Accelerating Strategies in Column Generation Methods for Vehicle Routing and Crew Scheduling Problems

Selected Topics in Column Generation

“…Application(s) Agarwal et al (1989); Desaulniers et al (2001b); Desrochers et al (1992); Löbel (1997Löbel ( , 1998; Ribeiro and Soumis (1994) various vehicle routing problems Borndörfer et al (2003); Desaulniers et al (2001b); Desrochers and Soumis (1989) crew scheduling Desrosiers et al (1984) multiple traveling salesman problem with time windows Krumke et al (2002) real-time dispatching of automobile service units Lübbecke and Zimmermann (2003); Sol (1994) multiple pickup and delivery problem with time windows Anbil et al (1998); Crainic and Rousseau (1987) airline crew pairing Barnhart and Schneur (1996) air network design for express shipment service Erdmann et al (2001) airline schedule generation Barnhart et al (1998a); Desaulniers et al (1997); Ioachim et al (1999) fleet assignment and aircraft routing and scheduling Crama and Oerlemans (1994) job grouping for flexible manufacturing systems Eben-Chaime et al (1996) grouping and packaging of electronic circuits Park et al (1996) bandwidth packing in telecommunication networks Ribeiro et al (1989) traffic assignment in satellite communication systems Sankaran (1995) course registration at a business school Vanderbeck (1994) graph partitioning e.g., in VLSI, compiler design Vanderbeck (1994) single-machine multi-item lot-sizing Hurkens et al (1997); Valério de Carvalho (1999, 2002b; Vance (1998); Vance et al (1994); Vanderbeck (1999) bin packing and cutting stock problems Alvelos and Valério de Carvalho (2000); …”

“…Elaborate hybrids may evolve, see e.g., Anbil, Forrest, and Pulleyblank (1998);Bixby et al (1992); Borndörfer et al (2003); Desaulniers, Desrosiers, and Solomon (2001b). Heuristics are used to construct or improve dual variable values at any time in the algorithm.…”

“…Generic algorithms for solving problems by integer programming column generation were presented by Barnhart et al (1998b) and Vanderbeck and Wolsey (1996). Algorithmic efficacy is considered by Desaulniers, Desrosiers, and Solomon (2001b). Some dissertations (Ben Amor, 2002;Sol, 1994;Vanderbeck, 1994;Villeneuve, 1999) are a rich source of computational testing.…”

An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem

“…For the theoretical equivalence between column generation and Lagrangean relaxation, we refer the reader to the recent book by Desaulniers et al [5]. The exploitation of this equivalence can be very influential on the effectiveness of a column generation algorithm, as shown for instance in reference [3].…”

Transforming Mathematical Models Using Declarative Reformulation Rules

“…A view based on complexity theory was proposed in [2], but since it requires a polynomial time mapping between the problems it already cuts off a number of well-known reformulation techniques where the mapping is pseudo-polynomial [6] or even exponential in theory [3,5,8], but quite effective in practice. Limited to MIP problems, general ideas based on variable redefinition were proposed by [13,14], without finding wide application due to its complexity, remaining unknown (or unused) by the "average" user.…”