Showing papers on "Integer programming published in 1993"
TL;DR: In this paper, a branch-and-cut procedure for stochastic integer programs with complete recourse and first stage binary variables is presented, which is shown to provide a finite exact algorithm for a number of integer programs, even in the presence of binary variables or continuous random variables in the second stage.
598 citations
TL;DR: This article proposes a reliability model for emergency service vehicle location, based on a reliability bound on the probability of system failure, and derives a 0-1 integer programming ( IP ) optimization model, and proposes the augmentation of the IP using certain valid inequalities as a preprocessing technique, and solves theIP using a branch-and-bound procedure.
Abstract: This article proposes a reliability model for emergency service vehicle location. Emergency services planners must solve the strategic problem of where to locate emergency services stations and the tactical problem of the number of vehicles to place in each station. We view the problem from a system reliability perspective, where system failure is interpreted as the inability of a vehicle to respond to a demand call within an acceptable amount of time. Our model handles the stochastic problem aspects in a more explicit way than previous models in the literature. Based on a reliability bound on the probability of system failure, we derive a 0-1 integer programming (IP) optimization model. We propose the augmentation of the IP using certain valid inequalities as a preprocessing technique, and solve the IP using a branch-and-bound procedure. Our computational results show that the preprocessing technique is highly effective. Also, sensitivity studies show that the planner can produce a variety of different d...
272 citations
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TL;DR: A decomposition framework and a column generation scheme for solving a min-cut clustering problem that is itself an NP-hard mixed integer programming problem and some efficient solution strategies are described.
Abstract: We describe a decomposition framework and a column generation scheme for solving a min-cut clustering problem. The subproblem to generate additional columns is itself an NP-hard mixed integer programming problem. We discuss strong valid inequalities for the subproblem and describe some efficient solution strategies. Computational results on compiler construction problems are reported.
229 citations
TL;DR: Several Linear Programming (LP) and Mixed Integer Programming (MIP) models for the production and capacity planning problems with uncertainty in demand are proposed and scenario-based models for formalizing implementable policies are presented.
Abstract: Several Linear Programming (LP) and Mixed Integer Programming (MIP) models for the production and capacity planning problems with uncertainty in demand are proposed. In contrast to traditional mathematical programming approaches, we use scenarios to characterize the uncertainty in demand. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield a nonanticipative or implementable policy. Such an approach makes it possible to model nonstationarity in demand as well as a variety of recourse decision types. Two scenario-based models for formalizing implementable policies are presented. The first model is a LP model for multi-product, multi-period, single-level production planning to determine the production volume and product inventory for each period, such that the expected cost of holding inventory and lost demand is minimized. The second model is a MIP model for multi-product, multi-period, single-level production planning to help in sourcing decisions for raw materials supply. Although these formulations lead to very large scale mathematical programming problems, our computational experience with LP models for real-life instances is very encouraging.
188 citations
TL;DR: The features of Bilevel Linear Programming are reviewed by presenting prior results as well as providing new results, including the capability of the problem to formulate any piecewise linear function and its connection to other optimization problems.
178 citations
TL;DR: New integer linear programminig formulations are provided, and results on the matroidal structure of a class of combinatorial problems are developed that can solve to optimality problems involving up to 60 vertices.
Abstract: Given a complete directed graph G = V, A, the delivery man problem DMP consists of determining a Hamiltonian circuit minimizing the sum of distances along the circuit from a given vertex v1, to every vertex of V, including v1 itself. There exists a number of applications of the DMP in the fields of distribution and machine scheduling. The DMP is NP-hard. The objective of this paper is to develop new theoretical results and an exact algorithm for the problem. A new, integer linear programming formulation is provided, and results on the matroidal structure of a class of combinatorial problems are developed. These are used to derive lower bounds for the DMP. These bounds are embedded into an enumerative algorithm. The largest problems solved to optimality with the proposed algorithm involve 60 vertices. This compares favorably with previously published methods.
161 citations
TL;DR: In this article, a systematic method to derive an optimal switching plan to achieve energy loss minimization for short-term and long-term operation of distribution systems is presented, which is further divided into several subproblems to find the largest energy loss reduction among all possible switching operations between two feeders.
