A branch‐and‐price algorithm for a hierarchical crew scheduling problem

Abstract

Abstract:We describe a real-life problem arising at a crane rental company. This problem is a generalization of the basic crew scheduling problem given in Mingozzi et al. [18] and Beasley and Cao [6]. We formulate the problem as an integer programming problem and establish ties with the integer multicommodity flow problem and the hierarchical interval scheduling problem. After establishing the complexity of the problem we propose a branch-and-price algorithm to solve it. We test this algorithm on a limited number of real-life instances.

A model of resilient supply chain network design: A two-stage programming with fuzzy shortest path

“…In order to find the global optimum of inventory allocation and transportation routings, Benders decomposition is an implemented solution algorithm where the master problem solution (inventory allocation) must be feasible to the sub-problem feasibility constraint (transportation routings with production scheduling). In addition to the previous contributions on TSP applications in SC networks design (i.e., Beasley & Cao, 1998;Cordeau, Laporte, & Mercier 2001;Mercier, Cordeau, & Soumis 2005;Mingozzi, Boschetti, Ricciardelli, & Bianco 1999;Stojkovic & Soumis, 2001;Yen and Birge, 2006), production scheduling (i.e., Faneyte, Spieksma, & Woeginger, 2002;Saharidis et al, 2010) and inventory allocation-vehicle routing problem (Federgruen & Zipkin, 1984), the current TSP considers simultaneously pickup and delivery transportation routings with production schedule constraints with variations in delivery lead times and batch size. The fuzzy shortest path algorithm is used to convert the SPPTWCC to the original SPP, and thus the problem is easier to solve.…”

Interval scheduling: A survey

“…In Section 5, we prove that the problem becomes NPcomplete for three machine types. In case there is an arbitrary distance given between each pair of jobs, and the cost of a machine depends on the amount of distance travelled by the machine to process its jobs, Faneyte et al [31] show that the problem with two machine types is already NP-complete.…”

“…In a first case each machine is only available for a given amount of time w, i.e., the latest ending time of an interval assigned to machine i minus the earliest starting time of an interval assigned to that machine i should not exceed w. A second case assumes that the sum of the lengths of the intervals assigned to a same machine should not exceed a given number w. Heuristics, lower bounds, and exact approaches are described. A specific problem involving hierarchies is described by Faneyte et al [31].…”