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A newsvendor game allows the players to collaborate on inventory pooling and share the resulting total cost. There are several possible ways to allocate the cost. Previous studies have focused on the core of the game. It is known that the core of the newsvendor game is nonempty, and one can use duality theory in stochastic programming to construct an allocation—referred to as the dual-based allocation—belonging to the core. Yet, an allocation that lies in the core does not necessarily guarantee the unhindered formation of a coalition, as some existing members' allocated costs may increase when new members are added in the process. In this work, we use the concept of population monotonic allocation scheme (PMAS), which requires the cost allocated to every member of a coalition to decrease as the coalition grows, to study allocation schemes in a growing population. We show that when the demands faced by the newsvendors are independent, log-concavity of their distributions is sufficient to guarantee the existence of a PMAS. Specifically, for continuous demands, log-concavity ensures that the game is convex, which in turn implies a PMAS exists. We also show that under the same condition the dual-based allocation scheme is a PMAS. For discrete and log-concave demands, however, the game may no longer be convex, but we manage to show that, even so, the dual-based allocation scheme is a PMAS. When the demands are dependent, the game is in general not convex. We derive a sufficient condition based on the dependence structure, measured by the copula, to ensure that the dual-based allocation scheme is still a PMAS. We also include an example of a game with no PMAS. This paper was accepted by Yinyu Ye, optimization. The online appendix is available at https://doi.org/10.1287/mnsc.2018.3053. [ABSTRACT FROM AUTHOR]

The technique of perturbation analysis has recently been introduced as an efficient way to compute parameter sensitivities for discrete event systems. Thus far, the statistical properties of perturbation analysis have been validated mainly through experiments. This paper considers, for an M/G/1 queueing system, the sensitivity of mean system time of a customer to a parameter of the arrival or service distribution. It shows analytically that (i) the steady state value of the perturbation analysis estimate of this sensitivity is unbiased, and (ii) a perturbation analysis algorithm implemented on a single sample path of the system gives asymptotically unbiased and strongly consistent estimates of this sensitivity. (No previous knowledge of peturbation analysis is assumed, so the paper also serves to introduce this technique to the unfamiliar reader.) Numerical extensions to GI/G/1 queues, and applications to optimization problems, are also illustrated. [ABSTRACT FROM AUTHOR]

This paper investigates equilibrium R&D investment strategies of firms endowed with different innovation potentials. To address this issue, this paper permits two stages of innovation and develops a simple stochastic game model involving two firms. It is shown that in equilibrium, a leader in the multiple stage innovation game invests more than a follower; firms compete more vigorously in the later stages of innovation than in the earlier stages; and a follower is more likely to choose a riskier innovation path than one requiring, on average, equivalent effort. It provides an explanation of how the expected benefits, the cost of R&D, and interactions between competing firms combine to determine dynamic R&D strategies over time. [ABSTRACT FROM AUTHOR]

This paper presents a class of utility functions (class A[sub ∞]) that contains all of the utility functions commonly used for mathematical modeling: the class consisting of those utility functions whose derivatives alternate in sign. A simple representation via mixtures of exponential utilities is provided for this class which is both mathematically convenient and conducive to functional operations. A connection with Laplace transforms and the resultant implications for preference relations, aggregation and utility assessment are discussed. [ABSTRACT FROM AUTHOR]

Queueing systems with interruptions serve as models for a variety of situations occurring in every day life. Usually, for each type of interruption, a separate queueing analysis is required. In this paper we present a single queueing model which can be used to analyze many such systems. The model is in the form of an approximation that is based upon several parameters, which reflect the particular queueing system under consideration. Applications to queueing systems with priorities and breakdowns are given in the paper. [ABSTRACT FROM AUTHOR]

This paper is based on the notion of discriminatory power of a pattern classifier acting over a feature space. Discriminant functions are normally used to trace out regions of the feature space corresponding to specific pattern classes. Indeterminate cases occur whenever a pattern lies on a class boundary. The number of occurrences of such indeterminacies measures the relative discriminatory power of a family of discriminant functions. In this paper these concepts are applied to majority voting decisions. It is first shown how regular majority voting leads to discriminant functions with insufficient discriminatory power whenever intransitive social ordering occurs. An (improved) family of discriminant functions is proposed to resolve such cases. [ABSTRACT FROM AUTHOR]

