Optimal selection of contracts and work shifts in multi-skill call centers

This paper deals with the problem of finding the most suitable contracts to be used when hiring the operators of a call center and deciding their optimal working schedule, to optimize the trade-off between the service level provided to the customers and the cost of the personnel. In a previous paper (Cordone et al. 2011), we proposed a heuristic method to quickly build an integer solution from the solution of the continuous relaxation of an integer linear programming model. In this paper, we generalize that model to take into account a much wider class of working contracts, allowing heterogeneous shift patterns, as well as legal constraints related to continuously active working environments. Since our original rounding heuristic cannot be extended to the new model, due to its huge size and to the involved correlations between different sets of integer variables, we introduce a more sophisticated heuristic based on decomposition and on a multi-level iterative structure. We compare the results of this heuristic with those of a Greedy Randomized Adaptive Search Procedure, both on real-world instances and on realistic random instances

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

Hybrid Algorithms Based on Integer Programming for the Search of Prioritized Test Data in Software Product Lines

In Software Product Lines (SPLs) it is not possible, in general, to test all products of the family. The number of products denoted by a SPL is very high due to the combinatorial explosion of features. For this reason, some coverage criteria have been proposed which try to test at least all feature interactions without the necessity to test all products, e.g., all pairs of features (pairwise coverage). In addition, it is desirable to first test products composed by a set of priority features. This problem is known as the Prioritized Pairwise Test Data Generation Problem. In this work we propose two hybrid algorithms using Integer Programming (IP) to generate a prioritized test suite. The first one is based on an integer linear formulation and the second one is based on a integer quadratic (nonlinear) formulation. We compare these techniques with two state-of-the-art algorithms, the Parallel Prioritized Genetic Solver (PPGS) and a greedy algorithm called prioritized-ICPL. Our study reveals that our hybrid nonlinear approach is clearly the best in both, solution quality and computation time. Moreover, the nonlinear variant (the fastest one) is 27 and 42 times faster than PPGS in the two groups of instances analyzed in this work.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Partially funded by the Spanish Ministry of Economy and Competitiveness and FEDER under contract TIN2014-57341-R, the University of Málaga, Andalucía Tech and the Spanish Network TIN2015-71841-REDT (SEBASENet)