Search

This paper deals with undiscounted infinite stage two-person zero-sum stochastic games with finite state and action spaces. It was recently shown that such games possess a value. But in general there are no optimal strategies. We prove that for each player there exists a nonempty set of easy initial states, i.e. starting states for which the player possesses an optimal stationary strategy. This result is proved with the aid of facts derived by Bewley and Kohlberg for the limit discount equation for stochastic games. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan [7] concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow [6] for linear fractional programming and to the quadratic parametric approach by Ritter [10]. The Appendix contains a numerical example. [ABSTRACT FROM AUTHOR]

Commentary is presented for an article published in the July 1960 issue of "Management Science," written by L. V. Kantorovich with an introductory note by T. C. Koopmans. According to the author, in his introduction Koopmans addresses in particular a linear programming problem and a matrix game presented by Kantorovich. Also presented is an interpretation of the article's treatment of decision variables and mathematical optimization. The author notes that the article presents algorithms that have been improved from their contemporary presentations.

Game-theoretic tools are becoming a popular design choice for distributed resource allocation algorithms. A central component of this design choice is the assignment of utility functions to the individual agents. The goal is to assign each agent an admissible utility function such that the resulting game possesses a host of desirable properties, including scalability, tractability, and existence and efficiency of pure Nash equilibria. In this paper we formally study this question of utility design on a class of games termed distributed welfare games. We identify several utility design methodologies that guarantee desirable game properties irrespective of the specific application domain. Lastly, we illustrate the results in this paper on two commonly studied classes of resource allocation problems: "coverage" problems and "coloring" problems. [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]

Zhao showed that the log barrier associated with the recourse function of two-stage stochastic linear programs behaves as a strongly self-concordant barrier and forms a self-concordant family on the first-stage solutions. In this paper, we show that the recourse function is also strongly self-concordant and forms a self-concordant family for the two-stage stochastic convex quadratic programs with recourse. This allows us to develop Bender's decomposition based linearly convergent interior point algorithms. An analysis of such an algorithm is given in this paper. [ABSTRACT FROM AUTHOR]

Time-series input processes occur naturally in the stochastic simulation of many service, communications, and manufacturing systems, and there are a variety of time-series input models available to match a given collection of properties, typically a marginal distribution and an autocorrelation structure specified via the use of one or more time lags. The focus of this paper is the situation in which the collection of properties are not "given," but data are available from which a time-series input model is to be estimated. The input model we consider is the very flexible autoregressive-to-anything (ARTA) model of Cario and Nelson [Cario, M. C., B. L. Nelson. 1996. Autoregressive to anything: Time-series input processes for simulation. Oper. Res. Lett. 19 51-58]. Recently, we developed a statistically valid algorithm (ARTAFIT) for fitting this model to stationary univariate time-series data using marginal distributions from the Johnson translation system. In this paper, we perform a comprehensive numerical study to assess the performance of our algorithm relative to the two most commonly used approaches: (a) fitting the marginal distribution but ignoring the autocorrelation structure, and (b) fitting separately the marginal distribution as in (a) and the autocorrelation structure using the sample autocorrelation function. We find that ARTAFIT, which fits the marginal distribution and the autocorrelation structure jointly, outperforms both (a) and (b), and we demonstrate the importance of taking dependencies into account while developing input models for stochastic simulation. [ABSTRACT FROM AUTHOR]

This paper contains a complete and updated review of the literature for multiobjective flowshop problems, which are among the most studied environments in the scheduling research area. No previous comprehensive reviews exist in the literature. Papers about lexicographical, goal programming, objective weighting, and Pareto approaches have been reviewed. Exact, heuristic, and metaheuristic methods have been surveyed. Furthermore, a complete computational evaluation is also carried out. A total of 23 different algorithms including both flowshop-specific methods as well as general multiobjective optimization approaches have been tested under three different two-criteria combinations with a comprehensive benchmark. All methods have been studied under recent state-of-the-art quality measures. Parametric and nonparametric statistical testing is profusely employed to support the observed performance of the compared methods. As a result, we have identified the best-performing methods from the literature, which along with the review, constitutes a reference work for further research. [ABSTRACT FROM AUTHOR]