The paper presents a method for solving the linear programming problems, which is itself a step towards the generalization of the classical Simlex Method. It replaces two basic variables by two non-basic variables at each iteration. Naturally this will reduce the total number of steps to reach the final solution. The paper also includes the solution of one example to illustrate the applicability of the method. [ABSTRACT FROM AUTHOR]

This paper explores several important notions relevant to modern utility theory. Restricting the discussion to the consideration of bivariate utility functions, the paper defines and examines the interrelationships between (1) independence in the utility sense, (2) trade-off or indifference curves, and (3) transformation curves (as defined herein). Following the form in which a set of basic axioms of utility are stated, independence is defined in terms of indifference between 50-50 gambles, and it is shown that, if the condition of the definition holds, then φ (x, y), the bivariate utility function, can be written as a function of x plus a function of y. The concepts of trade-off curve (indifference curve) and transformation curve are also defined on the basis of the indifference relation but are not concerned with gambles. After exploring relationships among the three notions it is shown how the utility curves for the two variables under independence can be constructed on the basis of two trade-off curves. [ABSTRACT FROM AUTHOR]

This paper describes a simple set of coordination structures that model certain kinds of information processing involved in organizations and markets. Four generic coordination structures are defined: product hierarchies, functional hierarchies, centralized markets, and decentralized markets. Then tradeoffs among these structures are analyzed in terms of production costs, coordination costs, and vulnerability costs. This model is unusual in that it includes detailed definitions of the structures at a micro-level and mathematical derivations of comparisons among them at a macro-level. In the final section of the paper, several connections are made between these formal results and previous work on organizational design. [ABSTRACT FROM AUTHOR]

The paradox involved in sequences of Prisoner's Dilemma games is due to the fact that game theoretic definitions of optimality rarely coincide with any natural meaning of the word. Decision makers should incorporate their beliefs and experience into any mathematical analysis of the games. Once this has been done, via subjective probabilites, use of the cooperative move in iterated Prisoner's Dilemma games can often be justified. The paper provides a simple algorithm for determining an optimal strategy, once the decision maker's subjective probabilities have been specified. [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]

It is well known that all betting systems applied to independent, repeated, and identically distributed trials will result in the same expected gain per average unit wagered as that which applies to a single trial. This paper develops the asymptotic and paradoxical manner in which that constant win rate is maintained for optimal proportional betting according to the Kelly criterion. The appropriateness of using this traditional measure of win rate for proportional betting is contrasted with that of various alternatives. [ABSTRACT FROM AUTHOR]

In a companion paper we developed a unified scheme for using poststratified sampling and control variables to improve the efficiency of regenerative queueing simulations. We adapted these variance reduction techniques to the estimation methods of replication analysis and regenerative analysis by exploiting the asymptotic joint normality of certain standardized concomitant variables that are defined on each input process sampled during a queueing simulation. In this paper we present an experimental evaluation of the reductions in point-estimator variance and confidence-interval width that can be achieved with each procedure in several closed and mixed machine-repair systems. For the analytically tractable model, nominal and actual confidence-interval coverage probabilities are also compared. Poststratification generally produced variance reductions ranging from 10% to 40% and confidence-interval reductions between 1% and 20%. The control-variates schemes yielded variance reductions ranging from 20% to 90% and confidence-interval reductions between 10% and 70%. In some instances where small sample sizes were used, the poststratification schemes produced confidence-interval width increases between 1% and 10%. With a small number of regenerative cycles, some loss of confidence-interval coverage was observed with both poststratified and controlled regenerative analysis. When larger sample sizes were used, all of the estimation schemes yielded fairly consistent efficiency gains. [ABSTRACT FROM AUTHOR]

