Hyo-Seong Lee

Production-Inventory Systems with Preventive Maintenance

We consider a production facility that produces items for which demand occurs according to a Poisson process. The facility is assumed to deteriorate while it is in operation, with an increasing fai...

Performance evaluation and design of a CONWIP system with inspections

Abstract In this paper, we analyze a CONWIP (Constant Work-In-Process) system which consists of three stations in series. We assume that raw parts are always available. When a finished part is consumed by a demand, a raw part is released immediately and gets processed at each station sequentially. The processings do not always meet the requirement of quality. Therefore, at the end of the processing at each station, a part is inspected randomly to determine if it satisfies the requirement of quality. We assume that the inspection time is negligible. If a part is inspected and found to be defective because of treatment at station j, the part is fed back to station j to be treated again. We consider that the stations have an exponential or a N-stage Coxian service time distribution. We propose an analytical method to evaluate the performance of this kind of system. We consider two cases: one is the saturated case where the supply of demands is infinite and the other is the non-saturated case where external demands arrive according to a Poisson process. Then we use the analytical method to show how the optimal conwip system can be designed for a chosen design criterion. Although we present the method only for three-station systems in this paper, it can be easily extended to systems with more than three stations.

Performance evaluation of open queueing networks with arbitrary configuration and finite buffers

We consider an open queueing network consisting of servers linked in an arbitrary configuration with exponential service times and separated by intermediate finite buffers. The model allows any number of saturated servers (never starved) and exit servers (never blocked). The considered blocking mechanism is blocking-after-service. In the case of simultaneous blocking, blocked customers enter the destination node on a first-blocked-first-enter basis. If feedback loops exist in the network, deadlocks may arise. We assume that a deadlock is detected and resolved instantaneously by transferring all the blocked customers simultaneously. In this paper, we present an approximation method to analyze this kind of networks. The method decomposes the original network into subsystems. Each subsystem is composed of one or many upstream servers and one downstream server, separated by a finite buffer. The upstream and downstream servers are characterized by exponential service time distributions. Based on the symmetrical approach [2], we develop an algorithm to determine the unknown parameters corresponding to each subsystem. The class of models considered in this paper includes the class of open loss models for feed-forward networks considered by Lee and Pollock [11]. For this class of models, we can show that the system of equations in our algorithm is equivalent to the one used in the algorithm proposed by Lee and Pollock. As a result, our algorithm provides the same results as the algorithm of Lee and Pollock for this class of models. However, it is observed that our algorithm takes less CPU execution time than the one proposed by Lee and Pollock. For the cases of networks with feedback loops, extensive numerical experiments show that the new algorithm, in general, converges very fast and yields accurate results compared with those obtained by simulation as long as deadlocks do not occur too frequently. Moreover, for the merge configuration, we provide the proof of the convergence of the algorithm as well as the existence and uniqueness of the solution by exploiting the properties associated with a symmetric approach.

Approximate Analysis for the Merge Configuration of an Open Queueing Network with Blocking

Abstract A merge configuration of open queueing networks with exponential service times and finite buffers is analysed. We offer an iterative algorithm to approximate the steady-state probabilities for each queue of the system. The procedure decomposes the queueing network into individual queues and analyses each individual queue in isolation. An M/M/l/N or M/G/l/N model is used for the analysis of the merging queues; an M/M/l/N with state dependent arrival rates is used for the receiving queue. The approximation method is easy to implement, requires little memory, is computationally fast and yields very accurate results.

Optimal control of the M X /G/1/K queue with multiple server vacations

Abstract We consider an M X / G /1/ K queue in which the removable server applies the following (ν, N ) policy: Every time the server completes service and finds ν customers in the system, the server takes a sequence of vacations. At the end of each vacation, the server inspects the length of the queue. If the queue length is greater than or equal to N , the server begins service until the number of customers drops to ν. Under a classical cost structure, we characterize an optimal policy and develop an algorithm to find an optimal policy which minimizes the expected cost per unit time.

A multi-class closed queueing maintenance network model with a parts inventory system

The system we address is a maintenance network of repairable items where a set of bases is supported by a centrally located repair depot and a consumable replacement parts inventory system. If an item fails, a replacement part must be obtained at the parts inventory system before the failed item enters the repair depot. The ordering policy for the parts is the (S,Q) inventory policy. An approximation method for this system is developed to obtain performance measures such as steady-state probabilities of the number of items at each site and the expected backorders at the parts inventory system. The proposed system is modelled as a multi-class closed queueing network with a synchronization station and analyzed using a product-form approximation method. Particularly, the product-form approximation method is adapted so that the computational effort on estimating the parameters of the equivalent multi-class network is minimized. In analyzing a sub-network, a recursive method is used to solve balance equations by exploiting the special structure of the Markov chain. Numerical tests show that the approximation method provides fairly good estimation of the performance measures of interests.

A PRODUCTION/INVENTORY POLICY FOR AN UNRELIABLE MACHINE

In this paper, the economic lot-sizing problem for an unreliable production facility is considered. As in the standard Economic Manufacturing Quantity (EMQ) model, the demand and production rates are assumed to be constant. Unlike the EMQmodel, the facility is assumed to deteriorate while it is in operation, with an increasing failure rate. However, a preventive maintenance overhaul of the facility is assumed to restore the facility to its original condition.

Optimal replacement policies for systems with multiple standby components

The authors consider two new preventive replacement policies for a multiple-component cold-standby system. The failure rate of the component in operation is constant. The system is inspected at random points over time to determine whether it is to be replaced. The replacement decision is based on the number of failed components at the time of inspection. There are two replacement options if the complete system fails during operation: (i) replace the system if an inspection reveals that it has failed (system failure is not self-announcing), and (ii) replace the system the instant it fails (system failure is self-announcing). There is a threshold value on the number of failed components (at the time of inspection) which minimizes the mean total cost. The authors develop a simple efficient procedure to find the optimal threshold value. They compare the cost of operating a system that is inspected at random points in time, with the cost of operating a system that is monitored continuously through an attached monitoring device, and discuss cost tradeoffs. >

Optimal dispatching of an infinite capacity shuttle with compound Poisson arrivals: control at a single terminal

Abstract We consider the optimal control of an infinite capacity shuttle which transports passengers between two terminals. Passengers arrive at each of two terminals according to independent compound Poisson processes. The travel time from one terminal to the other one is a random variable following an arbitrary distribution. The dispatcher can hold the shuttle at only one of the terminals. Thus, when the shuttle is dispatched at terminal 1, it transports all the passengers waiting at terminal 1 to terminal 2 and instantaneously picks up the passengers at terminal 2 and returns to terminal 1. Assuming that the dispatcher has complete information about the number of passengers waiting at each terminal, we consider the following control limit policy: dispatch the shuttle if, and only if, the total number of passengers waiting at both terminals is at least as large as some prespecified control limit, m . In this paper, under a linear cost structure, we provide an explicit expression for the expected cost per unit time as a function of the control value, m , and present a simple and efficient method for computing the optimal control value.

A short note on the Poisson input queuing system with start-up time and under control-operating policy

Abstract The control policy for the M/G/1 queuing system in which the server is started-up when the accumulated number of customers reaches a predetermined value m and serves the system until it is empty. The time required to start up the server follows a general distribution. The mean waiting time of an arbitrary customer for a given value of m is derived and the optimal control policy is presented under a linear cost structure.