Solving airline crew scheduling problems by branch-and-cut

Article Abstract:

Most airlines apply a mathematical modelling technique to define crew assignments according to their flight schedules. However, these models are not always capable of generating the optimal solution. A branch-and-cut solution to resolve the optimality issue is presented as an alternative. The branch-and-cut solution integrates the cuts generated by integer points with a tree-search algorithm where linear programming, heuristics and automatic reformulation procedures are used to reach the solution. The branch-and-cut solver has not been evaluated for closeness to the optimal solution since contractual labor requirements have not beeen adequately represented in crew schedules, aside from being treated as base constraints. However, airline crews whose companies have tried the solution appear to be satisfied because the method allows them more flying time than waiting time.

Air transportation, scheduled, Human resource management, Airlines, Scheduling (Management), Calendar, Flight crews

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Nelder-Mead simplex modifications for simulation optimization

Article Abstract:

The Nelder-Mead method was introduced in 1965 as an approach for optimizing deterministic functions but later became a popular method for optimizing stochastic simulation models. Unfortunately, the application of this method for the optimization of a stochastic system's expected response proves to be problematic since the simplex-resizing steps of Nelder-Mead carry the risk of inappropriate termination. An attempt is made to modify the method to avoid this problem. Based on the analytical and empirical results of a study of Nelder-Mead's performance when used to a response function with an additive white-noise error, new modifications are developed that generate more accurate estimates of the optimal expected response. A new modified approach, RS+S9, is found to be superior to other existing modifications.

Analysis, Simulation methods, Simulation, Stochastic processes, Experimental design, Research design, Simplex method, Simplexes (Mathematics)

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Locating tax facilities: a graphics-based microcomputer optimization model

Article Abstract:

A mathematical model used to select optimal locations for Posts-of-Duty (POD's) field offices of the Internal Revenue Service (IRS) is presented. A lagrangian-relaxation technique to measure optimality is also described. The model was used to develop a menu-driven, graphics-oriented, microcomputer-based system utilizing known heuristic solutions to facility location problems. The use of the model is illustrated with data from two IRS districts in Florida.

Finance, taxation, & monetary policy, Research, Usage, Location, Interactive computer systems, Interactive media, United States. Internal Revenue Service, Lagrangian functions

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