This paper is a comprehensive study of methods for assessing unidimensional expected utility functions. The paper describes the utility assessment process in decision analysis and then reviews problem formulation, sources of bias in preference judgments, and the analysis of risk attitudes. Two dozen utility assessment methods of which half appear for the first time are critically examined. These methods are grouped into preference comparison methods, probability equivalence methods, value equivalence methods, certainty equivalence methods, hybrid methods, paired-gamble methods, and other approaches. The paper emphasizes the nature of judgmental biases in comparing different assessment procedures. Since most multiattribute utility functions are decomposed into single-attribute functions, this study should facilitate such applications. The paper concludes with several directions for further developmental, empirical, and applied research. [ABSTRACT FROM AUTHOR]

Due to the complexity of optimum replacement problems over finite time horizons various asymptotic criteria based upon fixed age replacement policies have been employed in the literature and in practice. In this paper the relationships between the optimum policies under three alternative cost criteria are considered. An ordering of the accounting costs under two of these is obtained, and for distributions with Increasing Hazard Rate an ordering of the optimum replacement time is derived. For a finite time horizon the policies are compared to the optimal sequential and fixed-age replacement polices through the example of a gamma distribution previously investigated by Barlow and Proschan (1962, 1965). [ABSTRACT FROM AUTHOR]

The subject of this paper is a classification and discussion of algorithms for solution of nonlinear pure integer programming problems. The survey is organized by characterizing the mathematical form of the nonlinear optimization problems addressed by the various algorithms. If any method can be used without changes to solve mixed integer nonlinear programming problems that fact is mentioned in the description of the algorithm. However algorithms which must be applied only to mixed integer problems are not surveyed. [ABSTRACT FROM AUTHOR]

A question that recurs in the decision analysis literature is: What is the value of additional data gathering? We use a very general definition of data that includes subjective probability distributions provided by experts, calculations from models, and traditional experimental data. General expressions for the expected value of data have little practical use because they involve probability distributions whose arguments are themselves probability distributions. The traditional approach to alleviate the problem of dimensionality is to introduce arbitrary parameterization of the data. This paper shows that for an interesting class of decision problems, arbitrary parameterization is not necessary. For the class of decision problems in which the value function over outcomes is a quadratic function of the state and decision variables, the value of data depends on the state variables only through the prior covariances of the posterior means. To use this result in the calculation of the approximate value of data for practical problems, it is necessary to simplify the value function. The paper suggests simplifying the value function by expanding it in a Taylor series with respect to the state and decision variables. The resulting expressions for the approximate value of information should be useful and inexpensive to evaluate for practical decision problems. [ABSTRACT FROM AUTHOR]

This paper, which is presented in two parts, is a contribution to the theory of fractional programming, i.e. maximization of quotients subject to constraints. In Part 1, duality theory for linear and concave-convex fractional programs is developed and related to recent results by Bector, Craven-Mond, Jagannathan, Sharma-Swarup, et al. Basic duality theorems of linear, quadratic and convex programming are extended. In Part II Dinkelbach's algorithm solving fractional programs is considered. The rate of convergence as well as a priori and a posteriori error estimates are determined. In view of these results the stopping rule of the algorithm is changed. Also the starting rule is modified using duality as introduced in Part I. Furthermore a second algorithm is proposed. In contrast to Dinkelbach's procedure the rate of convergence is still controllable. Error estimates are obtained too. [ABSTRACT FROM AUTHOR]

In this paper, we present a branch-and-price method to solve special structured multistage stochastic integer programming problems. We validate our method on two different versions of a multistage stochastic batch-sizing problem (SBSP). One version adopts a recourse formulation, and the other is based on probabilistic constraints. Our algorithmic approach is applicable to both formulations. Our computational results suggest that both classes of problems can be solved using relatively few nodes of a branch-and-price tree. The success of our approach calls for extensions in methodology as well as applications. [ABSTRACT FROM AUTHOR]

