Browsing by Subject "Integer programming"

Now showing 1 - 20 of 67

Open Access
Algorithms for some discrete location problems
(2003-09) Özsoy, F. Aykut
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An integer programming model for designing causal networks
(2024-08) Haliloğlu, Ali İlhan
We propose a novel mixed integer programming formulation for the design of causal discovery networks. The model takes a set of rules that indicate sta-tistical dependency relations between features of a given dataset, the so-called d-connection and d-separation relations, and aims to fit a casual network with minimum (weighted) violations. Allowing feedback cycles and latent confounders, our formulation stands out from most of the existing attempts in the literature. Although our model can work as an unsupervised machine learning model, it possesses the necessary flexibility for the decision-maker to enter known causal relations. The performance of our model is tested with several synthetic datasets.
Open Access
Analysis of Lagrangian lower bounds for a graph partitioning problem
(Institute for Operations Research and the Management Sciences (INFORMS), 1999) Adil, G. K.; Ghosh, J. B.
Recently, Ahmadi and Tang (1991) demonstrated how various manufacturing problems can be modeled and solved as graph partitioning problems. They use Lagrangian relaxation of two different mixed integer programming formulations to obtain both heuristic solutions and lower bounds on optimal solution values. In this note, we point to certain inconsistencies in the reported results. Among other things, we show analytically that the first bound proposed is trivial (i.e., it can never have a value greater than zero) while the second is also trivial for certain sparse graphs. We also present limited empirical results on the behavior of this second bound as a function of graph density.
Open Access
Analytical loading models in flexible manufacturing systems
(Elsevier, 1993) Kırkavak, N.; Dinçer, C.
It would be difficult to efficiently implement a manufacturing system without solving its design and operational problems. Based on this framework, a system configuration and tooling problem is modeled. The model turns out to be a large mixed integer linear program, so that some alternative optimal seeking and heuristic techniques are used to solve the model for constructing a flow line structured Flexible Manufacturing System. As a result, it may be possible to construct flexible, efficient, simple and easily controllable manufacturing systems. © 1993.
Open Access
A beam search algorithm to optimize robustness under random machine breakdowns and processing time variability
(Institute of Industrial Engineers, 2007) Gören, S.; Sabuncuoğlu, İhsan
The vast majority of the machine scheduling research assumes complete information about the scheduling problem and a static environment in which scheduling systems operate. In practice, however, scheduling systems are subject to considerable uncertainty in dynamic environments. The ability to cope with the uncertainty in scheduling process is becoming increasingly important in today's highly dynamic and competitive business environments. In the literature, two approaches have appeared as the effective way: reactive and proactive scheduling. The objective in reactive scheduling is to revise schedules as necessary, while proactive scheduling attempts to incorporate future disruptions when generating schedules. In this paper we take a proactive scheduling approach to solve a machine scheduling problem with two sources of uncertainty: processing time variability and machine breakdowns. We define two robustness measures and develop a heuristic based on beam search methodology to optimize them. The computational results show that the proposed algorithms perform significantly better than a number of heuristics available in the literature.
Open Access
Binary integer formulation for mixed-model assembly line balancing problem
(Pergamon Press, 1998-04-01) Gökçen, H.; Erel, E.
The assembly line balancing problem has been a focus of interest to the academicians of production/operations management for the last 40 years. Although there are numerous studies published on the various aspects of the problem, the number of studies on mixed-model assembly lines are relatively small. In this paper, a binary integer programming model for the mixed-model assembly line balancing problem is developed and some computational properties of the model are given.
Open Access
A branch and price approach for routing and refueling station location model
(Elsevier, 2016) Yıldız, B.; Arslan, O.; Karaşan, O. E.
The deviation flow refueling location problem is to locate p refueling stations in order to maximize the flow volume that can be refueled respecting the range limitations of the alternative fuel vehicles and the shortest path deviation tolerances of the drivers. We first provide an enhanced compact model based on a combination of existing models in the literature for this relatively new operations research problem. We then extend this problem and introduce the refueling station location problem which adds the routing aspect of the individual drivers. Our proposed branch and price algorithm relaxes the simple path assumption generally adopted in the existing studies and implicitly takes into account deviation tolerances without the pregeneration of the routes. Therefore, the decrease in solution times with respect to existing models is significant and our algorithm scales very efficiently to more realistic network dimensions.
Open Access
A branch-and-cut algorithm for two-level survivable network design problems
(Elsevier, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through access networks (second network level). We consider two survivable structures in both network levels. One structure is a two-edge connected network, and the other structure is a ring. There is a limit on the number of nodes in each access network, and there are fixed costs associated with the hubs and the access and backbone links. The aim of the problem is to minimize the total cost. We give integer programming formulations and valid inequalities for the different versions of the problem, solve them using a branch-and-cut algorithm, and discuss computational results. Some of the new inequalities can be used also to solve other problems in the literature, like the plant cycle location problem and the hub location routing problem.
