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In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running times and are faster than some metaheuristics. Pairwise relative strength of the LP relaxations of these formulations are also analyzed from theoretical and experimental points of view. Finally, we present a new metaheuristic algorithm to solve QAP-R1 along with its computational analysis. Our study offers the first systematic experimental analysis of integer-programming models and heuristics for QAP-R1. The benchmark instances with various characteristics generated for our study are made available to the public for future research work. Some new polynomially solvable special cases are also introduced. Summary of Contribution: This paper aims to advance our knowledge and ability in solving an important special case of the quadratic assignment problem. It shows how to exploit inherent properties of an optimization problem to achieve computational advantages, a strategy that was followed by researchers in model building and algorithm developments for decades. Our computational results attest to this time-tested general philosophy. The paper presents the first systematic computational study of the rank one quadratic assignment problem, along with new mathematical programming models and complexity analysis. We believe the theoretical and computational results of this paper will inspire further research on the topic and will be of significant value to practitioners using rank one quadratic assignment models. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for an integrated operating room planning and scheduling problem. It combines the assignment of surgeries to operating rooms and scheduling over a short-term planning horizon. This integration results in more stable planning through consideration of the operational details at the scheduling level, and this increases the chance of successful implementation. We take into account the maximum daily working hours of surgeons, prevent the overlapping of surgeries performed by the same surgeon, allow time for the obligatory cleaning when switching from infectious to noninfectious cases, and respect the surgery deadlines. We formulate the problem using a mathematical programming model and develop a branch-and-price-and-cut algorithm based on a constraint programming model for the subproblem. We also develop dominance rules and a fast infeasibility-detection algorithm based on a multidimensional knapsack problem to improve the efficiency of the constraint programming model. The computational results show that our method has an average optimality gap of 2.81% and significantly outperforms a compact mathematical formulation in the literature. [ABSTRACT FROM AUTHOR]

In two-sided matching markets, the concept of stability proposed by Gale and Shapley is one of the most important solution concepts. In this paper, we consider a problem related to stability of a matching in a two-sided matching market with indifferences. It is known that stability does not guarantee Pareto efficiency in a two-sided matching market with indifferences. However, Erdil and Ergin proved that there always exists a stable and Pareto efficient matching in a many-to-one matching market with indifferences and gave a polynomial-time algorithm for finding it. Later on, Chen proved that there always exists a stable and Pareto efficient matching in a many-to-many matching market with indifferences and gave a polynomial-time algorithm for finding it. In this paper, we propose a new approach to the problem of finding a stable and Pareto efficient matching in a many-to-many matching market with indifferences. Our algorithm is an alternative proof of the existence of a stable and Pareto efficient matching in a many-to-many matching market with indifferences. [ABSTRACT FROM AUTHOR]

Lately, the problem of cell formation (CF) has gained a lot of attention in the industrial engineering literature. Since it was formulated (more than 50 years ago), the problem has incorporated additional industrial factors and constraints while its solution methods have been constantly improving in terms of the solution quality and CPU times. However, despite all the efforts made, the available solution methods (including those for a popular model based on the p-median problem, PMP) are prone to two major types of errors. The first error (the modeling one) occurs when the intended objective function of the CF (as a rule, verbally formulated) is substituted by the objective function of the PMP. The second error (the algorithmic one) occurs as a direct result of applying a heuristic for solving the PMP. In this paper we show that for instances that make sense in practice, the modeling error induced by the PMP is negligible. We exclude the algorithmic error completely by solving the adjusted pseudo-Boolean formulation of the PMP exactly, which takes less than one second on a general-purpose PC and software. Our experimental study shows that the PMP-based model produces high-quality cells and in most cases outperforms several contemporary approaches. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form max {u(y) y = (y1,…yn ∈ y1 x … x yn} i.e., in which the feasible region is a Cartesian product of finite sets y1 i ∈ N = (1, …, n). The contributions of this paper are twofold. In the first part of the paper, we broaden the existing results on convergence properties of the fictitious play algorithm on games with identical payoffs to include an approximate fictitious play algorithm that allows for errors in players 'best replies. Moreover, we introduce sampling-based approximate fictitious play that possesses the above convergence properties, and at the same time provides a computationally efficient method for implementing fictitious play. In the second part of the paper, we motivate the use of algorithms based on sampled fictitious play to solve optimization problems in the above form with particular focus on the problems in which the objective function u(·) comes from a "black box," such as a simulation model, where significant computational effort is required for each function evaluation. [ABSTRACT FROM AUTHOR]