We consider a constrained homogeneous random walk in ℤ+d. Such random walks are used to model various stochastic processes, most importantly multiclass Markovian queueing networks operating under state-dependent scheduling policies. These applications motivate the need to compute various performance measures, including stationary probability distributions and large deviations rates. In this paper, we show that computing the stationary probability distributions exactly is an algorithmically undecidable problem. That is no algorithm can possibly exist to solve this task. The problem remains undecidable even if a linear Lyapunov function that verifies positive recurrence of the underlying random walk is available as a part of the input. We then prove that computing large deviation rates for this model is also an undecidable problem. Specifically, we show that it is an undecidable problem to determine finiteness of large deviations rates. [ABSTRACT FROM AUTHOR]

This paper proposes an algorithm that automatically translates the "continuum approximation" (CA) recipes for location problems into discrete designs. It applies to terminal systems, but can also be used for other logistics problems. The study also systematically compares the logistics costs predicted by the CA approach with the actual costs for discrete designs obtained with the automated procedure. The predictions are quite accurate. The paper also gives conditions under which the discrete solution has a small optimality gap. [ABSTRACT FROM AUTHOR]

The notion of branch decompositions and its related connectivity invariant for graphs, branchwidth, were introduced by Robertson and Seymour in their series of papers that proved Wagner's conjecture. Branch decompositions can be used to solve NP-hard problems modeled on graphs, but finding optimal branch decompositions of graphs is also NP-hard. This is the first of two papers dealing with the relationship of branchwidth and planar graphs. A practical implementation of an algorithm of Seymour and Thomas for only computing the branchwidth (not optimal branch decomposition) of any planar hypergraph is proposed. This implementation is used in a practical implementation of an algorithm of Seymour and Thomas for computing the optimal branch decompositions for planar hypergraphs that is presented in the second paper. Since memory requirements can become an issue with this algorithm, two other variations of the algorithm to handle larger hypergraphs are also presented. [ABSTRACT FROM AUTHOR]

This is the second of two papers dealing with the relationship of branchwidth and planar graphs. Branch-width and branch decompositions, introduced by Robertson and Seymour, have been shown to be beneficial for both proving theoretical results on graphs and solving NP-hard problems modeled on graphs. The first practical implementation of an algorithm of Seymour and Thomas for computing optimal branch decompositions of planar hypergraphs is presented. This algorithm encompasses another algorithm of Seymour and Thomas for computing the branchwidth of any planar hypergraph, whose implementation is discussed in the first paper. The implementation also includes the addition of a heuristic to decrease the run times of the algorithm. This method, called the cycle method, is an improvement on the algorithm by using a "divide-and-conquer" approach. [ABSTRACT FROM AUTHOR]

Hub networks play an important role in many transportation and telecommunications systems. This paper introduces a new model called the hub arc location model. Rather than locate discrete hub facilities, this model locates hub arcs, which have reduced unit flow costs. Four special cases of the general hub arc location model are examined in detail. We provide motivation for the new models, and present examples and optimal solutions, using data for U.S. air passenger traffic. Results are used to compare optimal costs, hub locations, and hub arc locations with corresponding hub median optimal solutions. The results reveal interesting spatial patterns and help identify promising cities and regions for hubs. A companion paper (Campbell et al. 2005) presents integer programming formulations and solution algorithms for the new hub arc problems. It also provides details and computation times for these solution algorithms. [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]

In this paper we study the closest-string problem (CSP), which can be defined as follows: Given a finite set T = {s¹, s²,&hellip,sn} of strings, each string with length m, find a center string t of length m minimizing d, such that for every string sI ϵ T, dH(t, si) ≥ d. By dH(t, si we mean the Hamming distance between t and si . This is an NP-hard problem, with applications in molecular biology and coding theory. Even though there are good approximation algorithms for this problem, and exact algorithms for instances with d constant, there are no studies trying to solve it exactly for the general case. In this paper we propose three integer-programming (IP) formulations and a heuristic, which is used to provide upper bounds on the value of an optimal solution. We report computational results of a branch-and-bound algorithm based on one of the IP formulations, and of the heuristic, executed over randomly generated instances. These results show that it is possible to solve CSP instances of moderate size to optimality. [ABSTRACT FROM AUTHOR]

We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest. [ABSTRACT FROM AUTHOR]

