The analysis of a conveyor-serviced production station

Nawijn, W.M.; Jonge, R. de

doi:10.1016/0377-2217(81)90330-1

Cited by 7 publications

(1 citation statement)

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“…In fact, this policy will maximize the average number of customers served per unit of time. Special cases of this model have been considered in the literature on "Conveyor-serviced Production Stations" (see Beightler and Crisp [1968], Matsui and Shingu [1978], Nawijn and De Jonge [1981], and Nawijn [1983).…”

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The Optimal Look-Ahead Policy for Admission to a Single Server System

Nawijn

1985

Operations Research

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This paper considers a service system with a single server, finite waiting room, and a renewal arrival process. Customers who arrive while the server is busy are lost. Upon completing service, the server chooses between two actions: either he immediately starts a new service, provided a customer is present, or he admits the newly arrived customer to the system, but delays service pending the next arrival, whereupon he again chooses between these two actions. This process continues until either the system is full or a new service is started. Once a service has been started, all customers who arrive while the server is busy are lost. We assume that at each decision epoch the server knows the arrival epoch of the first arriving customer. We show that there exists an optimal control-limit policy that minimizes the average expected idle time per customer served (equivalently, maximizes the average number of customers served per unit of time). The special case of Poisson arrivals leads to an explicit expression for this delay that generalizes exisiting results.T HE MODEL considered in this paper originates from the following problem. Consider a work station, situated along a conveyor, comprised of a storage buffer of finite capacity and a machine served by an operator. Since the operator unloads the parts arriving on the conveyor and also performs the necessary operations on the parts, parts arriving during a service are lost. If the operator can always see the first oncoming part, the question arises as to which unloading policy will maximize the production rate of the work station.Our model is a service system with one server and finite waiting room. Customers arrive according to an ordinary renewal process. Upon terminating a service, the server notes the time that elapses until the next arrival. We assume that he immediately detects this time with certainty. Having observed this time, the server can choose between two actions: either instantaneously start a new service, provided a customer is present, or delay service until the next arrival and admit the newly arriving customer to the system. In the latter case he notes the arrival epoch of the subsequent customer, which has just become known to him, and Subject classification: 119 look-ahead policy for admission to single server system, 587 unloading policy for conveyor-serviced work station, 601 admission control to single server queue.

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