Abstract: A systematic method to derive an optimal switching plan to achieve energy loss minimization for short term and long term operation of distribution systems is presented. The short term optimal switching criterion is developed by binary integer programming with a branch and bound technique. An overall optimization problem is formulated for the optimal switching operation. It is further divided into several subproblems to find the largest energy loss reduction among all possible switching operations between two feeders. A quick method is applied to estimate the largest loss reduction for each feeder-pair in the distribution system during short term switching operation. The composite load profile of each feeder is derived by field tests over a one year period. After determining the hourly optimal network configuration by taking into the account the typical daily load patterns for all the distributed feeders, the long term optimal criterion for each season is derived and the corresponding critical switches are determined. >
152 citations
TL;DR: A model-based approach to nonpreemptive multi-project management problems, based on a hierarchical two-stage decomposition of the planning and scheduling process, resulting in a hierarchy of integer programming models aimed at assisting the planners in understanding the interrelations among the allocation of resources, the timing of the activities, the cash flows.
136 citations
TL;DR: In this paper, the authors analyzed the performance of constraint-expanded and multi-objective zero-one programming problems from facility siting and from other settings and analyzed for common features.
133 citations
TL;DR: The algorithm described is, in particular, a 2-approximation algorithm for the problem of minimizing the total weight of true variables, among all truth assignments to the 2-satisfiability problem, which has an identifiable subset of integer components that retain their value in an integer optimal solution of the problem.
Abstract: The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NP-complete, even when all variables are binary. This paper deals with integer linear minimization problems inn variables subject tom linear constraints with at most two variables per inequality, and with all variables bounded between 0 andU. For such systems, a 2-approximation algorithm is presented that runs in time O(mnU2 log(Un2m)), so it is polynomial in the input size if the upper boundU is polynomially bounded. The algorithm works by finding first a super-optimal feasible solution that consists of integer multiples of 1/2. That solution gives a tight bound on the value of the minimum. It furthermore has an identifiable subset of integer components that retain their value in an integer optimal solution of the problem. These properties are a generalization of the properties of the vertex cover problem. The algorithm described is, in particular, a 2-approximation algorithm for the problem of minimizing the total weight of true variables, among all truth assignments to the 2-satisfiability problem.
122 citations
TL;DR: In this article, the tabu search (TS) algorithm is used to solve the bandwidth packing problem in a capacitated graph, such that capacities are not violated and the total profit is maximized.
Abstract: The bandwidth packing (BWP) problem is a combinatorially difficult problem arising in the area of telecommunications. The problem consists of assigning calls to paths in a capacitated graph, such that capacities are not violated and the total profit is maximized. In this paper we discuss the development of a tabu search (TS) method for the BWP problem. The method makes use of an efficient implementation of the k-shortest path algorithm, that allows the identification of a controlled set of feasible paths for each call. A tabu search is then performed to find the best path assignment for each call. The TS method developed here incorporates a number of features that have proved useful for obtaining optimal and near optimal solutions to difficult combinatorial problems. We establish the effectiveness of our approach by comparing its performance in speed and solution quality to other specialized heuristics and to a standard optimization package applied to a 0-1 integer programming formulation of the problem.
TL;DR: In this article, it was shown that this procedure is inefficient when multiple constrained resources exist and that linear-integer programming is a much better planning tool and comes closder to achieving the TOC goal of maximizing throughput.
TL;DR: Problems derived from a real situation (a Belgian bank network) are solved under different scenarios: the deterministic case, and the stochastic case in which travel times are random.
TL;DR: In this article, the branch and bound solution of synthesis problems that are modeled as mixed-integer linear programming (MILP) problems is considered through symbolic integration within the numerical based branch-and-bound scheme.
TL;DR: The results indicate that the simulated annealing-based method tends to dominate the branch-and-bound algorithms and the other heuristics in terms of solution quality.
Abstract: This article presents the application of a simulated annealing heuristic to an NP-complete cyclic staff-scheduling problem. The new heuristic is compared to branch-and-bound integer programming algorithms, as well as construction and linear programming-based heuristics. It is designed for use in a continuously operating scheduling environment with the objective of minimizing the number of employees necessary to satisfy forecast demand. The results indicate that the simulated annealing-based method tends to dominate the branch-and-bound algorithms and the other heuristics in terms of solution quality. Moreover, the annealing algorithm exhibited rapid convergence to a low-cost solution. The simulated annealing heuristic is executed in a single program and does not require mathematical programming software. © 1993 John Wiley & Sons, Inc.
