A finite branch-and-bound algorithm for linear multiplicative programming

On the basis of Soland's rectangular branch-and-bound, we develop an algori thm for minimizing a product of p (greater than or equal to2) affine functi ons over a polytope. To tighten the lower bound on the value of each subpro blem, we install a second-stage bounding procedure, which requires O(p) add itional time in each iteration but remarkably reduces the number of branchi ng operations. Computational results indicate that the algorithm is practic al if p is less than 15, both in finding an exact optimal solution and an a pproximate solution.