Column generation for solving a compressor scheduling problem

The scheduling of compressors to gas-lifted oil wells can be thought of as a generalized facility location problem. The facilities (compressors) output a lift-gas rate at a pressure that depends nonlinearly on the rate. The clients (wells) demand lift-gas at given rates and pressures. The problem consists in deciding upon the installation of facilities to meet the demands of the clients, while keeping installation and operating costs to a minimum. Compressor scheduling is a mixed-integer nonlinear programming problem. This paper develops a column generation formulation that renders the problem a purely 0-1 program. To cope with the exponential number of columns (assignments of compressors to subsets of wells), a reduced master problem is obtained and the pricing sub-problem is approximated with a piecewise-linear reformulation.