Vehicle scheduling is the process of assigning vehicles to a set of predetermined trips with fixed starting and ending times, while minimizing capital and operating costs. This paper considers modeling, algorithmic, and computational aspects of the polynomially solvable case in which there is a single depot and vehicles are identical. A quasiassignment formulation is reviewed and an alternative asymmetric assignment formulation is given. The main contributions of the paper area new two-phase approach which is valid in the case of a special cost structure, an auction algorithm for the quasiassignment problem, a core-oriented approach, and an extensive computational study. New algorithms are compared with the most successful algorithms for the vehicle-scheduling problem, using both randomly generated and real-life data. The new algorithms show a significant performance improvement with respect to computation time. Such improvement can, for example, be very important when this particular vehicle-scheduling problem appears as a subproblem in more complex vehicle- and crew-scheduling problems. [ABSTRACT FROM AUTHOR]

In public policy decision making and in capital planning fractional criterion functions occur. For a given set of desirable target values (goals) τi, this paper develops an algorithm for solving a nonconvex programming problem of the type: Minx∈S Maxi{&phii(fi(x)/gi(x) - τi), i = 1,..., m} where fi are convex functions, gi, are concave functions over the convex subset S of Rn and φi are nondecreasing gauge functions. Here φi(&middot) is the penalty incurred whenever the fractional objective fi/gi deviates from the target value τi, the problem is then to choose an x that minimizes the maximum penalty incurred. [ABSTRACT FROM AUTHOR]

This paper combines two rival preference modeling techniques in a new approach to multi-attribute decision making. Currently existing multi-attribute procedures use either global or local preference modeling. In the global modeling technique, a single preference function is constructed in the large; its maximum is the optimal alternative. In the local procedure, sequential approximations of the preference function are constructed in the small. Each approximation generates a trial solution. Under suitable conditions, each trial solution is preferred to its predecessor, so the trial sequence eventually reaches the optimum. Each technique has advantages and disadvantages; this paper combines the desirable features of both techniques in a new improved method. This new method, called the proxy approach, uses the advantages of one technique to overcome the disadvantages of the other. This paper first develops the theoretical aspects of the proxy approach and then compares it to existing procedures. Finally, the proxy algorithm is applied to a curriculum planning problem and numerous insights are gained. [ABSTRACT FROM AUTHOR]

This paper studies the linear programming problem in which all coefficients (even those of the stipulations matrix) are rational functions of a single parameter t called ‘time,’ and provides an algorithm that can serve problems of the following two types: (1) Steady-state behavior [the algorithm can be used to determine the functional form x(t) of the optimal solution as a function of t, this form being valid for all ‘sufficiently large’ values of t], and (2) sensitivity analysis [if a value t0 of ‘time’ is given, the algorithm can be used to determine the two possible functional forms of the optimal solution for all values of t ‘sufficiently dose’ to t0 (the first functional form valid for t«t0, the second for t»t0)]. In addition, the paper gives certain qualitative information regarding steady-state behavior, including the following result: If for some one of the properties of consistency, boundedness, or bounded constraint set, there exists a sequence tn↗+∞ such that the linear program at tn has this property for all n, then the program has this property for all ‘sufficiently large’ values of t. [ABSTRACT FROM AUTHOR]

This paper introduces the multiconstraint team orienteering problem with multiple time windows (MC-TOP-MTW). In the MC-TOP-MTW, a set of vertices is given, each with a service time, one or more time windows, and a score. The goal is to maximize the sum of the collected scores, by a fixed number of tours. The tours are limited in length and restricted by the time windows and additional constraints. Next to a mathematical formulation of the MC-TOP-MTW, the main contribution of this paper is a fast and effective algorithm for tackling this problem, by hybridizing iterated local search with a greedy randomized adaptive search procedure. On a large test set, an average run has a score gap of only 5.19% with known high quality solutions, using 1.5 seconds of computational time. For 32% of the test instances, the known high quality solution was found or improved. This solution method also performs well on test instances of the TOPTW, the selective vehicle routing problem with time windows, and the MC-TOP-TW. A sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in the parameter settings. [ABSTRACT FROM AUTHOR]

Our primary query is to find conditions under which the closure of a preorder on a topological space remains transitive. We study this problem for translation invariant preorders on topological groups. The results are fairly positive; we find that the closure of preorders and normal orders remain as such in this context. The same is true for factor orders as well under quite general conditions. In turn, in the context of topological linear spaces, these results allow us to obtain a simple condition under which the order-duals with respect to a vector order and its closure coincide. Various order-theoretic applications of these results are also provided in the paper. [ABSTRACT FROM AUTHOR]