A cursory survey of the theory of games is presented. The basic models for games in extensive form, normal form, and characteristic function form are discussed, and some generalizations and extensions of these models are mentioned briefly. Some general remarks about the applicability of the theory are made in §2, and a few specific applications are referred to in sections subsequent to the description of the particular models. Mention is made throughout this paper to the other game theoretic articles in this issue in an attempt to place them somewhat within this outline of the subject. [ABSTRACT FROM AUTHOR]

This paper describes a stochastic game in which the play terminates in a finite number of steps with probability 1. The game is called a terminating stochastic game. When the play terminates at any step, the play is regarded to reach to an absorbing state in the Markov chain under consideration. Hence, the terminating stochastic game is a nonstationary Markov chain with rewards in which our concern is the transient behavior before absorption. In particular, when one of the players is a dummy, the stochastic game reduces to a Markovian decision process of special type. This paper discusses such games. We introduce a new concept of rewards and formulate three problems arising in the games by linear programming. Finally, numerical examples are presented. [ABSTRACT FROM AUTHOR]

The general problem of control of a set of individuals to achieve the objective of a controller is common to many areas such as business and government. This paper attempts a mathematical formulation and analysis of such problems. It is assumed that each individual is a rational being acting in his own self-interest. The interests of different individuals are, in general, conflicting, thus leading to a competitive situation which can be analyzed using Game Theory notions. An important aim of mathematical analysis of such a situation will be to study the effectiveness of various kinds of power that a controller might have over the individuals. Most of the results in this paper are concerning a class of 'coordination problems' where the controller's objective is to maximize the total utility to the whole group of individuals and where competition arises due to constraints on strategies. The analysis indicates that in such cases the simple power to accept or reject strategies which violate the constraints may be sufficient to realize the controller's goals. [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]

The first part of this paper is concerned with the semi-infinite linear programs studied by Charnes, Cooper and Kortanek. A form of the Farkas lemma stated by Haar appears to apply to such programs and leads to a duality theorem. In this paper an example of a semi-infinite program is given which is consistent and which has a finite minimum. However the dual program is found to be inconsistent. With a variation of the example a situation is exhibited in which both the program and its dual are consistent and have finite extrema. In this case, however, the minimum of the former is not equal to the maximum of the latter. The existence of such a ‘duality gap’ indicates that Haar's statement needs qualification. In the second part of the paper a correct form of Haar's theorem is stated and proved. The proof invokes the infinite programming theory of Duffin and Kretschmer. The last part of the paper develops a new duality theory for infinite programs which, as a special case, insures a weak form of duality for programs typified by the examples. This new duality theory is somewhat simpler than previous theories of infinite programming. [ABSTRACT FROM AUTHOR]

This study extends the results of a paper on inventory models by H. M. Wagner and T. M. Whitin. Particular attention is given to the usefulness of planning horizon theorems in simplifying computations. [ABSTRACT FROM AUTHOR]

The paper evaluates and compares classes of multi-item inventory problems where joint order of several items may save a part of the setup cost. A cost ratio and simple decision rule are determined for joint versus individual orders in specified cases. The comparisons call for the necessity of a new policy for reorder point-triggered random output multi-item systems. This policy, "the random joint order policy," operates through the determination of a reorder range within which several items can be ordered. The existence of an optimum reorder range is proved, and a computational technique is demonstrated with the help of a machine-interference type queueing model. Under favorable conditions the results exhibited on the diagram of optimum reorder ranges are generally applicable. The random joint order policy model is especially suitable for computer controlled inventory systems. [ABSTRACT FROM AUTHOR]

Recent studies have demonstrated the effectiveness of applying adaptive memory tabu search procedures to combinatorial optimization problems. In this paper we describe the development and use of such an approach to solve binary quadratic programs. Computational experience is reported, showing that the approach optimally solves the most difficult problems reported in the literature. For challenging problems of limited size, which are capable of being approached by exact procedures, we find optimal solutions considerably faster than the best reported exact method. Moreover, we demonstrate that our approach is significantly more efficient and yields better solutions than the best heuristic method reported to date. Finally, we give outcomes for larger problems that are considerably more challenging than any currently reported in the literature. [ABSTRACT FROM AUTHOR]

