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Algorithms for the vehicle routing and scheduling problems with time window constraints
 OPERATIONS RESEARCH, VOL. 35, NO. 2. (MAR. APR., 1987)
, 1987
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Minimum power broadcast trees for wireless networks: Optimizing using the viability lemma
 in Proc. IEEE Int. Symp. on Circuits and Systems
, 2002
"... Abstract — Wireless multicast/broadcast sessions, unlike wired networks, inherently reaches several nodes with a single transmission. For omnidirectional wireless broadcast to a node, all nodes closer will also be reached. An algorithm for constructing the minimum power tree in wireless networks was ..."
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Cited by 57 (2 self)
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Abstract — Wireless multicast/broadcast sessions, unlike wired networks, inherently reaches several nodes with a single transmission. For omnidirectional wireless broadcast to a node, all nodes closer will also be reached. An algorithm for constructing the minimum power tree in wireless networks was first proposed by Wieselthier �Ø �Ð. The �ÖÓ� � �×Ø �Ò Ö�Ñ�ÒØ�Ð ÔÓÛ�Ö (BIP) algorithm suggested by them is a “nodebased ” minimumcost tree algorithm for wireless networks. We propose an alternate search based paradigm wherein minimumcost trees in wireless networks are found through a search process. Two computationally efficient procedures for checking the feasibility (viability) of a solution in the search space are presented. A straightforward procedure for initializing the search using stochastically generated trees is also proposed. I.
Vehicle dispatching with timedependent travel times

, 2003
"... Most of the models for vehicle routing reported in the literature assume constant travel times. Clearly, ignoring the fact that the travel time between two locations does not depend only on the distance traveled, but on many other factors including the time of the day, impact the application of thes ..."
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Cited by 34 (1 self)
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Most of the models for vehicle routing reported in the literature assume constant travel times. Clearly, ignoring the fact that the travel time between two locations does not depend only on the distance traveled, but on many other factors including the time of the day, impact the application of these models to realworld problems. In this paper, we present a model based on timedependent travel speeds which satisfies the "firstinâfirstout" property. An experimental evaluation of the proposed model is performed in a static and a dynamic setting, using a parallel tabu search heuristic. It is shown that the timedependent model provides substantial improvements over a model based on fixed travel times.
Static Pickup and Delivery Problems: A Classification Scheme and Survey
, 2007
"... Pickup and delivery problems constitute an important class of vehicle routing problems in which objects or people have to be collected and distributed. This paper introduces a general framework to model a large collection of pickup and delivery problems, as well as a threefield classification schem ..."
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Cited by 32 (3 self)
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Pickup and delivery problems constitute an important class of vehicle routing problems in which objects or people have to be collected and distributed. This paper introduces a general framework to model a large collection of pickup and delivery problems, as well as a threefield classification scheme for these problems. It surveys the methods used for solving them.
A BranchandCut Algorithm for the DialaRide Problem
 Operations Research
, 2003
"... In the dialaride problem, users formulate requests for transportation from a specific origin to a specific destination. Transportation is carried out by vehicles providing a shared service. The problem consists of designing a set of minimum cost vehicle routes satisfying capacity, duration, tim ..."
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Cited by 29 (5 self)
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In the dialaride problem, users formulate requests for transportation from a specific origin to a specific destination. Transportation is carried out by vehicles providing a shared service. The problem consists of designing a set of minimum cost vehicle routes satisfying capacity, duration, time window, pairing, precedence and ride time constraints. This paper introduces a mixedinteger programming formulation of the problem and a branchandcut algorithm. The algorithm uses new valid inequalities for the dialaride problem as well as known valid inequalities for the pickup and delivery and the vehicle routing problems. Computational experiments performed on randomly generated instances show that the proposed approach can be used to solve small to medium size instances.
MIP models for connected facility location: A theoretical and computational study
 Computers & Operations Research
"... This article comprises the first theoretical and computational study on mixed integer programming (MIP) models for the connected facility location problem (ConFL). ConFL combines facility location and Steiner trees: given a set of customers, a set of potential facility locations and some interconne ..."
