] and [5]), the cutting plane algorithm [6], the branch and price algorithm [7,8], branch-and-cut algorithm for GAP with additional pair constraints [9] and with min-max regret criterion [10] were used. When the exact solution approaches are used, the solution time of the problem is quite prolonged.…”

“…However, many studies in the literature propose an heuristic algorithm for GAP. Wu et al [10], Souza et al [20], Sethanan and Pitakaso [21], and Moussavi et al [31] proposed an heuristic algorithm for the generalized assignment problem. Difference from the literature, in this study an heuristic algorithm is proposed for the multi-resource agent bottleneck generalized assignment problem with agent qualifications.…”