The Analytic Hierarchy Process developed by Saaty (1980) has proven to be an extremely useful method for decision making and planning. However, some researchers in these areas have raised concerns over the theoretical basis underlying this process. This paper addresses currently debated issues concerning the theoretical foundations of the Analytic Hierarchy Process. We also illustrate through proof and through examples the validity or fallaciousness of these criticisms. [ABSTRACT FROM AUTHOR]

In this paper we present a mathematical programming model for the Kanban system in a deterministic multi-stage capacitated assembly-tree-structure production setting. We discuss solution procedures to the problem and address three special cases of practical interest. [ABSTRACT FROM AUTHOR]

In this paper we develop a semi-Markov formulation for modelling transitions of physicians, nurse practitioners, and physician assistants between different settings and locations within a geographic area. The model predicts the supply of primary care providers over a planning horizon. We then compare the model predictions with estimates of future demand and need for primary care for a community. Statistical tests for validation and sensitivity analysis of the model are also performed to establish the appropriateness of the semi-Markov approach. With the likelihood of an oversupply of physicians during this decade, the model offers a useful tool for health planners, administrators, legislators, and regulators, for objective decision making. [ABSTRACT FROM AUTHOR]

This paper presents a procedure for determining the number of simulation observations required to achieve a preassigned confidence interval for means estimated by simulation. This procedure, which is simple to implement and efficient to use, is compared with two other methods for determining the required sample size in a simulation run. The empirical results show that this procedure gives good results in the precision of estimated means and in sample size requirement. [ABSTRACT FROM AUTHOR]

This paper studies the use of a scoring rule for the elicitation of forecasts in the form of probability distributions and for the subsequent evaluation of such forecasts. Given a metric (distance function) on a space of probability distributions, a scoring rule is said to be effective if the forecaster's expected score is a strictly decreasing function of the distance between the elicited and "tree" distributions. Two simple, well-known rules (the spherical and the quadratic) are shown to be effective with respect to suitable metrics. Examples and a practical application (in Foreign Exchange rate forecasting) are also provided. [ABSTRACT FROM AUTHOR]

Traditional sensitivity analysis of linear programming objective function coefficients concerns itself with variations in single parameters. In a recent book, Gal developed a theoretical framework to determine the effect of mutliple variations in the parameters. In this paper, we develop a methodology to implement and extend the theoretical results in the earlier work for interval variations of objective function coefficients. This methodology uses necessary and sufficient conditions to determine all optimal solutions to the linear programming problem for objective function coefficients within given intervals. The resulting procedure has been coded for computer use and tested on various types of test problems. Computational results and an example are presented. [ABSTRACT FROM AUTHOR]

This paper considers the problem of maximizing the expected value of multicommodity flows in a network in which the arcs experience probabilistic loss rates. Consideration of probabilistic losses are relevant, particularly, in communication and transportation networks. An arc-chain formulation of the problem and an efficient algorithm for computing an optimal solution are provided. The algorithm involves a modified column generation technique for identifying a constrained chain. Computational experience with the algorithm is included. [ABSTRACT FROM AUTHOR]

The graph median and center problems are well known with numerous possible applications. The first is suitable for locating a facility providing a routine service, by means of minimizing the average distance of customers to it. The second is appropriate for emergency services where the objective is to have the furthest customer as near as possible to the center. In reality a combination of both, usually antagonistic, goals is common. This paper presents a procedure to locate a facility on a graph, such that a convex combination of the median and the center objective functions is minimized. The term "cent-dian" is coined for this point of the graph. Since it is usually difficult to assign precise weights to the two objectives, when they are convexly combined, the procedure generates the cent-dians for all possible combinations. Finally, an equivalent median problem on an expanded graph is presented. [ABSTRACT FROM AUTHOR]

The ELSP is a time-honored problem that "has been around" since 1915. It is the problem of accommodating cyclical production patterns when several products are made on a single facility. Recent contributions to its resolution resulted in either analytical approaches to a restricted problem, or heuristic approaches to the entire problem. This paper reviews critically the various contributions to the problem, and extends the analysis in the following four directions: (a) An improved analytical approach (b) A test for feasibility, (c) A systematic means for escape from infeasibility, and (d) A procedure for the determination of a basic period for a given set of multipliers to achieve a feasible schedule. [ABSTRACT FROM AUTHOR]