In the generalized assignment problem (gap), a set of jobs seek to be assigned to a set of machines. For every job-machine pair, there are a specific value and an accommodated capacity for the assignment. The objective is to find an assignment that maximizes the total sum of values given that the capacity constraint of every machine is satisfied. The gap is a classic optimization problem and has been studied extensively from the algorithmic perspective. Dughmi and Ghosh [Dughmi S, Ghosh A (2010) Truthful assignment without money. ACM Conf. Electronic Commerce (ACM, New York), 325-334.] proposed the game theoretical framework in which every job is owned by a selfish agent who aims to maximize the value of his own assignment. They gave a logarithmic approximation truthful in expectation mechanism and left open the problem whether there exists a truthful mechanism with a constant approximation factor. In this paper, we give an affirmative answer to this question and provide a constant approximation mechanism that enjoys a stronger incentive property of universal truthfulness than that of truthfulness in expectation. Our mechanism is inspired by stable matching, which is a fundamental solution concept in the context of matching marketplaces. The mechanism uses a stable matching algorithm as a critical component and adopts other approaches like random sampling. [ABSTRACT FROM AUTHOR]

Given a simple and undirected graph, nonnegative node weights, a nonnegative integer j, and a positive integer k, a k-matching in the graph is a subgraph with no isolated nodes and with maximum degree no more than k, a j-restricted k-matching is a k-matching with each connected component having at least j C1 edges, and the total node weight of a j-restricted k-matching is the total weight of the nodes covered by the edges in the j-restricted k-matching. When j D1 and k D2, Kaneko [Kaneko A (2003) A necessary and sufficient condition for the existence of a path factor every component of which is a path of length at least two. J. Combin. Theory, B 88:195-218] and Kano et al. [Kano M, Katona G, Király Z (2005) Packing paths of length at least two. Discrete Math. 283:129-135] studied the problem of maximizing the number of nodes covered by the edges in a 1-restricted 2-matching. In this paper, we consider the problem of finding a j-restricted k-matching with the maximum total node weight. We present a polynomial-time algorithm for the problem as well as a min-max theorem in the case of j < k. We also prove that, when j < k < 2, the problem of maximizing the number of nodes covered by the edges in a j-restricted k-matching is NP-hard. [ABSTRACT FROM AUTHOR]

We present a new computational approach to the problem of placing n identical nonoverlapping disks in the unit square in such a way that their radii are maximized. The problem has been studied in a large number of papers, from both a theoretical and a computational point of view. In this paper, we conjecture that the problem possesses a so-called funneling landscape, a feature that is commonly found in molecular conformation problems. Based on this conjecture, we develop a stochastic search algorithm that displays excellent numerical performance. Thanks to this algorithm, we could improve over previously known putative optima in the range n ≤ 130 in as many as 32 instances, the smallest of which is n=53. [ABSTRACT FROM AUTHOR]

This paper presents the spiral array model and its associated algorithms for tonal induction, approximation, and segmentation. The spiral array is a geometric model for tonality that clusters perceptually similar tonal entities. The model summarizes music information as interior points inside an array of spirals. Distances in the spiral array space are used to quantify tonal similarity. The paper traces the evolution, and presents general forms, of the existing algorithms for key finding, pitch spelling, and segmentation, and proposes a new O(n) algorithm, Argus, for tonal segmentation. The proposed algorithm computes a value that quantifies the discrepancy between the local contexts in the future and past at each point in time. Discrepancy values exceeding control thresholds are shown to mark the segmentation boundaries of the test set that concur with expert analyses. A number of window sizes and threshold settings are investigated. The algorithm is demonstrated using Edward MacDowell's To A Wild Rose and tested on Franz Schubert's Allegretto from Moment Musical D780 No. 6 and Thema from Impromptu D935 No. 4. The algorithm accurately locates tonal boundaries in all three case studies. [ABSTRACT FROM AUTHOR]

We consider online versions of the traveling salesman problem (TSP) and traveling repairman problem (TRP) where instances are not known in advance. Cities (points) to be visited are revealed over time, while the server is en route serving previously released requests. These problems are known in the literature as the online TSP (TRP, respectively). The corresponding offline problems are the TSP (TRP) with release dates, problems where each point has to be visited at or after a given release date. In the current literature, the assumption is that a request becomes known at the time of its release date. In this paper we introduce the notion of a request's disclosure date, the time when a city's location and release date are revealed to the server. In a variety of disclosure date scenarios and metric spaces, we give new online algorithms and quantify the value of this advanced information in the form of improved competitive ratios. We also provide a general result on polynomial-time online algorithms for the online TSP. [ABSTRACT FROM AUTHOR]