TL;DR: Fathoming criteria based upon the concept of a network cut originally developed to solve the duration minimization version of this problem are extended in this paper to solved the net present value problem.
TL;DR: This paper identifies some special cases of this mixed-integer bilinear programming problem which are relatively more readily solvable, even though their continuous relaxations are still nonconvex, and designs a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm.
Abstract: This paper addresses a class of problems called mixed-integer bilinear programming problems. These problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued, and they arise in various production, location—allocation, and distribution application contexts. We first identify some special cases of this problem which are relatively more readily solvable, even though their continuous relaxations are still nonconvex. For the more general case, we employ a linearization technique and design a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm. Extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm.
TL;DR: In this paper, a four-step heuristic methodology for solving the facility layout problem is presented, which combines variable partitioning and integer programming methods to generate an open field type of layout.
Abstract: This facility layout of a flexible manufacturing system (FMS) involves the positioning of cells within given boundaries, so as to minimize the total projected travel time between cells. Defining the layout includes specifying the spatial coordinates of each cell, its orientation in either a horizontal or vertical position, and the location of its load/unload point. We refer to this problem as the FMS facility layout problem (FLP). In this paper we present a four-step heuristic methodology for solving the FLP. This heuristic combines variable partitioning and integer programming methods to generate an open field type of layout.
TL;DR: A branch and bound procedure which branches upon a particular path being used for a bandwidth routing is used to solve the IP.
Abstract: We describe a column generation branch and bound procedure for optimally solving the bandwidth packing problem. The objective of this problem is to allocate bandwidth in a telecommunications network to maximize total revenue. The problem is formulated as an integer programming problem and the linear programming relaxation solved using column generation and the simplex algorithm. A branch and bound procedure which branches upon a particular path being used for a bandwidth routing is used to solve the IP. We present computational results.
TL;DR: Sufficient conditions for the (Lipschitz) continuity of the expectation of second-stage costs are given for two-stage stochastic programs, where the optimization problem in the second stage is a mixed-integer linear program.
Abstract: Sufficient conditions for the (Lipschitz) continuity of the expectation of second-stage costs are given for two-stage stochastic programs, where the optimization problem in the second stage is a mixed-integer linear program. We also present counterexamples to show that, in general, the results can no longer be maintained when relaxing assumptions as well as multivariate probability distributions for which the theory works.
TL;DR: This work considers nonlinear programs in 0–1 variables with nonlinear constraints and surveys the main approaches to their solution: linearization; algebraic methods; enumerative methods and cutting-plane methods; Enumerative methods appear to be the most promising.
Abstract: We consider nonlinear programs in 0–1 variables with nonlinear constraints and survey the main approaches to their solution: (i) linearization; (ii) algebraic methods; (iii) enumerative methods and (iv) cutting-plane methods. We also present an extensive computational comparison of algorithms of all four categories. Enumerative methods appear to be the most promising. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
TL;DR: A unified formalism is presented for the synthesis of reaction-separation systems, while ensuring optimal energy management, using a target-based approach for reactor networks.
Abstract: Previous studies on process integration have generally considered reaction and separation as processes that occur sequentially in a flowsheet. In this paper, a unified formalism is presented for the synthesis of reaction-separation systems, while ensuring optimal energy management. The synthesis model stems from a target-based approach for reactor networks due to an earlier study. It is shown that, by postulating a species-dependent residence time distribution function, one can arrive at a general representation for a reaction-separation network. Optimization of this distribution function leads to a separation profile as a function of time along the length of the reactor. The synthesis model is formulated as a mixed integer optimal control problem, where the integer variables account for the fixed costs of separation. The control profiles include the temperature, the separation profile, and residence time distribution defined for the network. Costs for maintaining a separation profile are handled through a separation index (defined to model the intensity of separation), and a fixed charge for any separation between two components in the reaction mixture. Also, using an energy targeting formulation, the maintenance of the optimal temperature profile is integrated to the energy flows within the flowsheet. Strategies based on simultaneous optimization and modelmore » solution are presented for the optimization problem and demonstrated for two case studies.« less
TL;DR: This paper introduces the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in Stochastic continuous programs.
