CAVAP, A FORTRAN SUBROUTINE FOR SOLVING AN ASSIGNMENT PROBLEM WITH CONCAVE OBJECTIVE by

This document describes a FORTRAN IV subroutine named CAVAP (an acronym for conCAVe Assignment Problem) which uses a branch and bound method to solve a variant of the assignment problem in which the objective to be minimized is concave. It is assumed that m tasks are to be performed and n different kinds of machines have been defined for possible use in performing them. In general a task may be performed by several machines of one type, or a different number of machines of another type, or possibly only by certain combinations of machines. It is assumed that total cost, which Is to be minimized, is the sum of costs for each kind of machine, each of which Is in turn a concave function of the number of machines of that type required. > A detailed mathematical treatment of the problem and the solution method has been given elsewhere. CAVAP has been used to solve a space fleet selection problem with 20 space missions (tasks), 40 booster and spacecraft components (machines), and a number of alternative launch vehicle configurations and combinations for each mission. Running time was under 20 minutes on an IBM 360 model A4 with one disk.