The aircrew-scheduling problem consists of two important subproblems: the tours-of-duty planning problem to generate minimum-cost tours of duty (sequences of duty periods and rest periods) to cover all scheduled flights, and the rostering problem to assign tours of duty to individual crew members. Between 1986 and 1999, Air New Zealand staff and consultants in collaboration with the University of Auckland have developed eight application-specific optimization-based computer systems to solve all aspects of the tours-of-duty planning and rostering processes for Air New Zealand's national and international operations. These systems have saved NZ$15,655,000 per year while providing crew rosters that better respect crew members' preferences.

Capacity improvement and conditional penalties are two computational aides for fathoming subproblems in a branch-and-bound procedure. In this paper, we apply these techniques to the fixed charge transportation problem (FCTP) and show how relaxations of the FCTP subproblems can be posed as concave minimization problems (rather than LP relaxations). Using the concave relaxations, we propose a new conditional penalty and three new types of capacity improvement techniques for the FCTP. Based on computational experiments using a standard set of FCTP test problems, the new capacity improvement and penalty techniques are responsible for a three-fold reduction in the CPU time for the branch-and-bound algorithm and nearly a tenfold reduction In the number of subproblems that need to be evaluated in the branch-and-bound enumeration tree. (C) 1999 John Wiley & Sons, Inc.

NETSPEAK is an algebraic modelling language used to specify, solve, and analyze nonconvex (or linear) minimum cost network flow problems. A wide variety of network and network-related topologies can be modelled using NETSPEAK including pure networks, networks with side constraints and/or side variables, and generalized networks. Problems involving price based decomposition and integer valued variables can also be modelled using NETSPEAK. The language, which features flexible input/output, robust program control, and intuitive commands, is being developed as a Windows(TM) application.

Conditional penalties are used to obtain lower bounds to subproblems in a branch-and-bound procedure that can be tighter than the LP relaxation of the subproblems. For the fixed charge transportation problem (FCTP), branch-and-bound algorithms have been implemented using conditional penalties proposed by Driebeek (Driebeek, N. 1966. An algorithm for the solution of mixed integer programming problems. Management Sci. 12 576–587.), Cabot and Erenguc (Cabot, A. V., S. S. Erenguc. 1984. Some branch-and-bound procedures for fixed-cost transportation problems. Naval Res. Logistics 31 145–154.), and Palekar et al. (Palekar, V. S., M. H. Karwan, S. Zionts. 1990. A branch-and-bound method for the fixed charge transportation problem. Management Sci. 36 1092–1105.). The last conditional penalties are referred to as the “modified” penalties. In this paper, we show that the modified penalties are not valid conditional penalties. In fact, in nearly a quarter of the test problems examined, the modified penalties prevented the branch-and-bound algorithm from properly identifying the optimal solution to the FCTP. A simple change, which corrects a subcase in the penalty calculation, restores the validity of the modified penalties while retaining their efficiency. Computational tests indicate that the “revised-modified” penalties continue to dominate the Driebeek and the Cabot and Erenguc penalties.

Political redistricting involves the amalgamation of a large number of geographic or statistical units into a smaller set of electoral districts such that the districts satisfy various criteria prescribed by law, judicial mandate, or historical precedent. This paper describes a network-based optimization model that is currently being used by governmental decision-makers in New Zealand to assist in the preliminary stages of determining Parliamentary district boundaries. The model is capable of solving large-scale problems. In the New Zealand case, the procedure has been applied to problems involving over 35,000 geographic units (called “meshblocks”) and 95 Parliamentary districts. The model generates electoral districts that have roughly equal population and are generally compact in shape. One of the key features of the model is its flexibility. On the one hand, it can take into account currently existing features such as topographic terrain or previously existing electoral boundaries. On the other hand, it can also be used to generate an entirely new set of political boundaries as was mandated by the voters in a recent referendum in New Zealand.

NetSpeak is an algebraic modelling language used to specify, solve, and analyse nonconvex (or linear) minimum cost network flow problems. A wide variety of network topologies can be modelled using NetSpeak. Its features include flexible input/output, robust program control, and intuitive commands. Several examples are used to illustrate the capabilities of NetSpeak.