Open Access
A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations
(Elsevier Ltd, 2017) Ozbaygin G.; Ekin Karasan O.; Savelsbergh M.; Yaman, H.
We study the vehicle routing problem with roaming delivery locations in which the goal is to find a least-cost set of delivery routes for a fleet of capacitated vehicles and in which a customer order has to be delivered to the trunk of the customer's car during the time that the car is parked at one of the locations in the (known) customer's travel itinerary. We formulate the problem as a set-covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer's home or to the trunk of the customer's car. We evaluate the effectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the benefits of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set. © 2017 Elsevier Ltd
Open Access
Code scheduling for optimizing parallelism and data locality
(Springer, 2010-08-09) Yemliha, T.; Kandemir, M.; Öztürk, Özcan; Kultursay, E.; Muralidhara, S. P.
As chip multiprocessors proliferate, programming support for these devices is likely to receive a lot of attention in the near future. Parallelism and data locality are two critical issues in a chip multiprocessor environment. Unfortunately, most of the published work in the literature focuses only on one of these problems, and this can prevent one from achieving the best possible performance. The main goal of this paper is to propose and evaluate a compiler-directed code parallelization scheme, which considers both parallelism and data locality at the same time. Our compiler captures the inherent parallelism and data reuse in the application code being analyzed using a novel representation called the locality-parallelism graph (LPG). Our partitioning/scheduling algorithm assigns the nodes of this graph to the processors in the architecture and schedules them for execution. We implemented this algorithm and evaluated its effectiveness using a set of benchmark codes. The results collected so far indicate that our approach improves overall execution latency significantly. In this paper, we also introduce an ILP (Integer Linear Programming) based formulation of the problem, and implement the schedule obtained by the ILP solver. The results indicate that our approach gets within 4% of the ILP solution. © 2010 Springer-Verlag.
Open Access
A comparative study of computational procedures for the resource constrained project scheduling problem
(Elsevier, 1994) Oğuz, O.; Bala, H.
Performance of two new integer programming based heuristics together with some special purpose algorithms for project scheduling are tested from a computational point of view. The objective of the study is to compare the quality of solutions obtained by using these algorithms and reach conclusions about their relative merits on this specific problem. © 1994.
Open Access
Comparison of the formulations for a hub-and-spoke network design problem under congestion
(Elsevier, 2016) Kian, Ramer; Kargar, Kamyar
In this paper, we study the hub location problem with a power-law congestion cost and propose an exact solution approach. We formulate this problem in a conic quadratic form and use a strengthening method which rests on valid inequalities of perspective cuts in mixed integer nonlinear programming. In a numerical study, we compare two well known types of mathematical modeling in the hub-location problems which are solved with different branch and cut strategies. The strength and weakness of the formulations are summarized based on an extensive numerical study over the CAB data set. © 2016 Elsevier Ltd
Open Access
Compromising system and user interests in shelter location and evacuation planning
(Elsevier Ltd, 2015) Bayram V.; Tansel, B.T.; Yaman H.
Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. From the evacuation management authority's point of view, the desirable goal is to minimize the total evacuation time by computing a system optimum (SO). However, evacuees may not be willing to take long routes enforced on them by a SO solution; but they may consent to taking routes with lengths not longer than the shortest path to the nearest shelter site by more than a tolerable factor. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. As the travel time on a road segment is often modeled as a nonlinear function of the flow on the segment, the resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the importance of the number and locations of shelter sites and the trade-off between efficiency and fairness. © 2014 Elsevier Ltd.
Open Access
Constrained min-cut replication for K-way hypergraph partitioning
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014) Yazici V.; Aykanat, Cevdet
Replication is a widely-used technique in information retrieval and database systems for providing fault tolerance and reducing parallelization and processing costs. Combinatorial models based on hypergraph partitioning are proposed for various problems arising in information retrieval and database systems. We consider the possibility of using vertex replication to improve the quality of hypergraph partitioning. In this study, we focus on the constrained min-cut replication (CMCR) problem, where we are initially given a maximum replication capacity and a K-way hypergraph partition with an initial imbalance ratio. The objective in the CMCR problem is finding the optimal vertex replication sets for each part of the given partition such that the initial cut size of the partition is minimized, where the initial imbalance is either preserved or reduced under the given replication capacity constraint. In this study, we present a complexity analysis of the CMCR problem and propose a model based on a unique blend of coarsening and integer linear programming (ILP) schemes. This coarsening algorithm is derived from a novel utilization of the Dulmage-Mendelsohn decomposition. Experiments show that the ILP formulation coupled with the Dulmage-Mendelsohn decomposition-based coarsening provides high quality results in practical execution times for reducing the cut size of a given K-way hypergraph partition. © 2014 INFORMS.
Open Access
Design of translucent optical networks: Partitioning and restoration
(Kluwer, 2004) Karasan, E.; Arisoylu, M.
