A theorem was recently introduced to establish a relationship betweengoal programming and fuzzy programming for vectormaximum problems.In this short note it is shown that the relationship does not exist underall circumstances. The necessary correction is proposed.

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of pro...

We develop a bicriteria model for the resource allocation problem in PERT networks, in which the total direct costs of the project as the first objective, and the mean of project completion time as the second objective are minimized. The activity durations are assumed to be independent random variables with either exponential or Erlang distributions, in which the mean of each activity duration ...

In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision ...

Over a long and remarkably productive career, Professor William W. (Bill) Cooper has made many pioneering contributions to Operations Research and Management Science (OR/MS), with notable forays into the areas of (a) linear and non-linear programming, (b) goal programming, (c) chance-constrained programming, (d) data envelopment analysis, and (e) manpower planning, among others. His legendary p...

Automatic differentiation is used for the solution of optimal control problems. Original problem is reduced to a nonlinear programming problem using general RungeKutta integration formulas. Canonical formulas which use a fast automatic differentiation strategy are given to compute derivatives of goal function.

The A* algorithm belongs to the class of best first graph-search algorithms and is frequently used to find minimum-cost paths. Recently, A* has been generalised to solve multiple-objective search problems, returning the set of non-dominated solution paths. This paper presents METAL-A*, an admissible heuristic search algorithm for search problems with lexicographic goals that returns the set of ...