Morris proposed a set of axioms for combining experts’ probability assessments. It is here argued that one of these axioms is unsatisfactory. Its use leads to a conflict between the discrete and continuous cases which disappears in a coherent approach.
We consider the problem of determining a schedule of capacity expansions for m producing regions and a schedule of shipments from the regions to n markets so as to meet market demands over a T-period planning horizon at minimum discounted capacity expansion and shipment costs. The proposed algorithm permits capacity expansion costs to be arbitrary nonnegative increasing functions of the expansion amounts, but the shipment (and production) costs are restricted to be proportional to the amounts shipped. The algorithm does not require market demands to be increasing over time. The cost functions are allowed to be nonstationary and the possibility of imports is considered. The proposed heuristic algorithm improves on feasible solutions by simultaneously reassigning several capacity expansions to different regions and/or time periods. A look-ahead feature prevents the algorithm from becoming myopic and a self-learning feature dynamically updates computational parameters. The heuristic algorithm was tested on both randomly generated and real-life based problems with m ≤ 15, and n ≤ 15 and T ≤ 25. The test problems had increasing market demands, capacity expansion costs specified in the form of a concave power function or a fixed charge plus linear function, stationary costs (aside from a constant discount factor), and no imports. Results indicate that for the class of problems tested, the heuristic algorithm is computationally efficient and provides solutions that are closer to optimum than those obtained by previous algorithms.
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 probabilities, 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.
This note describes a simple procedure for assessing utility functions which avoids many difficulties of the standard techniques. The conventional methods suffer from at least three drawbacks; they (1) generate utility functions that depend on the probability levels used; (2) chain responses from one question to the next, so that any bias is propagated and even magnified; and (3) change ranges and reference points constantly, introducing range effects and other distortions. Noting the evidence linking the dependence of utility functions on the “certainty effect,” our method: (1) compares lotteries with other lotteries rather than certain amounts; (2) does not “chain” responses; and (3) consistently uses “elementary lotteries” which control for range and reference points. Experimental work supports the proposed procedure.
An empirical analysis indicates that the order of entry of a brand into a consumer product category is inversely related to its market share. Market share is modeled as a log linear function of order of entry, time between entries, advertising, and positioning effectiveness. The coefficients of the entry, advertising, and positioning variables are significant in a regression analysis on an initial sample of 82 brands across 24 categories. These findings are confirmed by predictions on 47 not previously analyzed brands in 12 categories. Managerial implications for pioneers and later entrants are identified.
Mixing the risky asset with the riskless asset. Levy and Kroll have developed stochastic dominance rules with borrowing and lending (SDR). These rules can be easily applied to discrete distributions (e.g., ex-post data). However, an infinite number of comparisons is involved when the distributions under consideration are continuous. This study suggests a method for applying the SDR criteria to continuous distributions where, in general, a small number of comparisons is involved. For some distributions (e.g., lognormal) the SDR relationship is stated in terms of the distributions' parameters, and hence only one comparison is required. These SDR relationships enable us to establish the lognormal efficient frontier.
This paper treats a continuous review, single product stochastic cycling problem with demand modelled as a Brownian motion process. A broad class of production policies is admitted: they may be nonstationary, non-Markovian, or, in fact, almost arbitrary. Control theory is used to show that, within this wide class of policies, a simple, stationary, two-number policy is optimal for the average cost minimization problem. This policy switches production on when it is currently off and net inventory reaches a low critical level, or switches it off when it is on and net inventory reaches a high critical level. Simple methods are developed for obtaining the optimal critical levels numerically. Examples are developed comparing the results with those given by Graves and Keilson for a different demand process having the same mean and variance per unit time.
In a queue with several different arrival streams, in general, the expected delay for customers from one stream is not equal to the expected delay for customers from the other streams. Two approximations are presented here for the expected delay for customers from a particular arrival stream in an arrival process that is the superposition of independent renewal processes. Both approximations yield errors less than 10 percent, on average, when compared to simulation estimates. One approximation, extended from Holtzman (Holtzman, J. M. 1982. Mean delays of individual streams into a queue: the ΣGI i /M/1 queue. Applied Probability-Computer Science: The Interface, I, Proc. Conf. in Boca Raton, 417–430.), yields better results for very sparse arrival streams and the other, empirically derived, is easier to calculate. These approximations are useful in comparing the expected delays for customers from different arrival processes to a single queue and for customers with different routes through a network of queues.
A methodology for determining optimal sampling plans for Bayesian multiattribute acceptance sampling models is developed. Inspections are assumed to be nondestructive and attributes are classified as scrappable or screenable according to the corrective action required when a lot is rejected on a given attribute. The effects of interactions among attributes on the resulting optimal sampling plan are examined and show that: (1) sampling plans for screenable attributes can be obtained by solving a set of independent single attribute models, (2) interactions of scrappable attributes on screenable attributes and conversely result in smaller sample sizes for screenable attributes than in single attribute plans, and (3) interactions among scrappable attributes result in either smaller sample sizes, lower acceptance probabilities or both, relative to single attribute plans. An iterative subproblem algorithm is developed, which is effective in finding near optimal multiattribute sampling plans having a large number of attributes.
Business Portfolio Planning techniques often suggest that firms should invest in industries with high profitability, high growth, or other attractive characteristics. Critiquing this view, we suggest that the same factors which lead to high profitability in an industry may cause its inefficient participants to earn lower profits. Higher growth, on the other hand, may benefit inefficient firms while reducing the gains of efficient competitors. The paper offers theory and evidence to support this view of performance dependencies for the special case of diversified firms.