1.1. INTRODUCTION In the beginning of the twenty-first century, large unsolved combinatorial optimization problems have been solved exactly. Two impressive cases should be mentioned. First are two instances of the Monde, Transfert) newspapers. This impressive media frenzy reflected the impact of the achievement, which was deemed of the same order of magnitude as the victory of IBMs parallel com...

This paper presents several branch and bound algorithms for a single machine scheduling problem with batching. Jobs are partitioned into families, and a set-up time is necessary when there is a switch from processing jobs of one family to jobs of another family. The objective is to minimize the total weighted completion time. A lower bound based on Lagrangean relaxation of the machine capacity ...

Most deterministic machine scheduling models assume that the processing time of a job on a machine is fixed externally and known in advance of scheduling. However, in most realistic situations, apart from the machines, it requires additional resources to process jobs, and the processing time of a job is determined internally by the amount of the resources allocated. In these situations, both th...

In this paper we consider a 3-echelon, multi-product supply chain design model with economies of scale in transport and warehousing that explicitly takes transport frequencies into consideration. Our model simultaneously optimizes locations and sizes of tank farms, material flows, and transport frequencies within the network. We consider all relevant costs: product cost, transport cost, tank re...

Inspired by the d-step approach used for investigating the diameter of polytopes, the following d-step conjecture was introduced by Deza and Franek : the number of runs in a string of length n with d distinct symbols is at most n− d. Bannai et al. showed that the number of runs in a string is less than its length by mapping each run to a set of starting positions of Lyndon roots. We show that B...

This article considers the problem of scheduling preemptive open shops to minimize total tardiness. The problem is known to be NP-hard. An efficient constructive heuristic is developed for solving large-sized problems. A branch-and-bound algorithm that incorporates a lower bound scheme based on the solution of an assignment problem as well as various dominance rules are presented for solving me...

The issue discussed in this paper is a bi-level problem in which two rivals compete in attracting customers and maximizing their profits which means that competitors competing for market share must compete in the centers that are going to be located in the near future. In this paper, a nonlinear model presented in the literature considering customer preferences is linearized. Customer behavior ...