Compound option valuation formulae give rise to the summation of a series of multinormal distribution functions. This paper presents an identity on sums of nested multinormal distributions of arbitrary dimension. We show that this identity generalizes some well-known low order identities for the multinormal distribution. We present three applications of the new identity to contingent claims valuation problems. The first and second applications show that by reducing significantly the number of integrals to be evaluated, faster and more accurate algorithms can be developed for implementing the Geske-Johnson American put valuation formula and the Roll-Geske-Whaley American call formula; the third gives new economic insights into the valuation of disaggregated coupon bonds. [ABSTRACT FROM AUTHOR]

This paper extends recent work on finding the stochastic queue median (SQM) on a network. The SQM is the optimal location of a single mobile server, when idle, who travels to customers in response to requests for service. Customer demands are limited to the nodes of the network and their requests for service arrive according to a time homogeneous Poisson process, independently from each node. When a service request finds the server busy with a previous customer, it is entered into an M/G/1 queue that is depleted in a first-in, first-out (FIFO) manner. The SQM is the point on the network at which the sum of mean queueing delay and mean travel time is minimized. In this paper the transportation network is restricted to be a tree. By discovering and exploiting convex properties of the objective function and related functions, an efficient finite-step algorithm is found for locating the SQM on a tree. [ABSTRACT FROM AUTHOR]

In this paper we consider linear multiple objective programs with coefficients of the criteria given by intervals. This class of problems is of practical interest since in many instances it is difficult to determine precisely the coefficients of the objective functions. A subproblem to test if a feasible extreme point is efficient in the problem considered is obtained. A branch and bound algorithm to solve the subproblem as well as computational results are provided. Extensions are discussed. [ABSTRACT FROM AUTHOR]

This paper considers optimization problems with a nonlinear-additive objective function and a single linear constraint. Such models have numerous direct applications and serve as subproblems in procedures for more complex problems. Some important portfolio selection problems can be expressed in this form, and the problem also arises in economic theory. Several authors have noticed independently that special cases and variants of the problem can be solved exactly by surprisingly simple, finite algorithms. The major purpose of this paper is to present these results in a unified framework, which then permits substantial generalizations and extensions. The results lend themselves to an appealing managerial interpretation, similar to the rate-of-return cutoff rules of capital budgeting. [ABSTRACT FROM AUTHOR]

The most popular approach to developing mathematical models of organizational decision processes, the decomposition approach, begins with a mathematical statement of an ideal organizational problem and follows a process of decomposition to derive sub-problems solved by separate units at (possibly) different levels of the organization. Conversely, the composition approach starts with mathematical statements of the subproblems solved by the separate units and proceeds to develop a solution algorithm as a means of coordinating the activities of the separate units. A process of composition must then be followed if one is to discover the derived, organizational problem actually solved. This paper offers an operational definition of an organizational decision process and relates this process to the anatomy of mathematical models purported as being representative of it. Implications regarding the potential of the decision process models as tools of organizational design are explored. [ABSTRACT FROM AUTHOR]

This paper presents a systematic procedure for obtaining the optimum packaging frequencies for a number of items which are manufactured jointly but packaged individually immediately after manufacture. The method described in the paper is equally applicable to those problems where the optimum purchasing policy is to be obtained for a number of items procured from a single supplier. An example involving twenty jointly replenished items is solved to illustrate the procedure given in the paper. [ABSTRACT FROM AUTHOR]

This paper formulates the optimal control problem for a class of mathematical models in which the system to be controlled is characterized by a finite-state discrete-time Markov process. The states of this internal process are not directly observable by the controller; rather, he has available a set of observable outputs that are only probabilistically related to the internal state of the system. The formulation is illustrated by a simple machine-maintenance example, and other specific application areas are also discussed. The paper demonstrates that, if there are only a finite number of control intervals remaining, then the optimal payoff function is a piecewise-linear, convex function of the current state probabilities of the internal Markov process. In addition, an algorithm for utilizing this property to calculate the optimal control policy and payoff function for any finite horizon is outlined. These results are illustrated by a numerical example for the machine-maintenance problem. [ABSTRACT FROM AUTHOR]

Peleg established a fundamental theorem which says that convex effectivity functions are stable. He also proved its partial converse: Within the class of maximal effectivity functions, stability implies convexity. The present paper provides another partial converse: Within the class of α-effectivity functions derived from extensive game forms (without chance moves), stability implies convexity. It also provides a geometric characterization of the stability condition for the latter class. [ABSTRACT FROM AUTHOR]

