Een rustige zomer

No abstract

Combinatorics in operations research

This is a collection of examples of the use of combinatorial techniques in practical decision situations. The emphasis is on the description of real-world problems, the formulation of mathematical models, and the development of algorithms for their solution. We survey related models and applications. Key Words & Phrases: traveling salesman, vehicle routing, multiple postmen, linear ordering, clique partitioning, test cover, bottleneck extrema, minimum cost flow, interval scheduling, job shop scheduling

Book review: The Travelling Salesman Problem: A Computational Study

No abstract

One machine scheduling with delayed precedence constraints

We study the one machine scheduling problem with release and delivery times and the minimum makespan objective, in the presence of constraints that for certain pairs of jobs require a delay between the completion of the first job and the start of the second (delayed precedence constraints). This problem arises naturally in the context of the Shifting Bottleneck Procedure for the general job shop scheduling problem, as a relaxation of the latter, tighter than the standard one machine relaxation. The paper first highlights the difference between the two relaxations through some relevant complexity results. Then it introduces a modified Longest Tail Heuristic whose analysis identifies those situations that permit efficient branching. As a result, an optimization algorithm is developed whose performance is comparable to that of the best algorithms for the standard one machine problem. Embedding this algorithm into a modified version of the Shifting Bottleneck Procedure that uses the tighter one machine relaxation discussed here results in a considerable overall improvement in performance on all classes of job shop scheduling problems