George L. Nemhauser We study a deterministic maritime inventory routing problem with a long planning horizon. For instances with many ports and many vessels, mixed-integer linear programming (MIP) solvers often require hours to produce good solutions even when the planning horizon is 90 or 120 periods. Building on the recent successes of approximate dynamic programming (ADP) for road-based … Read more
Performance variability of modern mixed-integer programming solvers and possible ways of exploiting this phenomenon present an interesting opportunity in the development of algorithms to solve mixed-integer linear programs (MILPs). We propose a framework using multiple branch-and-bound trees to solve MILPs while allowing them to share information in a parallel execution. We present computational results on … Read more
The minimum concave cost network flow problem (MCCNFP) is NP-hard, but efficient polynomial-time algorithms exist for some special cases such as the uncapacitated lot-sizing problem and many of its variants. We study the MCCNFP over a grid network with a general nonnegative separable concave cost function. We show that this problem is polynomially solvable when … Read more
We develop an exact algorithm for integer programs that uses restrictions of the problem to produce high-quality solutions quickly. Column generation is used both for generating these problem restrictions and for producing bounds on the value of the optimal solution. The performance of the algorithm is greatly enhanced by using structure, such as arises in … Read more
There are $n$ individual assets and $k$ of them are to be sold over two stages. The first-stage prices are known and the second-stage prices have a known distribution. The sell or hold problem (SHP) is to determine which assets are to be sold at each stage to maximize the total expected revenue. We show … Read more
We provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables. Under a simple probabilistic model of the problem parameters, we show that a simple split cut, i.e. a Gomory cut, is more likely to be better than a type 1 triangle cut in … Read more
Branching variable selection can greatly a ffect the eff ectiveness and efficiency of a branch-and- bound algorithm. Traditional approaches to branching variable selection rely on estimating the eff ect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from … Read more
We study the modeling of non-convex piecewise linear functions as Mixed Integer Programming (MIP) problems. We review several new and existing MIP formulations for continuous piecewise linear functions with special attention paid to multivariate non-separable functions. We compare these formulations with respect to their theoretical properties and their relative computational performance. In addition, we study … Read more
We consider optimization problems with some binary variables, where the objective function is linear in these variables. The stability region of a given solution of such a problem is the polyhedral set of objective coefficients for which the solution is optimal. A priori knowledge of this set provides valuable information for sensitivity analysis and re-optimization … Read more
Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We give a mixed-integer programming formulation for this special case and study the relaxation … Read more