Expert judgment is frequently used to assess parameter values of quantitative management science models, particularly in decision-making contexts. Experts can, however, only be expected to assess observable quantities, not abstract model parameters. This means that we need a method for translating expert assessed uncertainties on model outputs into uncertainties on model parameter values. This process is called probabilistic inversion. The probability distribution on model parameters obtained in this way can be used in a variety of ways, but in particular in an uncertainty analysis or as a Bayes prior. This paper discusses computational algorithms that have proven successful in various projects and gives examples from environmental modelling and banking. Those algorithms are given a theoretical basis by adopting a minimum information approach to modelling partial information. The role of minimum information is two-fold: It enables us to resolve the problem of nonuniqueness of distributions given the information we have, and it provides numerical stability to the algorithm by guaranteeing convergence properties. [ABSTRACT FROM AUTHOR]

In this paper we introduce the problem of shunting passenger train units in a railway station. Shunting occurs whenever train units are temporarily not needed to operate a given timetable. We discuss several aspects of this problem and focus on two subproblems. We propose mathematical models for the problem and both subproblems, one of which is solved with a solution method based on column generation. Furthermore, we introduce a new efficient and speedy solution technique for pricing problems in column generation algorithms. Finally, we present computational results based on real-life instances from Netherlands Railways. [ABSTRACT FROM AUTHOR]

This paper describes a practical algorithm based on Monte Carlo simulation for the pricing of multi- dimensional American (i.e., continuously exercisable) and Bermudan (i.e., discretely exercisable) options. The method generates both lower and upper bounds for the Bermudan option price and hence gives valid confidence intervals for the true value. Lower bounds can be generated using any number of primal algorithms. Upper bounds are generated using a new Monte Carlo algorithm based on the duality representation of the Bermudan value function suggested independently in Haugh and Kogan (2004) and Rogers (2002). Our proposed algorithm can handle virtually any type of process dynamics, factor structure, and payout specification. Computational results for a variety of multifactor equity and interest-rate options demonstrate the simplicity and efficiency of the proposed algorithm. In particular, we use the proposed method to examine and verify the tightness of frequently used exercise rules in Bermudan swaption markets. [ABSTRACT FROM AUTHOR]

In this paper, we consider an integer convex optimization problem where the objective function is the sum of separable convex functions (that is, of the form ∑[sub(i,j)∈Q]F[subij](W[subij])+∑[subi∈P]B[subi](µ[subi])), the constraints are similar to those arising in the dual of a minimum cost flow problem (that is, of the form µ[subi]-µ[subj]≤w[subij],(i,j)∈Q) with lower and upper bounds on variables. Let n =|P| m =|Q|, and U be the largest magnitude in the lower and upper bounds of variables. We call this problem the convex cost integer dual network flow problem. In this paper, we describe several applications of the convex cost integer dual network flow problem arising in a dial-a-ride transit problem, inverse spanning tree problem, project management, and regression analysis. We develop network flow-based algorithms to solve the convex cost integer dual network flow problem. We show that using the Lagrangian relaxation technique, the convex cost integer dual network flow problem can be transformed into a convex cost primal network flow problem where each cost function is a piecewise linear convex function with integer slopes. Its special structure allows the convex cost primal network flow problem to be solved in O(nmlog(n²/m)log (nU) time. This time bound is the same time needed to solve the minimum cost flow problem using the cost-scaling algorithm, and is also is best available time bound to solve the convex cost integer dual network flow problem. [ABSTRACT FROM AUTHOR]

One of the basic assumptions of the classical dynamic lot-sizing model is that the aggregate demand of a given period must be satisfied in that period. Under this assumption, if backlogging is not allowed, then the demand of a given period cannot be delivered earlier or later than the period. If backlogging is allowed, the demand of a given period cannot be delivered earlier than the period, but it can be delivered later at the expense of a backordering cost. Like most mathematical models, the classical dynamic lot-sizing model is a simplified paraphrase of what might actually happen in real life. In most real-life applications, the customer offers a grace period--we call it a demand time window--during which a particular demand can be satisfied with no penalty. That is, in association with each demand, the customer specifies an acceptable earliest and a latest delivery time. The time interval characterized by the earliest and latest delivery dates of a demand represents the corresponding time window. This paper studies the dynamic lot-sizing problem with demand time windows and provides polynomial time algorithms for computing its solution. If backlogging is not allowed, the complexity of the proposed algorithm is O(T²) where T is the length of the planning horizon. When backlogging is allowed, the complexity of the proposed algorithm is O(T³). [ABSTRACT FROM AUTHOR]