We study the strip packing problem, in which a set of two-dimensional rectangular items has to be packed in a rectangular strip of fixed width and infinite height, with the aim of minimizing the height used. The problem is important because it models a large number of real-world applications, including cutting operations where stocks of materials such as paper or wood come in large rolls and have to be cut with minimum waste, scheduling problems in which tasks require a contiguous subset of identical resources, and container loading problems arising in the transportation of items that cannot be stacked one over the other. The strip packing problem has been attacked in the literature with several heuristic and exact algorithms, nevertheless, benchmark instances of small size remain unsolved to proven optimality. In this paper we propose a new exact method that solves a large number of the open benchmark instances within a limited computational effort. Our method is based on a Benders' decomposition, in which in the master we cut items into unit-width slices and pack them contiguously in the strip, and in the slave we attempt to reconstruct the rectangular items by fixing the vertical positions of their unit-width slices. If the slave proves that the reconstruction of the items is not possible, then a cut is added to the master, and the algorithm is reiterated. We show that both the master and the slave are strongly NP-hard problems and solve them with tailored preprocessing, lower and upper bounding techniques, and exact algorithms. We also propose several new techniques to improve the standard Benders' cuts, using the so-called combinatorial Benders' cuts, and an additional lifting procedure. Extensive computational tests show that the proposed algorithm provides a substantial breakthrough with respect to previously published algorithms. [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]

This paper proposes and analyzes a periodic review inventory system with two replenishment modes. Regular orders are placed periodically following a base stock policy on inventory position, and arrive at the stocking location after a deterministic lead time. The location also has the option of placing emergency orders, characterized by a shorter lead time but higher acquisition cost, in case of imminent stock outs. Thus, at some appropriate time in the replenishment cycle, the necessity and size of an emergency order is determined according to a base stock policy on net stock. The timing of the emergency order is such that this order arrives and can be used to satisfy the demand in the time period just before the arrival of a regular order, when the likelihood of a stockout is highest. An approximate cost model is developed which can easily be optimized with respect to the order-up-to parameters. This model is used as the basis for a heuristic algorithm, which leads to solutions that are very close to the exact optimal solutions determined through simulation. It is shown that the proposed system offers substantial cost savings relative to a system without the emergency replenishment option. [ABSTRACT FROM AUTHOR]

The article presents a zero-one linear program and a dynamic programming algorithm for finding the shortest route containing exactly q arcs from node 1 to node n in a network (N, A) with distances c(i, j). This note shows that the linear programming formulation and his extension based on it are defective, and that the dynamic programming algorithm can lead to suboptimal solutions, but a minor change in the dynamic programming formulation relieves the difficulty. A special feature of this linear program is that there can never be a loop in the basis, because the vectors corresponding to the variables of a loop are linearly dependent. The last comment is related to the dynamic programming algorithm. One is allowed to pass through a node more than once in the shortest route . The proposed method for solving this program consists of converting it into a shortest route problem containing exactly q arcs. But for some arbitrary reason, the dynamic program is formulated in such a way that one can never have starting node 1 more than once in the final solution.

In this paper, a sanitation routing problem called the Rollon-Rolloff Vehicle Routing Problem (RRVRP) is defined. In the RRVRP, tractors move large trailers between locations and a disposal facility. The trailers are so large that the tractor can only transport one trailer at a time. In this paper, the RRVRP is defined, a mathematical programming formulation is presented, and two lower bounds and four heuristic algorithms are developed and tested on 20 different problems. Conclusions are derived and recommendations for further research are presented. [ABSTRACT FROM AUTHOR]

The Canadian traveler problem (CTP) is a simple, yet challenging, stochastic optimization problem wherein an agent is given a graph where some edges are blocked with certain probabilities and the status of these edges can be disambiguated dynamically upon reaching an incident vertex. The goal is to devise a traversal policy that results in the shortest expected walk length between a given starting vertex and a termination vertex. CTP has been shown to be intractable in many broad settings. In this paper, we introduce an optimal algorithm for the problem based on a Markov decision process formulation, which is a new improvement on AO* search that takes advantage of the special problem structure in CTP. We call our algorithm CAO*, which stands for AO* with caching. CAO* uses a caching mechanism to avoid re-expansion of previously visited states and makes use of admissible upper bounds at a node level for dynamic state-space pruning. CAO* is not polynomial time, but it can dramatically shorten the execution time needed to find an exact solution for moderately sized instances. We present computational experiments on a realistic variant of the problem involving an actual maritime minefield data set. [ABSTRACT FROM AUTHOR]

