Fluid flow models are used in the performance evaluation of production, computer, and telecommunication systems. In order to develop a methodology to analyze general Markovian continuous material flow production systems with two processing stages with an intermediate finite buffer, a general single-buffer fluid flow system is modelled as a continuous time, continuous-discrete state space stochastic process and the steady state distribution is determined. Various performance measures such as the production rate and the expected buffer level are determined from the steady-state distributions. The flexibility of this methodology allows analysis of a wide range of models by specifying only the transition rates and the flow rates associated with the discrete states of each stage. Therefore the method is proposed as a tool for performance evaluation of general Markovian continuous flow systems with a finite buffer. The solution methodology is illustrated by analyzing a production system where each machine has multiple up and down states associated with their quality characteristics.
In this study we present a planning methodology for a firm whose objective is to match the random supply of annual premium fruits and vegetables from a number of contracted farms and the random demand from the retailers during the planning period. The supply uncertainty is due to the uncertainty of the maturation time, harvest time, and yield. The demand uncertainty is the uncertainty of weekly demand from the retailers.We provide a planning methodology to determine the farm areas and the seeding times for annual plants that survive for only one growing season in such a way that the expected total profit is maximized. Both the single period and the multi period cases are analyzed depending on the type of the plant. The performance of the solution methodology is evaluated by using numerical experiments. These experiments show that the proposed methodology matches random supply and random demand in a very effective way and improves the expected profit substantially compared to the planning approaches where the uncertainties are not taken into consideration.
We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system, when it is managed according to this policy, is evaluated.
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