Flow shop scheduling with earliness,tardiness, and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding), and intermediate (work‐in‐process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two different, but closely related, Dantzig‐Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig‐Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two different lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near‐optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with different types of strongly ????‐hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near‐optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Concise RLT forms of binary programs: A computational study of the quadratic knapsack problem

The reformulation‐linearization technique (RLT) is a methodology for constructing tight linear programming relaxations of mixed discrete problems. A key construct is the multiplication of “product factors” of the discrete variables with problem constraints to form polynomial restrictions, which are subsequently linearized. For special problem forms, the structure of these linearized constraints tends to suggest that certain classes may be more beneficial than others. We examine the usefulness of subsets of constraints for a family of 0–1 quadratic multidimensional knapsack programs and perform extensive computational tests on a classical special case known as the 0–1 quadratic knapsack problem. We consider RLT forms both with and without these inequalities, and their comparisons with linearizations derived from published methods. Interestingly, the computational results depend in part upon the commercial software used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A new reformulation approach for the generalized partial covering problem

In this paper, we consider a situation in which a group of facilities must be constructed in order to serve a given set of customers, where the facilities might not be able to guarantee an absolute coverage to the different customers. We examine the problem of maximizing the total service reliability of the system subject to a budgetary constraint. We propose a new reformulation of this problem that facilitates the generation of tight lower and upper bounds. These bounding mechanisms are embedded within the framework of a branch‐and‐bound procedure. Computational results on problem instances ranging in size up to 100 facilities and 200 customers reveal the efficacy of the proposed exact and heuristic approaches. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Robust tower location for code division multiple access networks

Designing Code Division Multiple Access networks includes determining optimal locations of radio towers and assigning customer markets to the towers. In this paper, we describe a deterministic model for tower location and a stochastic model to optimize revenue given a set of constructed towers. We integrate these models in a stochastic integer programming problem with simple recourse that optimizes the location of towers under demand uncertainty. We develop algorithms using Benders' reformulation, and we provide computational results. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007