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47

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August 2008 - present

## Publications

Publications (47)

The capacitated vehicle routing problem with stochastic demands (CVRPSD) is a variant of the deterministic capacitated vehicle routing problem where customer demands are random variables. While the most successful formulations for several deterministic vehicle-routing problem variants are based on a set-partitioning formulation, adapting such formu...

The Capacitated Vehicle Routing Problem (CVRP) consists of finding the cheapest way to serve a set of customers with a fleet of vehicles of a given capacity. While serving a particular customer, each vehicle picks up its demand and carries its weight throughout the rest of its route. While costs in the classical CVRP are measured in terms of a give...

In this study we present an optimization problem where machine scheduling and personnel allocation decisions are solved simultaneously. The machine scheduling consists of solving a variant of the job shop problem where jobs are allocated in batches and multitasking is allowed. On the other hand, the personnel allocation problem searches for the opt...

Uncertainty modelling is key to obtain a realistically feasible solution for large-scale optimization problems. In this study, we consider two-stage stochastic programming to model discrete-time batch process operations with a type II endogenous (decision dependent) uncertainty, where time of uncertainty realizations are dependent on the model deci...

Periodic rescheduling is a commonly used method for scheduling short-term operations. Through computational experiments that vary plant parameters, such as the load and the capacity of a facility, we investigate the effects these parameters have on plant performance under periodic rescheduling. The results show that choosing a suitable rescheduling...

Choosing an efficient time representation is an important consideration when solving short-term scheduling problems. Improving the efficiency of scheduling operations may lead to increased yield, or reduced makespan, resulting in greater profits or customer satisfaction. When formulating these problems, one must choose a time representation for exe...

Split cuts are arguably the most effective class of cutting planes within a branch-and-cut framework for solving general Mixed-Integer Programs (MIP). Sparsity, on the other hand, is a common characteristic of MIP problems, and it is an important part of why the simplex method works so well inside branch-and-cut. In this work, we evaluate the stren...

Craniosynostosis, a condition affecting 1 in 2000 infants, is caused by premature fusing of cranial vault sutures, and manifests itself in abnormal skull growth patterns. Left untreated, the condition may lead to severe developmental impairment. Standard practice is to apply corrective cranial bandeau remodeling surgery in the first year of the inf...

This work contemplates the optimal scheduling of multi-tasking production environments where the processing tasks are subject to uncertain success rates. Such problems arise in many industrial applications that have the potential to yield non compliant products, which must then be reprocessed. We address this problem by mapping the multi-tasking se...

This study addresses short-term scheduling problems with throughput and makespan as conflicting objectives, focusing on a priori multi-objective methods. Two contributions are presented. The first contribution is to propose a priori methods based on the hybridization of compromise programming and the ε-constraint method that have computational bene...

The basis matrices corresponding to consecutive iterations of the simplex method only differ in a single column. This fact is commonly exploited in current linear programming solvers to avoid having to compute a new factorization of the basis at every iteration. Instead, a previous factorization is updated to reflect the modified column. Several me...

When generating cutting-planes for mixed-integer programs from multiple rows of the simplex tableau, the usual approach has been to relax the integrality of the non-basic variables, compute an intersection cut, then strengthen the cut coefficients corresponding to integral non-basic variables using the so-called trivial lifting procedure. Although...

We consider the problem of generating inequalities that are valid for one-row relaxations of a simplex tableau, with the integrality constraints preserved for one or more non-basic variables. These relaxations are interesting because they can be used to generate cutting planes for general mixed-integer problems. We first consider the case of a sing...

This paper describes the development and implementation of an optimization model to solve the integrated problem of personnel allocation and machine scheduling for industrial size multipurpose plants. Although each of these problems has been extensively studied separately, works that study an integrated approach are very limited, particularly for l...

Let E be a finite set of elements, and let L be a clutter over ground set E. We say distinct elements e, f are opposite if every member and every minimal cover of L contains at most one of e, f. In this paper, we investigate opposite elements and reveal a rich theory underlying such a seemingly simple restriction. The clutter C obtained from L afte...

The resolution of integer programming problems is typically performed via branch and bound. Nodes of the branch-and-bound tree are pruned whenever the corresponding subproblem is proven not to contain a solution better than the best solution found so far. This is a key ingredient for achieving reasonable solution times. However, since subproblems a...

A key decision in scheduling problems is deciding when to perform certain operations and the quality of solutions depends on how time is represented. The two main classes of time representation are discrete-time approaches (with uniform or non-uniform discretization schemes) and continuous-time approaches. In this work, we compare the performance o...

We study the chance-constrained vehicle routing problem (CCVRP), a version of the vehicle routing problem (VRP) with stochastic demands, where a limit is imposed on the probability that each vehicle’s capacity is exceeded. A distinguishing feature of our proposed methodologies is that they allow correlation between random demands, whereas nearly al...

The pollution-routing problem (PRP) aims to determine a set of routes and speed over each leg of the routes simultaneously to minimize the total operational and environmental costs. A common approach to solve the PRP exactly is through speed discretization, i.e., assuming that speed over each arc is chosen from a prescribed set of values. In this p...

Short-term scheduling in multipurpose batch plants has received significant attention in the past two decades. Both discrete-time and continuous-time formulations have been proposed to model the problem; however, multipurpose plants that have machines with the ability to process multiple tasks at the same time, i.e. multitasking, have been overlook...

We study the chance-constrained vehicle routing problem (CCVRP), a version of the vehicle routing problem (VRP) with stochastic demands, where a limit is imposed on the probability that each vehicle’s capacity is exceeded. A distinguishing feature of our proposed methodologies is that they allow correlation between random demands, whereas nearly al...