In a recent paper, Lippman presents sufficient conditions for Denardo's N-stage contraction in discounted semi-Markov decision processes with unbounded rewards. In this note it is demonstrated that Lippman's conditions may be replaced by weaker conditions which even imply l-stage contraction. The verification of the conditions of this note is somewhat easier. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to take stock of what is known and to suggest some conceptual foundations for future progress in the areas of postoptimality analysis and parametric optimization techniques for integer programming. [ABSTRACT FROM AUTHOR]

In 1970, abortion on demand was legalized in several sections of the United States. Due to increased demand for abortions, free standing abortion clinics came into existence. This paper develops a methodology for determining the optimal design of a free standing abortion clinic, in order to maximize its profits. An example of a clinic which was actually designed employing the methodology is presented, and the results suggest that the methodology is relevant and useful. [ABSTRACT FROM AUTHOR]

Most serial bond issues are sold competitively on an NIC (net interest cost) basis. The municipality awards the issue to the bidder submitting the lowest NIC. Although it is often acknowledged that NIC is a defective measure of the interest cost and sometimes a costly one to the issuer, an alternative measure, the TIC (true interest cost, effective interest cost, interest cost according to the Canadian method, or the internal rate of return) is often regarded as too computationally difficult to employ. State and local governments are becoming increasingly aware of the internal rate of return or TIC as a measure of interest expense. The use of TIC as a method of awarding bond issues to underwriters is growing very rapidly. This paper contains a simple computer algorithm for calculating optimal bids on a TIC basis. [ABSTRACT FROM AUTHOR]

This paper deals with the optimal issuing sequence of units, say batteries, from storage to the field when field lives are stochastic. Several appealing forms of the field life survival probability F(y | x) are given when the battery has been on the shelf a length of time x. These forms are used to investigate the optimality of LIFO (issue youngest) or FIFO (issue oldest) policies in two basic models. These models correspond to issuing batteries either according to a possibly random schedule (the independent case) or one after another as the successive batteries fail (the dependent case). [ABSTRACT FROM AUTHOR]

The paper presents a means of attempting to account for overhead, as well as function evaluations, in evaluating unconstrained optimization techniques. Criteria are established which compare techniques on classes of algorithms. While not completely machine independent, and certainly not programmer independent, the new method eliminates much of the machine dependency of earlier criteria. The criteria are applied to three known and one new quasi-Newton algorithm, with interesting results. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the relationship between the expected optimal value of a stochastic linear program and a stochastic program with recourse and the degree of uncertainty in the objective function coefficients c and the stipulation vector b. It is shown that under certain conditions the expected objective value is nondecreasing as the degree of uncertainty in c increases and the opposite is true for the case of b. The degree of uncertainty of a random vector is defined in terms of a covariance matrix. Some managerial interpretations are also given. [ABSTRACT FROM AUTHOR]

The author responds to the paper "The Loading Problem," by Eilon and Christofides. He focuses on suggesting a solution to the problem. The recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the one proposed by Eilon and Christofides. It is suggested that the simpler algorithm offered by the author reaches mathematical optimization as often as the aforementioned algorithm. It is further proposed that the algorithm presented by Eilon and Christofides cannot be used to solve multi-dimensional programming problems. The author goes on to discuss a numerical analysis that can be used for the allocation of industrial resources. Related mathematical models are discussed in detail. A table comparing the results of the two algorithms is also presented.

