In this paper we introduce a new method for generating heuristic solutions to binary optimization problems. We develop a technique based on binary decision diagrams. We use these structures to provide an under-approximation to the set of feasible solutions. We show that the proposed algorithm delivers comparable solutions to a state-of-the-art general-purpose optimization solver on randomly generated set covering and set packing problems.

Company (Deere), one of the world's leading producers of machinery, manufactures products composed of various features, within which a customer may select one of a number of possible options. On any given Deere product line, there may be tens of thousands of combinations of options (configurations) that are feasible. Maintaining such a large number of configurations inflates overhead costs; consequently, Deere wishes to reduce the number of configurations from their product lines without upsetting customers or sacrificing profits. In this paper, we provide a detailed explanation of the marketing and operational methodology used, and tools built, to evaluate the potential for streamlining two product lines at Deere. We illustrate our work with computational results from Deere, highlighting important customer behavior characteristics that impact product line diversity. For the two very different studied product lines, a potential increase in profit from 8% to 18% has been identified, possible through reducing the number of configurations by 20% to 50% from present levels, while maintaining the current high customer service levels. Based on our analysis and the insights it generated, Deere recently implemented a new product line strategy. We briefly detail this strategy, which has thus far increased profits by tens of millions of dollars.

The scheduling needs of umpires and referees differ from the needs of sports teams. In some sports leagues, such as Major League Baseball in the United States, umpires travel throughout the league's territory; they do not have a "home base." For such leagues, balancing the need to minimize umpire travel and the objective that an umpire should not handle the games of a particular team too frequently is important. We have used our approach, which is based on network optimization and simulated annealing, to successfully schedule Major League Baseball umpires. To develop this approach, we created the traveling umpire problem, which includes the major umpire scheduling issues and also provides a test bed for alternative techniques.

No abstract

We address the problem of designing appointment scheduling strategies in a stochastic environment accounting for patient no-shows, non-punctuality, general stochastic service times, and unscheduled emergency walk-ins. A good appointment schedule seeks to help outpatient clinics to utilize their resources efficiently while containing patients' waiting times. The task of identifying an optimal schedule is modeled as a nonlinear integer program, where the objective function is the outcome of stochastic analysis in transient state. We maintain the discrete nature of the appointment scheduling problem by considering arrival epochs with discrete supports. By looking at discrete-time snapshots of the random evolution of a single-server queueing model, we characterize probabilistically the system's workload over time as a function of an appointment schedule and we derive recursive expressions for the performance measures of interest. Subsequently, we unfold discrete convexity properties of the optimization problem. We prove that under general conditions the objective function is supermodular and componentwise convex. Under assumptions on patient punctuality, we prove that the optimal scheduling strategy minimizes a multimodular function; a property which guarantees that a locally optimal schedule is also globally optimal. The size of the local neighborhood, however, grows exponentially with the dimension of the problem. To the best of our knowledge, this study is the first to develop and implement an algorithm for minimizing locally a multimodular function over nonnegative integer vectors via submodular set-function minimization over ring families; a task that can be performed in polynomial time.