This paper studies the container handling process for a newly designed container terminal, known as the Frame Bridge based Automated Container Terminal (FB-ACT). The system was shown to be an effective solution to the next generation container terminal, but its efficiency depends on the dispatching of frame trolleys (FTs), which transport containers along the apron. We address the FT dispatching problem to ensure conflict-free movements, while considering the handshakes with other devices in the system. A mixed-integer programming (MIP)model is formulated to minimize the make span considering FT conflicts and handshakes. An algorithm based on filtered beam search is developed to solve the problem. In this algorithm, two filtering approaches are used to guide the search for beam nodes at each level. The first approach uses a surrogate model to effectively screen out the less promising nodes. Then, the second approach uses a reduced MIP model to further identify the beam nodes for the next level. Numerical experiments show that our proposed algorithm yields near-optimal solutions in small-scale problems. In large-scale problems, our algorithm significantly outperforms two other algorithms based on first come, first served (FCFS) or FCFS with dedicated vehicle assignment. Some interesting insights about the FB-ACT system are also shown in the study. [ABSTRACT FROM AUTHOR]

This paper examines the effect of stochastic task times on the total operating costs of a continuously paced assembly line under the assumption that the line is stopped whenever at least one work station requires more time than allotted. A comprehensive stochastic cost function is integrated into an efficient balancing algorithm to enable an approximately minimum cost balance to be obtained. An experiment was conducted to determine the cost savings resulting from using the stochastic method as compared to two deterministic methods. The stochastic method of this paper produced lower cost balances in most cases studied. [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]

The motivation for this paper is a problem faced by banks which process large volumes of deposited checks. The checks must be separated by bank number before shipment to the Federal Reserve or other banks. The sorting is usually accomplished using a reader-sorter which reads the magnetic ink characters on the checks and separates them into different "pockets." This paper characterizes the optimal sorting strategy and describes an efficient procedure for finding the optimal solution for problems of the size generally found in practice. The algorithm is based on a two state dynamic programming recursion in which characterization theorems are used to drastically reduce the size of the state space and in which the storage requirements are minimal. The paper includes an analysis of computational experience and describes how the algorithm can be used in a real time environment with deadlines. [ABSTRACT FROM AUTHOR]

This note presents a description of a time-sharing computer program written to implement a man-machine interactive algorithm for the solution of the multiple criteria problem. The interactive algorithm was suggested in a recent paper by Geoffrion, "Vector Maximal Decomposition Programming," Working Paper No. 164, Western Management Science Institute, University of California, Los Angeles, September 1970. A unique feature of this program is the man-machine dialog which obtains information from the decision-maker through a series of simple, ordinal comparisons. [ABSTRACT FROM AUTHOR]

This paper is concerned with a linear fractional problem of the form: max[sub x] min[sub y] F(X, Y) = (cX + dY + α)/(fX + gY + β), subject to AX + BY less than or equal to b; X, Y greater than or equal to O. This problem represents a generalization of a problem considered in the literature in which F(X, Y) is assumed to be linear. A number of results for the linear case are extended; and, in particular, it is shown that this fractional max-min problem is equivalent to a quasi-convex programming problem whose optimal solution lies at a vertex of the feasible region. Using these results, we develop an algorithm for solving this problem. The paper concludes with a numerical example. [ABSTRACT FROM AUTHOR]

In an earlier paper [Opns. Res. 20, 1153-1161 (1972)] we proved that any feasible integer solution to the linear program associated with the equality-constrained set-covering problem can be obtained from any other feasible integer solution by a sequence of less than m pivots (where m is the number of equations), such that each solution generated in the sequence is integer. However, degeneracy makes it difficult to find a sequence of pivots leading to an integer optimum. In this paper we give a constructive characterization of adjacency relations between integer vertices of the feasible set that enables us to generate edges (all, if necessary) connecting a given integer vertex to adjacent integer vertices. This helps overcome the difficulties caused by degeneracy and leads to a class of algorithms, of which we discuss two. [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 investigates conditions under which two learning algorithms playing a zero-sum sequential stochastic game would arrive at optimal pure strategies. Neither player has knowledge of either the pay-off matrix or the choice of strategies available to the other and both players update their own strategies at every stage entirely on the basis of the random outcome at that stage. The proposed learning algorithms are shown to converge to the optimal pure strategies when they exist with probabilities as close to ! as desired. [ABSTRACT FROM AUTHOR]