This paper considers the maximization of certain equivalent reward generated by a Markov decision process with constant risk sensitivity. First, value iteration is used to optimize possibly time-varying processes of finite duration. Then a policy iteration procedure is developed to find the stationary policy with highest certain equivalent gain for the infinite duration case. A simple example demonstrates both procedures. [ABSTRACT FROM AUTHOR]

This paper describes the use of multiple ranking procedures to analyze data generated from computer simulation experiments with models of management systems. After outlining the rationale for the use of multiple ranking procedures with computer simulation experiments and defining some basic terminology, we examine several specific multiple ranking procedures. Careful attention is given to the assumptions underlying the different multiple ranking procedures and the extent to which these assumptions are satisfied by the data generated by simulation experiments. An example model is included to illustrate the applicability of multiple ranking procedures to simulation experiments in management science. [ABSTRACT FROM AUTHOR]

A framework of concepts is developed which helps to unify a substantial portion of the literature on large-scale mathematical programming. These concepts fall into two categories. The first category consists of problem manipulations that can be used to derive what are often referred to as "master" problems; the principal manipulations discussed are Projection, Inner Linearization, and Outer Linearization. The second category consists of solution strategies that can be used to solve the master problems, often with the result that "subproblems" arise which can then be solved by specialized algorithms. The Piecewise, Restriction, and Relaxation strategies are the principal ones discussed. Numerous algorithms found in the literature are classified according to the manipulation/strategy pattern they can be viewed as using, and the usefulness of the framework is demonstrated by using it (see Part II of this paper) to rederive a representative selection of algorithms. The material presented is listed in the following order: The first section is introductory in nature, and discusses types of large-scale problems, the scope of discussion and the literature, and the notation used. The second section, entitled "Problem Manipulation: Source of 'Master' Problems" covers the subjects of projection, inner linearization and outer linearization. The third section, "Solution Strategies: Source of 'Subproblems'," discusses piecewise strategy, restriction and relaxation. The fourth section is entitled "Synthesizing Known Algorithms from Manipulations and Strategies," and is followed by a concluding section and an extensive bibliography. [ABSTRACT FROM AUTHOR]

A series of probabilistic models are formulated for the credit granting policy of a firm. First, a single-period analysis is presented for the two-action problem, "give credit or do not give credit." Then a multi-period analysis for the same problem is presented, showing that the single-period analysis ignores important future benefits. The multi-period analysis contains a Bayesian approach to revisions of the probability of collection as collection experience is gained. The multi-period analysis is modified by adding discounting to reflect the time value of money and a probability that the customer will cease purchasing. Next, a dynamic programming formulation of the multi-media problem is presented, and this formulation is then adapted to include a decision on how much credit to offer. The paper closes with a series of remarks concerning the practical application of the analysis. A series of probabilistic models are formulated for the credit granting policy of a firm. First, a single-period analysis is presented for the two-action problem, "give credit or do not give credit." Then a multi-period analysis for the same problem is presented, showing that the single-period analysis ignores important future benefits. The multi-period analysis contains a Bayesian approach to revisions of the probability of collection as collection experience is gained. The multi-period analysis is modified by adding discounting to reflect the time value of money and a probability that the customer will cease purchasing. Next, a dynamic programming formulation of the multi-media problem is presented, and this formulation is then adapted to include a decision on how much credit to offer. The paper closes with a series of remarks concerning the practical application of the analysis. [ABSTRACT FROM AUTHOR]

In this paper the Fiacco-McCormick SUMT technique is embedded in a class of inside-out algorithms. Convergence is demonstrated for the nonlinear programming problem under fairly general conditions and the algorithms are interpreted in a geometric structure. [ABSTRACT FROM AUTHOR]

Beckmann [1] and Mills [7] consider production smoothing problems in which demands are random variables. This paper generalizes and extends Beckmann's results which predicate backlogging of excess demand. Convex expected holding and penalty cost functions pertain to inventory and the cost of changing the production rate is proportional to the change. The model has a finite horizon and permits nonstationary costs and demand distributions. Beckmann shows that two curves in the plane determine an optimal policy (minimum expected discounted cost) each period. It is shown here that the curves have slopes between minus one and zero, are differentiable, and are bounded by two straight lines with a slope of minus one. The results are not changed by an upper bound on the quantity produced or by a lag between the time a product is manufactured and the time it is available to satisfy demand. [ABSTRACT FROM AUTHOR]