We discuss the problem of designing translucent optical networks composed of restorable, transparent subnetworks interconnected via transponders. We develop an integer linear programming (ILP) formulation for partitioning an optical network topology into subnetworks, where the subnetworks are determined subject to the constraints that each subnetwork satisfies size limitations, and it is two-connected. A greedy heuristic partitioning algorithm is proposed for planar network topologies. We use section restoration for translucent networks where failed connections are rerouted within the subnetwork which contains the failed link. The network design problem of determining working and restoration capacities with section restoration is formulated as an ILP problem. Numerical results show that fiber costs with section restoration are close to those with path restoration for mesh topologies used in this study. It is also shown that the number of transponders with the translucent network architecture is substantially reduced compared to opaque networks.
Open Access
Designing a road network for hazardous materials shipments
(Elsevier, 2007) Erkut, E.; Alp, O.
We consider the problem of designating hazardous materials routes in and through a major population center. Initially, we restrict our attention to a minimally connected network (a tree) where we can predict accurately the flows on the network. We formulate the tree design problem as an integer programming problem with an objective of minimizing the total transport risk. Such design problems of moderate size can be solved using commercial solvers. We then develop a simple construction heuristic to expand the solution of the tree design problem by adding road segments. Such additions provide carriers with routing choices, which usually increase risks but reduce costs. The heuristic adds paths incrementally, which allows local authorities to trade off risk and cost. We use the road network of the city of Ravenna, Italy, to demonstrate the solution of our integer programming model and our path-addition heuristic.
Open Access
The discrete resource allocation problem in flow lines
(Institute for Operations Research and the Management Sciences (INFORMS), 1995) Karabati, S.; Kouvelis, P.; Yu, G.
In this paper we address the discrete resource allocation problem in a deterministic flow line. We assume that the processing times are convex and noningcreasing in the amount of resources allocated to the machines. We consider the resource allocation problem for a fixed sequence of jobs for various performance criteria (makespan, weighted sum of completion times, cycle time for cyclic schedules) and develop a formulation of the problem as a convex program, where the number of constraints grows exponentially with the number of jobs and machines. We also present a generalization of the formulation for resource allocation problems in a cyclic directed graphs. We demonstrate that the problem is NP-complete in the strong sense and present an effective solution procedure. The solution procedure is an implicit enumeration scheme where a surrogate relaxation of the formulation is used to generate upper and lower bounds on the optimal objective function value. Finally, we address the simultaneous scheduling and resource allocation problem, and we present an approximate and iterative solution procedure for the problem.
Open Access
Double bound method for solving the p-center location problem
(Elsevier, 2013) Calik, H.; Tansel, B. C.
We give a review of existing methods for solving the absolute and vertex restricted p-center problems on networks and propose a new integer programming formulation, a tightened version of this formulation and a new method based on successive restrictions of the new formulation. A specialization of the new method with two-element restrictions obtains the optimal p-center solution by solving a series of simple structured integer programs in recognition form. This specialization is called the double bound method. A relaxation of the proposed formulation gives the tightest known lower bound in the literature (obtained earlier by Elloumi et al., [1]). A polynomial time algorithm is presented to compute this bound. New lower and upper bounds are proposed. Problems from the OR-Library [2] and TSPLIB [3] are solved by the proposed algorithms with up to 3038 nodes. Previous computational results were restricted to networks with at most 1817 nodes.
Open Access
Dynamic lot sizing with multiple suppliers, backlogging and quantity discounts
(Elsevier Ltd, 2017) Ghaniabadi, M.; Mazinani, A.
This paper studies the dynamic lot sizing problem with supplier selection, backlogging and quantity discounts. Two known discount types are considered separately, incremental and all-units quantity discounts. Mixed integer linear programming (MILP) formulations are presented for each case and solved using a commercial optimization software. In order to timely solve the problem, a recursive formulation and its efficient implementation are introduced for each case which result in an optimal and a near optimal solution for incremental and all-units quantity discount cases, respectively. Finally, the execution times of the MILP models and forward dynamic programming models obtained from the recursive formulations are presented and compared. The results demonstrate the efficiency of the dynamic programming models, as they can solve even large-sized instances quite timely. © 2017
Open Access
Energy minimizing vehicle routing problem
(Springer, 2007) Kara, İ.; Kara, Bahar Y.; Yetiş, M. K.
This paper proposes a new cost function based on distance and load of the vehicle for the Capacitated Vehicle Routing Problem. The vehicle-routing problem with this new load-based cost objective is called the Energy Minimizing Vehicle Routing Problem (EMVRP). Integer linear programming formulations with O(n 2) binary variables and O(n2) constraints are developed for the collection and delivery cases, separately. The proposed models are tested and illustrated by classical Capacitated Vehicle Routing Problem (CVRP) instances from the literature using CPLEX 8.0.