Classic vehicle routing models usually treat fuel cost as input data, but fuel consumption heavily depends on the travel speed, which leads to the study of optimizing speeds over a route to improve fuel efficiency. In this paper, we propose a joint vehicle routing and speed optimization problem to minimize the total operating cost including fuel co...

Cranio-orbital remodeling aims to correct the dysmorphic skull associated with craniosynostosis. Traditionally, the skull is reconstructed into a shape that is subjectively normal according to the surgeon's perception. We present a novel technique using a mathematical algorithm to define the optimal location for bony osteotomies and to objectively...

We study a variant of the capacitated vehicle routing problem where the cost over each arc is defined as the product of the arc length and the weight of the vehicle when it traverses that arc. We propose two new mixed-integer linear programming formulations for the problem: an arc-load formulation and a set partitioning formulation based on q-route...

Success of companies in the scientific services sector highly relies on the effective scheduling of operations as large numbers of samples from customers are received and analyzed and reports are generated for each sample. Therefore, it is extremely important to efficiently use all the various resources (labor and machine) for such facilities to re...

The mixing set with a knapsack constraint arises as a substructure in
mixed-integer programming reformulations of chance-constrained programs with
stochastic right-hand-sides over a finite discrete distribution. Recently,
Luedtke et al. (2010) and K\"u\c{c}\"ukyavuz (2012) studied valid inequalities
for such sets. However, most of their results wer...

We propose algorithms to compute tight lower bounds and high quality upper bounds (UBs) for the multilevel capacitated minimum spanning tree problem. We first develop a branch-and-cut algorithm, introducing some new features: (i) the exact separation of cuts corresponding to some master equality polyhedra found in the formulation; (ii) the separati...

In recent years there has been growing interest in generating valid inequalities for mixed-integer programs using sets with two or more constraints. In particular, Andersen et al. (2007) [2] and Borozan and Cornuéjols (2009) [3] have studied sets defined by equations that contain exactly one integer variable per row. The integer variables are not r...

Gomory cuts have played an important role in integer and mixed-integer programming for over 50 years. This article reviews these much studied cuts, surveying some of the research that has been done over the years as well as looks into new research directions that have appeared in the last few years.

Lifting, tilting and fractional programming, though seemingly different, reduce to a common optimization problem. This connection allows us to revisit key properties of these three problems on mixed integer linear sets. We introduce a simple common framework for these problems, and extend known results from each to the other two.

The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP),
where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of
vertices can be solved routinely, there are very challenging TDTSP instances with less than 60 vertic...

We describe a simple process for generating numerically safe cutting planes using floating-point arithmetic and the mixed-integer rounding (MIR) procedure. Apply- ing this method to the rows of the simplex tableau permits the generation of Gomory mixed-integer cuts that are guaranteed to be satisfied by all feasible solutions to a mixed-integer pro...

The master equality polyhedron (MEP) is a canonical set that generalizes the master cyclic group polyhedron (MCGP) of Gomory.
We recently characterized a nontrivial polar for the MEP, i.e., a polyhedron T such that an inequality defines a nontrivial facet of the MEP if and only if its coefficient vector forms a vertex of T. In this paper, we study...

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The
variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence problem in order to make
it solvable in pseudo-polynomial time. Traditional inequalities over the arc...

We study the Master Equality Polyhedron (MEP) which generalizes the Master Cyclic Group Polyhedron and the Master Knapsack
Polyhedron.
We present an explicit characterization of the nontrivial facet-defining inequalities for MEP. This result generalizes similar
results for the Master Cyclic Group Polyhedron by Gomory[9] and for the Master Knapsack...

During the last decades, much research has been conducted deriving classes of valid inequalities for single-row mixed integer programming polyhedrons. However, no such class has had as much practical success as the MIR inequality when used in cutting plane algorithms for general mixed integer programming problems. In this work we analyze this empir...

We study the master equality polyhedron (MEP) which generalizes the
master cyclic group polyhedron (MCGP) and the master knapsack polyhedron (MKP).
We present an explicit characterization of the polar of the nontrivial facet-defining
inequalities for MEP. This result generalizes similar results for the MCGP by Gomory
(1969) and for the MKP by Araóz...

The best exact algorithms for the capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the...

The best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean
relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection
of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the...

A pervasive problem in freight railroad operations is to determine a feasible flow of cars to meet the required demands within a certain period of time. In this work we present a method to determine an optimal flow of loaded and empty cars in order to maximize profits, revenue or tonnage transported, given the schedule of the trains, together with...

During the last decades, much research has been conducted on deriving classes of valid inequalities for mixed integer knapsack
sets, which we call knapsack cuts. Bixby etal. (The sharpest cut: the impact of Manfred Padberg and his work. MPS/SIAM Series on Optimization, pp. 309–326,
2004) empirically observe that, within the context of branch-and-cu...

The best exact algorithms for the capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the...

We describe a simple process for generating numerically accurate cutting planes using floating-point arithmetic and the mixed-integer rounding (MIR) procedure. Applying this method to the rows of the simplex tableau permits the generation of Gomory mixed- integer cuts that are guaranteed to be satisfied by all feasible solutions to a mixed-integer...

Single-row mixed-integer programming (MIP) problems have been studied thoroughly under many different perspectives over the years. While not many practical applications can be modeled as a single-row MIP, their importance lies in the fact that they are simple, natural and very useful relaxations of generic MIPs. This thesis will focus on such MIPs...