In this paper, we focus on a useful modeling concept that is frequently ignored while formulating discrete optimization problems. Very often, there exists a natural symmetry inherent in the problem itself that, if propagated to the model, can hopelessly mire a branch-and-bound solver by burdening it to explore and eliminate such alternative symmetric solutions. We discuss three applications where such a symmetry arises: a telecommunications network design problem, a noise pollution problem, and a machine procurement and operation problem. For each case, we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability, while using a popular modern-day commercial branch-and-cut software (CPLEX 6.5). [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for finding the K loopless paths that have the shortest lengths from one node to another node in a network. The significance of the new algorithm is that its computational upper bound increases only linearly with the value of K. Consequently, in general, the new algorithm is extremely efficient as compared with the algorithms proposed by Bock, Kantner, and Haynes [2], Pollack [7], [8], Clarke, Krikorian, and Rausan [3], Sakarovitch [9] and others. This paper first reviews the algorithms presently available for finding the K shortest loopless paths in terms of the computational effort and memory addresses they require. This is followed by the presentation of the new algorithm and its justification. Finally, the efficiency of the new algorithm is examined and compared with that of other algorithms. [ABSTRACT FROM AUTHOR]

The paper presents a new approach to solving a class of combinatorial economic allocation problems. One member of this class is known as the quadratic assignment problem. Besides presenting an algorithm to solve this problem, we will discuss in general terms the techniques for treating combinatorial problems. A novel feature of the paper is the development of the statistical properties of the criterion function. These statistical properties are used in conjunction with a general enumerative procedure to form the main parts of the algorithm. Using the idea of confidence level enumeration, an extension of the algorithm is proposed which should allow for the effective treatment of large scale combinatorial problems. Finally we present some computational results in order to illustrate the effectiveness of the general approach. [ABSTRACT FROM AUTHOR]

In this paper we study a model that minimizes the sum of production, employment smoothing, and inventory costs subject to a schedule of known demand requirements over a finite time horizon. The three instrumental variables are work force producing at regular-time, work force producing on overtime, and the total work force. Overtime is limited to be not more than a fixed multiple of regular time. The idle portion of the work force and the levels of inventory are resultant variables. We postulate the following shape characteristics for the cost functions production costs are convexlike, smoothing costs are V-shaped, and holding costs are increasing, both the production and holding cost functions need not be stationary. In this paper, we provide upper and lower bounds on the cumulative regular-time plus overtime work force for any sequence of demand requirements. We also give the form of an optimal policy when demands are monotone (either increasing or decreasing). Finally, we derive the asymptotic behavior of optimal policies when demands are monotone and the planning horizon becomes arbitrarily long. All of these results, which convey information about the numerical values of optimal policies, given specific demands and an initial level of inventory, depend only on the shape characteristics of the cost functions. Algorithmic techniques are discussed elsewhere. [ABSTRACT FROM AUTHOR]

This paper considers "critical path" networks which are used for the planning and scheduling of projects that consist of well defined sequences of individual activities. When the number of activities is large, it becomes difficult to prepare a network for the project as one unit, and it may also be difficult to store the network in the high speed memory of a digital computer. Also, in the cases where there are two or more independent projects, which are weakly inter-related by common activities, the problem of efficient scheduling of all the projects becomes quite difficult. This paper presents a method to "tear" or "decompose" a project network into several subnetworks, schedule the subnetworks and then to put the subnetworks back together. A computational algorithm is first given for time-only networks; then two computational formulations are given for cost-time network of project subnetworks. The latter essentially generalize the algorithm due to Fulkerson, in order to handle piecewise linear, convex, cost-time curves for some or all of the activities. [ABSTRACT FROM AUTHOR]

This paper gives a detailed description of an algorithm for the solution of a specialized Linear Programming model, to be called the Machine Loading model. It is a generalization of the Transportation Problem, in that weighting factors are applied to the individual elements which form the row and column sums. For the Machine Loading model, the simplex method reduces to a specialized algorithm which generalizes the stepping stone method of the Transportation Problem [2], [3]. With the resulting generalized stepping stone method, it becomes practicable to solve many large-scale problems for which the direct application of the simplex method would be impracticable. The present paper is restricted to a discussion of the following topics: (I) the general characteristics of the model and its topological features; (ii) a detailed solution algorithm, including a consideration of degenerate cases and the use of a computer; (iii) a more restrictive capacitated model and the corresponding modifications to the solution algorithm; and (iv) the complete illustrative solution of a numerical example. The purpose is to aid interested readers in gaining familiarity with the algorithm and facility in the solution of numerical problems. No derivations or proofs will be included. [ABSTRACT FROM AUTHOR]

