We consider the optimal control of two parallel servers in a two-stage tandem queuing system with two flexible servers. New jobs arrive at station 1, after which a series of two operations must be performed before they leave the system. Holding costs are incurred at rate h1 per unit time for each job at station 1 and at rate h2 per unit time for each job at station 2.The system is considered under two scenarios; the collaborative case and the noncollaborative case. In the prior, the servers can collaborate to work on the same job, whereas in the latter, each server can work on a unique job although they can work on separate jobs at the same station. We provide simple conditions under which it is optimal to allocate both servers to station 1 or 2 in the collaborative case. In the noncollaborative case, we show that the same condition as in the collaborative case guarantees the existence of an optimal policy that is exhaustive at station 1. However, the condition for exhaustive service at station 2 to be optimal does not carry over. This case is examined via a numerical study.
We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.
In most deterministic manufacturing decision models, demand is either known or induced by pricing decisions in the period that the demand is experienced. However, in more realistic market scenarios consumers make purchase decisions with respect to price, not only in the current period, but also in past and future periods. We model a joint manufacturing/pricing decision problem, accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods. We formulate a mathematical programming model and develop solution techniques. We identify structural properties of our models and develop closed-form solutions and effective heuristics for various special cases of our models. Finally, we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights.
We examine the impact of consumer valuation interdependence and capacity on a firm’s optimal selling strategies. We consider a seller who can offer a single product to consumers twice, in advance and in spot. Consumers choose whether and when to buy, but if they buy in advance, they are uncertain about their own valuations. Whether they buy in advance or in spot, consumers’ valuations are realized in the spot period and they may range from fully independent to perfectly correlated, creating markets with different characteristics of aggregate demand for the seller. Facing these consumers, the seller chooses a portion of the total capacity to offer in advance and prices in both periods. We describe how the optimal strategy and benefits of advance selling depend on the interdependence of consumer valuation, as well as capacity level and other market parameters. We find that a change in valuation interdependence can lead to dramatically different policies for the seller. For example, when individual valuations are highly diverse and the consumer population is large, the seller must offer a discount during advance selling but may limit the advance sales. On the other hand, when valuations are highly correlated, the seller can charge a premium price during advance selling. For the same valuation interdependence, the qualitative nature of the optimal strategy changes with available capacity. This paper was accepted by Martin Lariviere, operations management.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.