Tallys H. Yunes

Hybrid Column Generation Approaches for Urban Transit Crew Management Problems

This article considers the overall crew management problem arising from the daily operation of an urban transit bus company that serves the metropolitan area of the city of Belo Horizonte, Brazil. Due to its intrinsic complexity, the problem is divided in two distinct subproblems:crew scheduling andcrew rostering. We have investigated each of these problems using mathematical programming (MP) and constraint logic programming (CLP) approaches. In addition, we developed hybrid column generation algorithms for solving these problems, combining MP and CLP. The hybrid algorithms always performed better, when obtaining optimal solutions, than the two previous isolated approaches. In particular, they proved to be much faster for the scheduling problem. All the proposed algorithms have been implemented and tested over real-world data obtained from the aforementioned company. The coefficient matrix of the linear program associated with some instances of the scheduling problem contains tens of millions of columns; this number is even larger for the rostering problem. The analysis of our experiments indicates that it was possible to find high-quality, and many times optimal, solutions that were suitable for the companys needs. These solutions were obtained within reasonable computational times on a desktop PC.

An Integrated Solver for Optimization Problems

One of the central trends in the optimization community over the past several years has been the steady improvement of general-purpose solvers. A logical next step in this evolution is to combine mixed-integer linear programming, constraint programming, and global optimization in a single system. Recent research in the area of integrated problem solving suggests that the right combination of different technologies can simplify modeling and speed up computation substantially. Nevertheless, integration often requires special-purpose coding, which is time consuming and error prone. We present a general-purpose solver, SIMPL, that allows its user to replicate (and sometimes improve on) the results of custom implementations with concise models written in a high-level language. We apply SIMPL to production planning, product configuration, machine scheduling, and truss structure design problems on which customized integrated methods have shown significant computational advantage. We obtain results that either match or surpass the original codes at a fraction of the implementation effort.

Building Efficient Product Portfolios at John Deere and Company

John Deere & Company (Deere), one of the worlds 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.

Scheduling Major League Baseball Umpires and the Traveling Umpire Problem

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 leagues 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.

SIMPL: A System for Integrating Optimization Techniques

In recent years, the Constraint Programming (CP) and Operations Research (OR) communities have explored the advantages of combining CP and OR techniques to formulate and solve combinatorial optimization problems. These advantages include a more versatile modeling framework and the ability to combine complementary strengths of the two solution technologies. This research has reached a stage at which further development would benefit from a general-purpose modeling and solution system. We introduce here a system for integrated modeling and solution called SIMPL. Our approach is to view CP and OR techniques as special cases of a single method rather than as separate methods to be combined. This overarching method consists of an infer-relax-restrict cycle in which CP and OR techniques may interact at any stage. We describe the main features of SIMPL and illustrate its usage with examples.

A Hybrid Approach for Solving Large Scale Crew Scheduling Problems

We consider several strategies for computing optimal solutions to large scale crew scheduling problems. Provably optimal solutions for very large real instances of such problems were computed using a hybrid approach that integrates mathematical and constraint programming techniques. The declarative nature of the latter proved instrumen- tal when modeling complex problem restrictions and, particularly, in efficiently searching the very large space of feasible solutions. The code was tested on real problem instances, containing an excess of 1:8 x 109 entries, which were solved to optimality in an acceptable running time when executing on a typical desktop PC.

BDD-based heuristics for binary optimization

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.

Solving very large crew scheduling problems to optimality

In this article, we present a hybrid methodology for the exact solution of large scale real world crew scheduling problems. Our approach integrates mathematical programming and constraint satisfaction techniques, taking advantage of their particular abilities in modeling and solving specific parts of the problem. An Integer Programming framework was responsible for guiding the overall search process and for obtaining lower bounds on the value of the optimal solution. Complex constraints were easily expressed, in a declarative way, using a Constraint Logic Programming language. Moreover, with an effective constraint-based model, the huge space of feasible solutions could be implicitly considered in a fairly efficient way. Our code was tested on real problem instances arising from the daily operation of an ordinary urban transit company that serves a major metropolitan area with an excess of two million inhabitants. Using a typical desktop PC, we were able find, in an acceptable running time, an optimal solution to instances with more than 1.5 billion entries.

Improved bounds for the traveling umpire problem: A stronger formulation and a relax-and-fix heuristic

Given a double round-robin tournament, the traveling umpire problem (TUP) consists of determining which games will be handled by each one of several umpire crews during the tournament. The objective is to minimize the total distance traveled by the umpires, while respecting constraints that include visiting every team at home, and not seeing a team or venue too often. We strengthen a known integer programming formulation for the TUP and use it to implement a relax-and-fix heuristic that improves the quality of 24 out of 25 best-known feasible solutions to instances in the TUP benchmark. We also improve all best-known lower bounds for those instances and, for the first time, provide lower bounds for instances with more than 16 teams.

On the Sum Constraint: Relaxation and Applications

The global constraint sum can be used as a tool to implement summations over sets of variables whose indices are not known in advance. This paper has two major contributions. On the theoretical side, we present the convex hull relaxation for the sum constraint in terms of linear inequalities, whose importance in the context of hybrid models is then justified. On the practical side, we demonstrate the applicability of the sum constraint in a scheduling problem that arises as part of the development of new products in the pharmaceutical and agrochemical industries. This problem can be modeled in two alternative ways: by using the sum constraint in a natural and straightforward manner, or by using the element constraint in a trickier fashion. With the convex hull relaxation developed earlier, we prove that the linear relaxation obtained from the former model is tighter than the one obtained from the latter. Moreover, our computational experiments indicate that the CP model based on the sum constraint is significantly more efficient as well.