The bond portfolio problem is viewed as a multistage decision problem in which buy, sell, and hold decisions are made at successive (discrete) points in time. Normative models of this decision problem tend to become very large, particularly when its dynamic structure and the uncertainty of future interest rates and cash flows are incorporated in the model. In this paper we present a multiple period bond portfolio model and suggest a new approach for efficiently solving problems which are large enough to make use of as much information as portfolio managers can reasonably provide. The procedure utilizes the decomposition algorithm of mathematical programming and an efficient technique developed for solving subproblems of the overall portfolio model. The key to the procedure is the definition of subproblems which are easily solved via a simple recursive relationship. [ABSTRACT FROM AUTHOR]

The article presents comments on the management science paper "On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs," by William L. Maxwell. The paper focused on an integer programming formulation of a one-machine job shop problem. The author contends that Maxwell made in error in proving the validity of an optimal algorithm by applying cutting plane constraints to the problem. The author explains that the problem cannot be solved through traditional cutting plane procedures. The author provides a mathematical model in an attempt to correct the proof.

The minimum cost flow problem is to determine a least cost shipment of a commodity through a network G = (N, A) in order to satisfy demands at certain nodes from available supplies at other nodes. In this paper, we study a variant of the minimum cost flow problem where we are given a set R subset or is equal to A of arcs and require that each arc in R must carry the same amount of flow. This problem, which we call the simple equal flow problem, arose while modeling a water resource system management in Sardinia, Italy. We consider the simple equal flow problem in a directed network with n nodes, m arcs, and where all arc capacities and node supplies are integer and bounded by U. We develop several algorithms for the simple equal flow problem--the network simplex algorithm, the parametric simplex algorithm, the combinatorial parametric algorithm, the binary search algorithm, and the capacity scaling algorithm. The binary search algorithm solves the simple equal flow problem in O(log(nU)) applications of any minimum cost flow algorithm. The capacity scaling algorithm solves it in O(m(m + n log n) log (nU)) time, which is almost the same time needed to solve the minimum cost flow problem by the capacity scaling algorithm. These algorithms can be easily modified to obtain an integer solution of the simple equal flow problem. [ABSTRACT FROM AUTHOR]

Sensor systems as critical components of a transportation network provide a variety of real-time traffic surveillance information for traffic management and control. The deployment of sensors significantly affects their overall surveillance effectiveness. This paper proposes a reliable sensor location model to optimize surveillance effectiveness when sensors are subject to site-dependent probabilistic failures, and a general effectiveness measure is proposed to encompass most existing measures needed for engineering practice (e.g., flow volume coverage, vehicle-mile coverage, and squared error reduction). The problem is first formulated into a compact mixed-integer program, and we develop a variety of solution algorithms (including a custom-designed Lagrangian relaxation algorithm) and analyze their properties. We also propose alternative formulations including a continuum approximation model for single corridor problems and reliable fixed-charge sensor location models. Numerical case studies are conducted to test the performance of the proposed algorithms and draw managerial insights on how different parameter settings (e.g., failure probability and spatial heterogeneity) affect overall surveillance effectiveness and the optimal sensor deployment. [ABSTRACT FROM AUTHOR]

In this paper we examine computational complexity issues and develop algorithms for a class of"shoreline" single-vehicle routing and scheduling problems with release time constraints. Problems in this class are interesting for both practical and theoretical reasons. From a practical perspective, these problems arise in several transportation environments. For instance, in the routing and scheduling of cargo ships, the routing structure is "easy" because the ports to be visited are usually located along a shoreline. However, because release times of cargoes at ports generally complicate the routing structure, the combined routing and scheduling problem is nontrivial. For the straight-line case (a restriction of the shoreline case), our analysis shows that the problem of minimizing the maximum completion time can be solved exactly in quadratic time by dynamic programming. For the shoreline case we develop and analyze heuristic algorithms. We derive data-dependent worst-case performance ratios for these heuristics that are bounded by constant. We also discuss how these algorithms perform on practical data. [ABSTRACT FROM AUTHOR]

In this paper we study the problem of coordinating the purchase and shipment of I items in a one-warehouse, N-retailer inventory system. The model includes positive echelon holding costs, fixed costs for ordering and shipping each item, and a fixed joint item order cost at each retailer. Demand for each item at each retailer is assumed to occur at a constant and continuous rate. A mathematical model is developed based on these assumptions and the assumption that a stationary nested policy is followed. An efficient algorithm is presented based on the problem's structure that involves only sorting and runs in O(NI log NI) time. The cost of the policy computed is proven to be within 6% of the cost of an optimal nested policy. An example is presented to illustrate the problem structure and the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper surveys models and algorithms dealing with partially observable Markov decision processes. A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process which permits uncertainty regarding the state of a Markov process and allows for state information acquisition. A general framework for finite state and action POMDP's is presented. Next, there is a brief discussion of the development of POMDP's and their relationship with other decision processes. A wide range of models in such areas as quality control, machine maintenance, internal auditing, learning, and optimal stopping are discussed within the POMDP-framework. Lastly, algorithms for computing optimal solutions to POMDP's are presented. [ABSTRACT FROM AUTHOR]