We analyze a finite-horizon dynamic pricing model in which demand at each period depends on not only the current price but also past prices through reference prices. A unique feature but also a significant challenge in this model is the asymmetry in reference price effect, which implies that the underlying optimization problem is nonsmooth and no standard optimization methods can be applied. We identify a few key structural properties of the problem, which enable us to develop strongly polynomial-time algorithms to compute the optimal prices for several plausible scenarios. We complement our exact algorithms by proposing an approximation heuristic and provide an upper bound on the optimal objective value. Finally, we conduct numerical experiments to study the optimal price path and demonstrate the value of dynamic pricing when demands are seasonal. We further compare numerically one of the exact algorithms with the heuristic and offer managerial suggestions. This paper was accepted by Yinyu Ye, optimization. [ABSTRACT FROM AUTHOR]

This letter calls attention to the problems of validating the claim made for algorithms in published papers, and proposes a system for review that will validate such claims thoroughly before publication. [ABSTRACT FROM AUTHOR]

This paper examines properties and interrelations of several concepts of generalized concavity. It shows that the class of functions that are both ‘generalized concave’ and ‘generalized convex’ is closely related to the class of monotone functions of a single variable. After excluding a certain small class of exceptions, the paper shows that, for arbitrary (perhaps not differentiable) functions, concave implies pseudoconcave, pseudoconcave implies strictly quasiconcave, and strictly quasiconcave implies quasiconcave. Several results characterizing the extreme values of generalized concave functions are given. [ABSTRACT FROM AUTHOR]

This paper deals with a nonstationary discrete-time Markov process whose transition probabilities vary periodically in time. Each transition results in a reward that varies within the same cycle as the transition matrix. For infinite processes a policy-iteration algorithm is developed that effectively determines an optimal policy maximizing the total discounted reward. The paper represents an extension of R. A. HOWARD's policy-iteration technique for stationary Markov processes. A numerical example is given in which the developed iteration algorithm is demonstrated. [ABSTRACT FROM AUTHOR]

This paper considers the mathematical properties of chance constrained programming problems where the restriction is on the joint probability of a multivariate random event. One model that is considered arises when the right-hand side constants of the linear constraints are random. Another model treated here occurs when the coefficients of the linear programming variables are described by a multinormal distribution. It is shown that under certain restrictions both situations can be viewed as a deterministic nonlinear programming problem. Since most computational methods for solving nonlinear programming models require the constraints be concave, this paper explores whether the resultant problem meets the concavity assumption. For many probability laws of practical importance, the constraint in the first type of model is shown to violate concavity. However, a simple logarithmic transformation does produce a concave restriction for an important class of problems. The paper also surveys the `generalized linear programming' method for solving such problems when the logarithmic transformation is justified. For the second type model, the constraint is demonstrated to be nonconcave. [ABSTRACT FROM AUTHOR]

This paper deals with a nonstationary discrete-time Markov process whose transition probabilities vary periodically in time. Each transition results in a reward that varies within the same cycle as the transition matrix. For infinite processes a policy-iteration algorithm is developed that effectively determines an optimal policy maximizing the total discounted reward. The paper represents an extension of B. A. HOWARD'S policy-iteration technique for stationary Markov processes, A numerical example is given in which the developed iteration algorithm is demonstrated. [ABSTRACT FROM AUTHOR]

The multi-index transportation problem is defined and a summary of the algorithm described in an earlier paper is given. This paper discusses the theorems justifying the use of the algorithm and gives a necessary condition for the existence of a solution. It also describes the formulation of three special-structure linear-programming problems as examples of multi-index problems. The three problems discussed are the capacitated Hitchcock problem, transportation where there is more than one method of transport available, and the transformation of one type of multi-index problem into another. A final section describes problems that have restrictions in the form of inequalities. [ABSTRACT FROM AUTHOR]

