A branch-and-bound algorithm for solving a fixed charge problem in the profit optimization of sawn timber production

This paper deals with the problem of profit optimization in sawn timber production, utilizing a special type of sawmill. Expected rejects and resetting costs are taken into consideration. The present problem is formulated as a fixed charge linear programming problem involving identical fixed charges, one equality constraint and explicit bounds on the variables. Based on the greedy sorting of the variables the authors develop a branch-and-bound algorithm working on a special subset of all solutions. Through usage of the problem structure for constructing bounds they arrive at an acceptable CPU-time (on a 80386 personal computer) for practical purposes.