Abstract: Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic continuous programs. Analytical as well as computational properties of the expected recourse function of simple integer recourse problems are studied. This includes sharp bounds on this function and the study of the convex hull. Finally, a finite termination algorithm is obtained that solves two classes of stochastic simple integer recourse problems.
01 Jun 1993
TL;DR: The work presented here defines a set of genetic algorithm implementation alternatives for distributed-memory computers, in which strategies with some centralization are included, and shows that implementations incurring higher overheads can produce as good or better solutions faster than than very "efficient" implementations, depending on the characteristics of the problem at hand.
Abstract: The implementation of parallel genetic algorithms raises many important issues. These issues can be divided into two main classes: genetic search quality and execution performance. In the context of parallel genetic algorithms on distributed-memory computers, performance considerations have always driven the design of implementations. Thus, centralized implementations have almost always been excluded from any consideration for distributed-memory architectures. .pp The work we present here defines a set of genetic algorithm implementation alternatives for distributed-memory computers, in which strategies with some centralization are included. Each of our implementation alternatives uses a different level of distribution of the population, from the single logically centralized population to a totally distributed set of subpopulations. .pp The design alternatives we define can be applied to the implementation of any parallel genetic algorithm. As an example of such an implementation, we study the quality of the search and the execution performance of our strategies on the 0-1 Integer Linear Programming problem, on a Transputer network. Our results show that implementations incurring higher overheads can produce as good or better solutions faster than than very "efficient" implementations, depending on the characteristics of the problem at hand. More specifically, in some cases, utilizing more centralized parallel genetic search strategies results in the fastest convergence towards the optimal solution, therefore reducing the number of generations needed by the algorithm.
TL;DR: In this article, a technique for the control of mapped quadrilateral and hexahedral meshes generated inside a collection of connected subregions is presented, where target division numbers on the subregion edges are given as input.
Abstract: A novel technique is presented for the control of mapped quadrilateral and hexahedral meshes generated inside a collection of connected subregions. Target division numbers on the subregion edges are given as input. By allowing these numbers to vary, meshes can be found which satisfy both the subregion constraints imposed by the mesh patterns being employed, and the compatibility constraints on edges shared by two or more adjacent subregions. Among all such feasible solutions the optimal one is obtained by minimizing the changes to the division numbers, using an integer programming technique.
TL;DR: A practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of Lovasz and Scarf (1988), which allows us to avoid the ellipsoidal approximations required in Lenstra's algorithm.
Abstract: In recent years many advances have been made in solution techniques for specially structured 0–1 integer programming problems. In contrast, very little progress has been made on solving general (mixed) integer problems. This, of course, is not true when viewed from the theoretical side: H. W. Lenstra (1983) made a major breakthrough, obtaining a polynomial-time algorithm when the number of integer variables is fixed. We discuss a practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of L. Lovasz and H. E. Scarf (1988). This method allows us to avoid the ellipsoidal approximations required in Lenstra's algorithm. We report on the solution of a number of small (but difficult) examples, with up to 100 integer variables. Our computer code uses the linear programming optimizer CPLEX as a subroutine to solve the linear programming problems that arise. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under I...
Journal Article•
TL;DR: A mixed integer linear programming model is formulated and a Lagrangian relaxation-based procedure is developed to solve the problem of determining optimal purchasing and shipping quantities for arborescent, multi-echelon physical distribution systems with deterministic, time-varying demands.
Abstract: We consider the problem of determining optimal purchasing and shipping quantities over a finite planning horizon for arborescent, multi-echelon physical distribution systems with deterministic, time-varying demands. We assume that the inventory holding cost at a given warehouse of the distribution network is a linear function of the inventory level, and that the total procurement cost (i.e., ordering, plus purchasing, plus transportation and reception costs) is a general piecewise-linear function of the quantities shipped to and from the warehouse. We formulate a mixed integer linear programming model of the problem and develop a Lagrangian relaxation-based procedure to solve it. We show computational results for problems with 12 periods, up to 15 warehouses, and 3 transportation price ranges.