Dynamic resource allocation in a multi-product make-to-stock production system

We consider optimal policies for a production facility in which several (K) products are made to stock in order to satisfy exogenous demand for each. The single machine version of this problem in which the facility manufactures at most one product at a time to minimise inventory costs has been much studied. We achieve a major generalisation by formulating the production problem as one involving dynamic allocation of a key resource which drives the manufacture of all products under an assumption that each additional unit of resource allocated to a product achieves a diminishing return of increased production rate. A Lagrangian relaxation of the production problem induces a decomposition into K single product problems in which the production rate may be varied but is subject to charge. These reduced problems are of interest in their own right. Under mild conditions of full indexability the Lagrangian relaxation is solved by a production policy with simple index-like structure. This in turn suggests a natural index heuristic for the original production problem which performs strongly in a numerical study. The paper discusses the importance of full indexability and makes proposals for the construction of production policies involving resource idling when it fails

Reaction times of younger and older men: effects of compound samples and a prechoice signal on delayed matching-to-sample performances.

Five younger (18 to 23 yrs) and five older (65 to 73 yrs) men were exposed to a series of immediate and delayed (0 to 15 seconds) matching-to-sample problems. Presentation of the pairs of delayed comparison stimuli was either signaled or unsignaled, and the sample contained either 1, 2, or 3 elements, one of which appeared as the positive stimulus. During initial sessions, unlimited time was available to respond. Subsequently, correct responses were reinforced only if they occurred within a specified time limit. A general finding was slower responding with increased delay and with increased number of sample elements. These effects were reduced when the comparison stimuli were signaled and when time limits were in effect. Errors increased as a function of the manipulations of sample complexity and time limits, but did not change systematically when the delay between sample and comparison stimuli was varied. Although the younger men generally responded more quickly than the older ones, men of both ages showed increased speeds when limits were placed on response time, and these changes were maintained when the temporal contingencies were removed

Reaction times of younger and older men and temporal contingencies of reinforcement.

Influences of extended training and temporal contingencies on reaction time were studied in relation to developmental differences. Older and younger men were trained on a chained schedule in which completion of a variable interval produced a terminal link in which reaction time was measured. The reaction-time procedure involved a conditional discrimination with matching to sample in one component and oddity matching in the other. During baseline training, no time limit was placed on the response to the discrimination choice stimuli. Subsequently, increasingly severe time limits were imposed over a series of sessions. Older and younger men showed increased speeds (decreased reaction times) when temporal contingencies were imposed, and these changes were maintained during post-training baseline sessions when there was unlimited time in which to respond. The younger men generally responded faster than the older ones, and age differences were not appreciably reduced during the course of the experiment. The results indicated the feasibility of studying reaction time in human subjects using operant procedures analogous to those developed for the study of nonverbal organisms