This paper examines the performance of three heuristic methods (Senju-Toyoda, Kochenberger et al., and Hillier) when applied to the 0-1 linear programming problem with nonnegative coefficients. Their effectiveness, measured in terms of computing time, error and relative error, is evaluated on a set of problems from the literature and randomly generated 0-1 test problems with nonnegative coefficients. Analysis of variance and stepwise regressions are employed to study the effect of the number of variables, number of constraints and degree of constraint slackness. The methods exhibited some similarities but also marked differences in their behavior. Interestingly enough, the larger the number of variables the better the accuracy of each method. Error differences among the three methods were significant (1:0.8:0.2) yet small (less than 2% on the average) for many practical situations. Hillier's algorithm was the most accurate but much slower and more core demanding than the other two, which makes it difficult or impossible to use for solving large 0-1 problems. Kochenberger's et al. heuristic was the fastest (most accurate) of the three in tightly (loosely) constrained problems. In general the Senju-Toyoda algorithm was the fastest, but least accurate on small and medium size problems. Suggestions are made for selecting the "best" heuristic based on the problem characteristics. [ABSTRACT FROM AUTHOR]

This article describes a modified algorithm for critical path method time-cost tradeoff. The algorithm suggests rules for choosing paths and minimizing the total cost of expediting activities in order to complete projects in the time desired. Several examples of the algorithm's usage are presented. The author observes that the algorithm presented in this paper provides the optimum solution to all the network problems he solved. Comparisons are made of the effectiveness of the critical path method time-cost tradeoff algorithm and other algorithms.

This paper explores the normative theory of simulation within the context of an optimization algorithm for a linear programming model of the experimental setting. The simulation is viewed as a random generalized mathematical function which provides an uncertain evaluation of any policy within a specified constraint set. A sequential experimental design aimed at identifying the feasible levels of the policy variables which provide the optimal level of expected response is presented and analyzed. The results of numerical tests of the proposed procedure are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to determining the optimal facility locations for uncapacitated location problems in two stages. First, it is shown that a subset of all solutions to the uncapacitated public facility location problem can be obtained by considering a closely related private location problem. The exact nature of the problem is established using the Generalised Lagrange Multiplier results given by Everett. In the second section of the paper a particularly efficient parametric decomposition algorithm, which is based on the results of the first section, is presented. Computational results are given which summarize the current level of experience with the algorithm. [ABSTRACT FROM AUTHOR]

This part of the paper introduces some possible implementations of Self-Scaling Variable Metric algorithms based on the theory presented in Part I. These implementations are analyzed theoretically and discussed qualitatively. A special class of SSVM algorithms is introduced, which has the additional property of being invariant under scaling of the objective function or of the variables. Experimental results are provided for a particular case of this class. This case has been tested in comparison to the DFP algorithm on a variety of functions with up to 50 variables. The results indicate that the new method has substantial advantage for functions with a large number of variables. [ABSTRACT FROM AUTHOR]

One approach to coping with the apparent difficulty of many schedule-optimization problems, such as occur in machine shops and computer processing, is to devise efficient algorithms that find schedules guaranteed to be "near-optimal." This paper presents an introduction to this approach by describing its application to a well-known multiprocessor scheduling model and illustrating the variety of algorithms and results that are possible. The paper concludes with a brief survey of what has been accomplished to date in the area of scheduling using this approach. [ABSTRACT FROM AUTHOR]

This paper presents a branch-and-bound algorithm for minimizing the sum of a convex function in x, a convex function in y and a bilinear term in x and y over a closed set. Such an objective function is called biconvex with biconcave functions similarly defined, The feasible region of this model permits joint constraints in x and y to be expressed. The bilinear programming problem becomes a special case of the problem addressed in this paper. We prove that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point. The algorithm is proven to converge to a global solution of the nonconvex program. We discuss extensions of the general model and computational experience in solving jointly constrained bilinear programs, for which the algorithm has been implemented. [ABSTRACT FROM AUTHOR]

In this paper we consider the optimal location of a single facility with respect to a set of demand points on a tree network. The demands of the points to be served are dynamic and our model takes into account predictable changes in these demands. We study problems with both linear and nonlinear demand functions. We make use of the analytical properties of tree networks and sensitivity analysis, and devise efficient algorithms to construct the optimal trajectory of the parametric location problem. We also give theory that exploits the network topology. [ABSTRACT FROM AUTHOR]