This paper presents a hybrid of a general heuristic framework and a general purpose mixed-integer programming (MIP) solver. The framework is based on local search and an adaptive procedure which chooses between a set of large neighborhoods to be searched. A mixed integer programming solver and its built-in feasibility heuristics is used to search a neighborhood for improving solutions. The general reoptimization approach used for repairing solutions is specifically suited for combinatorial problems where it may be hard to otherwise design suitable repair neighborhoods. The hybrid heuristic framework is applied to the multi-item capacitated lot sizing problem with setup times, where experiments have been conducted on a series of instances from the literature and a newly generated extension of these. On average the presented heuristic outperforms the best heuristics from the literature, and the upper bounds found by the commercial MIP solver ILOG CPLEX using state-of-the-art MIP formulations. Furthermore, we improve the best known solutions on 60 out of 100 and improve the lower bound on all 100 instances from the literature.

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Motivated by addressing probabilistic 0-1 programs we study the conic quadratic knapsack polytope with generalized upper bound (GUB) constraints. In particular, we investigate separating and extending GUB cover inequalities. We show that, unlike in the linear case, determining whether a cover can be extended with a single variable is -hard. We describe and compare a number of exact and heuristic separation and extension algorithms which make use of the structure of the constraints. Computational experiments are performed for comparing the proposed separation and extension algorithms. These experiments show that a judicious application of the extended GUB cover cuts can reduce the solution time of conic quadratic 0-1 programs with GUB constraints substantially.

A big passenger transport company experienced problems with the utilization of their maintenance crews. Large amounts of overtime were logged, while at the same time a lot of idle time was experienced. This paper describes the development on a microcomputer of a Decision Support System (DSS) to improve their shift scheduling. Central to the DSS is a heuristic algorithm which generates shift schedules. This algorithm is easy .to understand and provides good results, while it solves the real life problem rapidly on a microcomputer.