We consider the multilevel lot-sizing problem with production capacities (MLSP-PC), in which production and trans- portation decisions are made for a serial supply chain with capacitated production and concave cost functions. Existing approaches to the multistage version of this problem are limited to nonspeculative cost functions--up to now, no algorithm for the multistage version of this model with general concave cost functions has been developed. In this paper, we develop the first polynomial algorithm for the MLSP-PC with general concave costs at all of the stages, and we introduce a novel approach to overcome the limitations of previous approaches. In contrast to traditional approaches to lot-sizing problems, in which the problem is decomposed by time periods and is analyzed unidirectionally in time, we solve the problem by introducing the concept of a basis path, which is characterized by time and stage. Our dynamic programming algorithm proceeds both forward and backward in time along this basis path, enabling us to solve the problem in polynomial time. [ABSTRACT FROM AUTHOR]

Long-haul carriers must comply with various safety rules which are rarely taken into account in models and algorithms for vehicle routing problems. In this paper, we consider the rules on truck driver safety during long-haul trips in the United States. The problem under study has two dominant features: a routing component that consists of determining the sequence of customers visited by each vehicle and a scheduling component that consists of planning the rest periods and the service time of each customer. We have developed different scheduling algorithms embedded within a tabu search heuristic. The overall solution methods were tested on modified Solomon instances, and the computational results confirm the benefits of using a sophisticated scheduling procedure when planning long-haul transportation. [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]

This paper presents an exact method for solving the symmetric two-echelon capacitated vehicle routing problem, a transportation problem concerned with the distribution of goods from a depot to a set of customers through a set of satellite locations. The presented method is based on an edge flow model that is a relaxation and provides a valid lower bound. A specialized branching scheme is employed to obtain feasible solutions. Out of a test set of 93 instances the algorithm is able to solve 47 to optimality, surpassing previous exact algorithms. [ABSTRACT FROM AUTHOR]

This paper presents the first full-fledged branch-and-price (bap) algorithm for the capacitated arc-routing problem (CARP). Prior exact solution techniques either rely on cutting planes or the transformation of the CARP into a node-routing problem. The drawbacks are either models with inherent symmetry, dense underlying networks, or a formulation where edge flows in a potential solution do not allow the reconstruction of unique CARP tours. The proposed algorithm circumvents all these drawbacks by taking the beneficial ingredients from existing CARP methods and combining them in a new way. The first step is the solution of the one-index formulation of the CARP in order to produce strong cuts and an excellent lower bound. It is known that this bound is typically stronger than relaxations of a pure set-partitioning CARP model. Such a set-partitioning master program results from a Dantzig-Wolfe decomposition. In the second phase, the master program is initialized with the strong cuts, CARP tours are iteratively generated by a pricing procedure, and branching is required to produce integer solutions. This is a cut-first bap-second algorithm and its main function is, in fact, the splitting of edge flows into unique CARP tours. [ABSTRACT FROM AUTHOR]

The long chain has been an important concept in the design of flexible processes. This design concept, as well as other sparse designs, have been applied by the automotive and other industries as a way to increase flexibility in order to better match available capacities with variable demands. Numerous empirical studies have validated the effectiveness of these designs. However, there is little theory that explains the effectiveness of the long chain, except when the system size is large, i.e., by applying an asymptotic analysis. Our attempt in this paper is to develop a theory that explains the effectiveness of long chain designs for finite size systems. First, we uncover a fundamental property of long chains, supermodularity, that serves as an important building block in our analysis. This property is used to show that the marginal benefit, i.e., the increase in expected sales, increases as the long chain is constructed, and the largest benefit is always achieved when the chain is closed by adding the last arc to the system. Then, supermodularity is used to show that the performance of the long chain is characterized by the difference between the performances of two open chains. This characterization immediately leads to the optimality of the long chain among 2-flexibility designs. Finally, under independent and identically distributed (i.i.d.) demand, this characterization gives rise to three developments: (i) an effective algorithm to compute the performances of long chains using only matrix multiplications; (ii) a result that the gap between the fill rate of full flexibility and that of the long chain increases with system size, thus implying that the effectiveness of the long chain relative to full flexibility increases as the number of products decreases; (iii) a risk-pooling result implying that the fill rate of a long chain increases with the number of products, but this increase converges to zero exponentially fast. [ABSTRACT FROM AUTHOR]

