Knowledge that Transforms

In this paper we present a heuristic method, based on Lagrangian relaxation, for multilevel lot-sizing when there is a single bottleneck facility. A series of Lagrangian relaxations (one for each item in the product structure) is imbedded in a branch and bound procedure. The objective is to find a production schedule that fits within available capacity at minimum cost. The method has two solution phases, dual and primal. In the dual phase of the procedure, implied costs of setups and production are determined based on a tentative schedule. The primal phase is repeated with these new prices and we iterate to reach a good solution. The solution procedure is first tested on two special cases: uncapacitated multilevel lot-sizing and the capacitated, single-level multi-item lot sizing problem. The results show that the solution procedure can provide better solutions than some heuristics designed especially for those problems. Test results on the bottleneck problem indicate that good feasible solutions are found for problems too difficult to solve with exact methods.

This paper describes a simulation procedure for estimating the distribution function of the shortest path length in a network with random arc lengths. The method extends the concept of conditional Monte Carlo utilizing special properties of the Uniformly Directed Cutsets and the unique arcs. The objective here is to reduce the sampling effort and utilize known probability information to derive multivariate integrals of lower dimension. The experimental results show that the proposed method is substantially cost effective and performs better than traditional Monte Carlo and conditional methods.

A theory based upon random search within a fixed population of technological possibilities is used to explain the manufacturing progress function. The theory is consistent with the power function relation between unit costs and cumulative output that has frequently been observed. It is also consistent with initial rates of improvement smaller than those predicted later by the power function relation, the eventual cessation of cost reduction, and an irregularity of improvements. Existing theories in the literature either fail to agree with the main empirical phenomena or else assume precisely what they attempt to explain.

The Herstein–Milnor independence axiom is a necessary condition for recursion analysis of decisions in extensive (=tree) form.

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.