Knowledge that Transforms

This paper presents a mathematical model of sequential investment behavior under conditions of uncertainty. The model addresses the problem of an investor with access to a limited pool of capital, who makes sequential decisions on long-lasting investments, under uncertainty as to the timing or the quality of future opportunities. We derive optimal investment strategies for the cases where the return from investment is a convex or concave function, we present closed form solutions for commonly adopted return functions, and we evaluate how the optimal investment behavior should change when changes occur in the environment, or the underlying probability distributions. In addition, we analyze three modifications of the problem. The results presented in this paper extend previous results on investment behavior for long-lasting (irreversible) decisions; in addition, some results are in accordance with existing ones from portfolio theory and/or search theory.

In this paper we examine several models for systems subject to both repairable and nonrepairable failures. A repairable failure can be remedied by the application of a repair kit (spare part, standby system, etc.), whereas a nonrepairable failure terminates the life of the system. The stochastic properties of key system parameters are derived under appropriate assumptions. These results are then used to determine the optimal number of repair kits to stock in order to maintain a system having a specified cost structure. The applicability of such models to problems of systems design is illustrated in several examples. Our results make use of distributions of phase type, and demonstrate that this family of distributions provides considerable flexibility and computational tractability in reliability modeling.

In this note we consider the one-period inventory model in which it is required to determine the order quantity which maximizes the probability of realizing a predetermined level of profit R. We give a condition for determining the optimal order quantity and provide explicit expressions for the optimal order quantity in three special cases.

Technical expertise, human judgment, and the time spent by an analyst are often believed to be key factors in determining the accuracy of forecasts obtained with the use of a time series forecasting method. A control experiment was designed to empirically test these beliefs. It involved the participation of experts and persons with limited training. Forecasts were generated for 25 time series with the use of the Box-Jenkins, Holt-Winters and Carbone-Longini filtering methods. Results of the nonparametric tests used to compare the forecasts confirmed that technical expertise, judgmental adjustment, and individualized analyses were of little value in improving forecast accuracy as compared to black box approaches. In addition, simpler methods were found to provide significantly more accurate forecasts than the Box-Jenkins method when applied by persons with limited training.

In an important study reviewing the literature on econometric studies of the relationship between advertising and sales Clarke (Clarke, Darral G. 1976. Econometric measurement of the duration of advertising effects on sales. J. Marketing Res. 13 (November) 345–357.) concluded that the implied duration interval of the effects of advertising on sales were too long when the studies used annual data. A theoretical explanation is provided here for the observation of parameter estimates which vary with the data interval employed in the analysis. Parameter estimates are developed on the basis of data aggregated at various levels of temporal aggregation and compared with theoretical values. It is demonstrated that it is possible to recover bimonthly parameters when only annual data are available.

“Public agencies are very keen on amassing statistics—they collect them, add them, raise them to the nth power, take the cube root and prepare wonderful diagrams. But what you must never forget is that every one of those figures comes in the first instance from the village watchman, who just puts down what he damn pleases.” (Sir Josiah Stamp) The assessment of the conditional probabilities of events is useful and needed for forecasting, planning, and decision making. In this paper the difficulties associated with the assessment of these conditional probabilities are examined. The necessary and sufficient conditions that the elicited information on conditional probabilities must satisfy are evaluated against actual assessments in several different controlled settings. A high frequency of implicit violations of the probability calculus was observed. The consistency of the assessments is affected by the causal/diagnostic and positive/negative relationships of the events. Use of a judgmental aid in the form of a joint probability table reduces the number of inconsistent responses significantly. Using the probability axioms, it is also shown that only the first order conditional probabilities need be assessed, as higher order probabilities are robust to the unconditional and first order conditional assessments.

A flexible manufacturing system (FMS) is an integrated, computer-controlled complex of automated material handling devices and numerically controlled machine tools that can simultaneously process medium-sized volumes of a variety of part types. FMSs are becoming an attractive substitute for the conventional means of batch manufacturing, especially in the metal-cutting industry. This new production technology has been designed to attain the efficiency of well-balanced, machine-paced transfer lines, while utilizing the flexibility that job shops have to simultaneously machine multiple part types. Some properties and constraints of these systems are similar to those of flow and job shops, while others are different. This technology creates the need to develop new and appropriate planning and control procedures that take advantage of the system's capabilities for higher production rates. This paper defines a set of five production planning problems that must be solved for efficient use of an FMS, and addresses specifically the grouping and loading problems. These two problems are first formulated in detail as nonlinear 0-1 mixed integer programs. In an effort to develop solution methodologies for these two planning problems, several linearization methods are examined and applied to data from an existing FMS. To decrease computational time, the constraint size of the linearized integer problems is reduced according to various methods. Several real world problems are solved in very reasonable time using the linearization that results in the fewest additional constraints and/or variables. The problem characteristics that determine which linearization to use, and the application of the linearized models in the solution of actual planning problems, are also discussed.

In this paper, we develop a complete and practical method for efficient compulation of the sensitivity information of a transfer line throughput. Our approach, which is a combination of analysis and experimentation, is fundamentally different from the existing solution methods. Using this approach the gradient information of the line throughput with respect to various decision variables is made available by a single observation of the line production history plus computation based on the observed data. These calculations are simple enough to be implemented on microcomputers. After an analytical development, three applications and experimental verifications are presented, namely the optimization of the line throughput with respect to the buffer sizes, the cycle times and the repair times. The study provides useful insights to line performance improvement. For example, buffer sizes are but one set of decision variables, not necessarily the most important. Cycle time and repair time can be more significant parameters on the line performance optimization. In addition, the method provides a useful management support system in identifying the line critical points, where local improvement due to change in a parameter can result in most significant improvement in the overall line throughput performance.

This paper describes a branch and bound algorithm which can solve assembly line balancing probems with nine modifications to the originally formulated problem of minimizing the required number of assembly stations, given a cycle time, a set of tasks with given deterministic performance times, and between-task precedence relationships. The first two formulation modifications are those of permitting planned imbalance in the total of task performance times at each assembly station, and allowing specific tasks to be assigned to specific types of assembly stations. Seven further problem modifications can be solved by the proposed algorithm, or by any algorithm or heuristic that can solve problems containing these first two modifications. They are: treatment of stochastic task performance times on unpaced lines; requirement of particular tasks to be assigned to particular stations; requirement of task groupings according to task skill levels; requirement of particular tasks to be assigned to only a left-of-line or right-of line station; required task separations; some mixed model situations; and where paralleling of a specified task into two (or more stations) is permitted. The algorithm is presented in both conceptual and detailed form. Computer computation times to solve a selected cross-sectional sample of problems are provided.

We consider a GI/M/s queuing system that is controlled by either accepting or rejecting arriving customers. Under weak conditions on the cost structure, Stidham (Stidham, S., Jr., 1978. Socially and individually optimal control of arrivals to a GI/M/1 queue. Management Sci. 24 1598–1610.) showed that a control limit policy is optimal. In this paper we show how the special structure of this queuing system can be exploited to develop efficient procedures to determine an optimal control limit. An explicit algorithm for computing the optimal control as well as an example and some computational results are included.