This paper studies an infinite horizon adverse selection model with an underlying Markov information process. It introduces a graphic representation of continuation contracts and continuation payoff frontiers, namely finite policy graph, and provides an algorithm to approximate the optimal policy graph through iterations. The algorithm performs an additional step after each value iteration--replacing dominated points on the previous continuation payoff frontier by points on the new frontier and reevaluating the new frontier. This dominance-free reevaluation step accelerates the convergence of the continuation payoff frontiers. Numerical examples demonstrate the effectiveness of this algorithm and properties of the optimal contracts. [ABSTRACT FROM AUTHOR]

One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformulation of the problem of interest and solving the resulting problem by a fast first order saddle point method utilizing smoothness of the saddle point cost function. In this paper, we demonstrate that when the saddle point cost function is polynomial, the precise gradients of the cost function required by deterministic first order saddle point algorithms and becoming prohibitively computationally expensive in the extremely large-scale case, can be replaced with incomparably cheaper computationally unbiased random estimates of the gradients. We show that for large-scale problems with favorable geometry, this randomization accelerates, progressively as the sizes of the problem grow, the solution process. This extends significantly previous results on acceleration by randomization, which, to the best of our knowledge, dealt solely with bilinear saddle point problems. We illustrate our theoretical findings by instructive and encouraging numerical experiments. [ABSTRACT FROM AUTHOR]

In the classical k-median problem, we are given a metric space and want to open k centers so as to minimize the sum (over all the vertices) of the distance of each vertex to its nearest open center. In this paper we present the first constant-factor approximation algorithms for two natural generalizations of this problem that handle matroid or knapsack constraints. In the matroid median problem, there is an underlying matroid on the vertices and the set of open centers is constrained to be independent in this matroid. When the matroid is uniform, we recover the k-median problem. Another previously studied special case is the red-blue median problem where we have a partition matroid with two parts. Our algorithm for matroid median is based on rounding a natural linear programming relaxation in two stages, and it relies on a connection to matroid intersection. In the knapsack median problem, centers have weights and the total weight of open centers is constrained to be at most a given capacity. When all weights are uniform, this reduces to the k-median problem. The algorithm for knapsack median is based on a novel LP relaxation that constrains the set of centers that each vertex can get connected to. The rounding procedure uses a two-stage approach similar to that for matroid median. [ABSTRACT FROM AUTHOR]

This paper provides the first exact analysis of a preemptive M=M=c queue with two priority classes having different service rates. To perform our analysis, we introduce a new technique to reduce the two-dimensionally infinite Markov chain (MC), representing the two class state space, into a one-dimensionally infinite MC, from which the generating function (GF) of the number of low-priority jobs can be derived in closed form. (The high-priority jobs form a simple M/M/c system and are thus easy to solve.) We demonstrate our methodology for the c = 1,2 cases; when c >2, the closed-form expression of the GF becomes cumbersome. We thus develop an exact algorithm to calculate the moments of the number of low-priority jobs for any c ≥ 2. Numerical examples demonstrate the accuracy of our algorithm and generate insights on (i) the relative effect of improving the service rate of either priority class on the mean sojourn time of low-priority jobs; (ii) the performance of a system having many slow servers compared with one having fewer fast servers; and (iii) the validity of the square root staffing rule in maintaining a fixed service level for the low-priority class. Finally, we demonstrate the potential of our methodology to solve other problems using the M/M/c queue with two priority classes, where the high-priority class is completely impatient. [ABSTRACT FROM AUTHOR]

This paper presents a methodology based on generic evolutionary algorithms to solve a dynamic pickup and delivery problem formulated under a hybrid predictive control approach. The solution scheme is designed to support the dispatcher of a dial-a-ride service, where quick and efficient real-time solutions are needed. The scheme considers different configurations of particle swarm optimization and genetic algorithms within a proposed ad-hoc methodology to solve in real time the nonlinear mixed-integer optimization problem related with the hybrid predictive control approach. These consist of different techniques to handle the operational constraints (penalization, Baldwinian, and Lamarckian repair) and encodings (continuous and integer). For parameter tuning, a new approach based on multiobjective optimization is proposed and used to select and study some of the evolutionary algorithms. The multiobjective feature arises when deciding the parameters with the best trade-off between performance and computational effort. Simulation results are presented to compare the different schemes proposed and to advise conditions for the application of the method in real instances. [ABSTRACT FROM AUTHOR]