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Cited by 16 (6 self)
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This article comprises the first theoretical and computational study on mixed integer programming (MIP) models for the connected facility location problem (ConFL). ConFL combines facility location and Steiner trees: given a set of customers, a set of potential facility locations and some interconnection nodes, ConFL searches for the minimumcost way of assigning each customer to exactly one open facility, and connecting the open facilities via a Steiner tree. The costs needed for building the Steiner tree, facility opening costs and the assignment costs need to be minimized. We model ConFL using eight compact and two exponential mixed integer programming formulations. We also show how to transform ConFL into the Steiner arborescence problem. A full hierarchy between the models is provided. For the two exponential size models we develop a branchandcut algorithm. An extensive computational study is based on two benchmark sets of randomly generated instances with up to 1,300 nodes and 115,000 edges. We empirically compare the presented models with respect to the quality of obtained bounds and the corresponding running time. We report optimal values for all but 16 instances for which the obtained gaps are below 0.6%.
Models and branchandcut algorithms for the Steiner tree problem with revenues, budget and hop constraints
, 2006
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Teaching Integer Programming Formulations Using The Traveling Salesman Problem
 SIAM REV
, 2003
"... We designed a simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem. Using commercial IP software, and a short (60 line long) Matlab code, students can optimally solve instances with up to 70 cities in a few minutes by adding cuts ..."
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Cited by 11 (0 self)
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We designed a simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem. Using commercial IP software, and a short (60 line long) Matlab code, students can optimally solve instances with up to 70 cities in a few minutes by adding cuts from the stronger formulation to the weaker, but simpler one.
A Home Health Care Routing and Scheduling Problem
, 1998
"... this paper is posed in the context of a home health care problem. Despite the fact that in this industry, health care is provided by many qualified individuals such as registered nurses, physical therapists and home health aides, for notational simplicity, we will refer to the employees as simply nu ..."
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Cited by 10 (1 self)
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this paper is posed in the context of a home health care problem. Despite the fact that in this industry, health care is provided by many qualified individuals such as registered nurses, physical therapists and home health aides, for notational simplicity, we will refer to the employees as simply nurses. The only differentiation that we make is between salaried workers (fulltime nurses) and nonsalaried workers (parttime nurses). Salaried workers are paid for a fulltime shift everyday, whether or not they are scheduled to work the entire time. They are paid overtime if they are required to work for longer than the standard shift length. Parttime nurses are paid by the hour. The differences in the nurses' qualifications are represented by a binary relationship with each patient; a nursepatient pair is thus, either a feasible match or an infeasible match. Accordingly, the nurse may be scheduled to visit the patient, or he or she may not. Additionally, a company in this industry would like to not only satisfy a customer's need for health care, but also keep the customer happy by providing dependable service (i.e. providing health care when the customer requests it). Thus, most home health care companies allow the customer to specify a time window during which he or she will be at home awaiting the requested care. In summary, the problem is to find an optimal schedule such that each nurse that is scheduled to work leaves from his or her home, visits a set of "feasible" patients within their time windows, takes a lunch break within the nurse's lunch time window, and returns home, all within the nurse's time window (which indicates the times during which the nurse is willing to work) and within the known limit on the length of a shift. The optimal schedule minimizes th...
Projection, lifting and extended formulation in integer and combinatorial optimization
 Annals of Operations Research
, 2005
"... Abstract. This is an overview of the significance and main uses of projection, lifting and extended formulation in integer and combinatorial optimization. Its first two sections deal with those basic properties of projection that make it such an effective and useful bridge between problem formulati ..."
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Cited by 10 (0 self)
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Abstract. This is an overview of the significance and main uses of projection, lifting and extended formulation in integer and combinatorial optimization. Its first two sections deal with those basic properties of projection that make it such an effective and useful bridge between problem formulations in different spaces, i.e. different sets of variables. They discuss topics like projection and restriction, the integralitypreserving property of projection, the dimension of projected polyhedra, conditions for facets of a polyhedron to project into facets of its projections, and so on. The next two sections describe the use of projection for comparing the strength of different formulations of the same problem, and for proving the integrality of polyhedra by using extended formulations or lifting. Section 5 deals with disjunctive programming, or optimization over unions of polyhedra, whose most important incarnation are mixed 01 programs and their partial relaxations. It discusses the compact representation of the convex hull of a union of polyhedra through extended formulation, the connection between the projection of the latter and the polar of the convex hull, as well as the sequential convexification of facial disjunctive programs, among them mixed 01 programs, with the related concept of disjunctive rank. Section 6 reviews liftandproject cuts, the construction of cut generating linear programs, and techniques for lifting and for strengthening disjunctive cuts. Section 7 discusses the recently discovered possibility of solving the higher dimensional cut generating linear program without explicitly constructing it, by a sequence of properly chosen pivots in the simplex tableau of the linear programming relaxation. Finally, section 8 deals with different ways of combining cuts with branch and bound, and briefly discusses computational experience with liftandproject cuts.