Elvin Coban

Mixed integer programming vs logic-based Benders decomposition for planning and scheduling

A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logic-based Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that described in the literature they cite and therefore results in much slower performance than previously reported. We find that when correctly implemented, the Benders method remains 2 to 3 orders of magnitude faster than the latest commercial mixed integer software on larger instances, thus reversing the conclusion of the earlier paper.

Single-Facility scheduling over long time horizons by logic-based benders decomposition

Logic-based Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size scales up. We solve single-facility non-preemptive scheduling problems with time windows and long time horizons that are divided into segments separated by shutdown times (such as weekends). The objective is to find feasible solutions, minimize makespan, or minimize total tardiness.

Single-facility scheduling by logic-based Benders decomposition

Logic-based Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size scales up. We solve single-facility non-preemptive scheduling problems with time windows and long time horizons. The Benders master problem assigns jobs to predefined segments of the time horizon, where the subproblem schedules them. In one version of the problem, jobs may not overlap the segment boundaries (which represent shutdown times, such as weekends), and in another version, there is no such restriction. The objective is to find feasible solutions, minimize makespan, or minimize total tardiness.

Logic-based benders decomposition for planning and scheduling: a computational analysis

Logic-based Benders decomposition (LBBD) has improved the state of the art for solving a variety of planning and scheduling problems, in part by combining the complementary strengths of constraint programming (CP) and mixed integer programming (MIP). We undertake a computational analysis of specific factors that contribute to the success of LBBD, to provide guidance for future implementations. We study a problem class that assign tasks to multiple resources and poses a cumulative scheduling problem on each resource. We find that LBBD is at least 1000 times faster than state-of-the-art MIP on larger instances, despite recent advances in the latter. Further, we conclude that LBBD is most effective when the planning and scheduling aspects of the problem are roughly balanced in difficulty. The most effective device for improving LBBD is the inclusion of a subproblem relaxation in the master problem. The strengthening of Benders cuts also plays an important role when the master and subproblem complexity are properly balanced. These findings suggest future research directions.

Robust Scheduling with Logic-Based Benders Decomposition

We study project scheduling at a large IT services delivery center in which there are unpredictable delays. We apply robust optimization to minimize tardiness while informing the customer of a reasonable worst-case completion time, based on empirically determined uncertainty sets. We introduce a new solution method based on logic-based Benders decomposition. We show that when the uncertainty set is polyhedral, the decomposition simplifies substantially, leading to a model of tractable size. Preliminary computational experience indicates that this approach is superior to a mixed integer programming model solved by state-of-the-art software.

Column generation approaches to a robust airline crew pairing model for managing extra flights

The airline crew pairing problem (CPP) is one of the classical problems in airline operations research due to its crucial impact on the cost structure of an airline. Moreover, the complex crew regulations and the large scale of the resulting mathematical programming models have rendered it an academically interesting problem over decades. The CPP is a tactical problem, typically solved over a monthly planning horizon, with the objective of creating a set of crew pairings so that every ight in the schedule is covered, where a crew pairing refers to a sequence of ights operated by a single crew starting and ending at the same crew base. This paper discusses how an airline may hedge against a certain type of operational disruption by incorporating robustness into the pairings generated at the planning level. In particular, we address how a set of extra fights may be added into the fight schedule at the time of operation by modifying the pairings at hand and without delaying or canceling the existing fights in the schedule. We assume that the set of potential extra fights and their associated departure time windows areknown at the planning stage. We note that this study was partially motivated during our interactions with the smaller local airlines in Turkey which sometimes have to add extra fights to their schedule at short notice, e.g., charter fights. These airlines can typically estimate the potential time windows of the extra fights based on their past experiences, but prefer to ignore this information during planning since these flights may not need to be actually operated. Typically, these extra flights are then handled by recovery procedures at the time of operation which may lead to substantial deviations from the planned crew pairings and costs. The reader is referred to [3] for an in-depth discussion of the conceptual framework of this problem which we refer to as the Robust Crew Pairing for Managing Extra Flights (RCPEF). In [3], the authors introduce how an extra flight may be accommodated by modifying the existing pairings and introduce a set of integer programming models that provide natural recovery options without disrupting the existing flights. These recovery options are available at the planning stage and render operational recovery procedures that pertain to crew pairing unnecessary

Flow-Based Combinatorial Chance Constraints

We study stochastic variants of flow-based global constraints as combinatorial chance constraints. As a specific case study, we focus on the stochastic weighted alldifferent constraint. We first show that determining the consistency of this constraint is NP-hard. We then show how the combinatorial structure of the alldifferent constraint can be used to define chance-based filtering, and to compute a policy. Our propagation algorithm can be extended immediately to related flow-based constraints such as the weighted cardinality constraint. The main benefits of our approach are that our chance-constrained global constraints can be integrated naturally in classical deterministic CP systems, and are more scalable than existing approaches for stochastic constraint programming.

Improving blood products supply through donation tailoring

Abstract Recent technological advances, called Multicomponent Apheresis, allow tailoring the blood donations based on the demand and current inventory levels of blood products. Different from the most common type of blood donation (known as Whole Blood Donation), Multicomponent Apheresis allows the donation of one or more transfusable units of one or more blood products. Considering the changing demand for blood products during a planning horizon, deferral times, perishability of blood products, and limited donor pool, Multicomponent Apheresisprovides an opportunity for increased donor utilization and hence a better managed blood supply chain. However, except some general guidelines proposed by blood donation organizations, the literature lacks analytical tools which can be used to fully explore the potential advantages of Multicomponent Apheresis, including the reduction in donation related costs and better utilization of the donor pool. In this paper, we develop models and solution approaches for tailoring the donations in order to quantify the potential benefits of Multicomponent Apheresis. More specifically, we define the Blood Donation Tailoring Problem where the objective is to minimize the total donation, inventory and disposal costs of blood products while satisfying the demand for blood products during a planning horizon by determining the donation schedule of a given donor pool. We develop a mathematical model and a column generation approach to tailor the donations. We also propose a more practical rule-of-thumb which can be easily implemented by the blood donation organizations. We compare the performances of the proposed approaches against a lower bound and the current practice at an apheresis facility. Finally, we also show that the proposed column generation approach can easily be modified to handle realistic aspects of the problem including stock-out and donor eligibility/preferences.

Blood Supply Chain Management and Future Research Opportunities

In this chapter, we discuss the challenges and research opportunities in the blood collection operations and explore the benefits of recent advances in the blood donation process. According to the regulations, donated blood has to be processed in a processing facility within 6 h of donation. This forces blood donation organizations to schedule continuous pickups from donation sites. The underlying mathematical problem is a variant of well-known Vehicle Routing Problem (VRP). The main differences are the perishability of the product to be collected, and the continuity of donations. We discuss the implications of such differences on collection routes from donation centers. Recent advances such as multicomponent apheresis (MCA) allow the donation of more than one component and/or more than one transfusable unit of each blood product. MCA provides several opportunities including (1) increasing the donor utilization, (2) tailoring the donations based on demand, and (3) reducing the infection risks in the transfusion. We also discuss MCA, its potential benefits and how to best use MCA in order to improve blood products availability and manage donation/disposal costs.