Allen H. Tai

Detection of machine failure: Hidden Markov Model approach

Hidden Markov Models (HMMs) are widely used in applied sciences and engineering. The potential applications in manufacturing industries have not yet been fully explored. In this paper, we propose to apply HMM to detect machine failure in process control. We propose models for both cases of indistinguishable production units and distinguishable production units. Numerical examples are given to illustrate the effectiveness of the proposed models.

Economic production quantity models for deteriorating/imperfect products and service with rework

In this paper, two economic production quantity (EPQ) models are proposed for deteriorating/imperfect items with rework process. The production process is imperfect, and imperfect quality items are reworked to become serviceable. At the same time, the remaining good quality items may deteriorate. The inspection of deteriorated items is also imperfect, so that deteriorated items may be sold to customers, which will create negative impact on corporate image. In the first model, a single production-rework plant system is considered. The optimal production times and the economic production quantities are obtained analytically. In the second model, a system that consists of n production plants and one rework plant is considered. A solution procedure is developed in order to obtain the optimal operating cost. Numerical examples are provided to compare the performance of the two systems.

A quantity-time-based dispatching policy for a VMI system

In a Vendor-Managed Inventory (VMI) system, the supplier or the distributor is authorized to coordinate and consolidate the inventories at the retailers. The advantage of VMI is that the bullwhip effect can be minimized and the stock-out situations can also be reduced. Moreover, it provides a framework for synchronizing transportation decisions and hence reduce the transportation cost significantly. In this paper, we present an analytic model for quantity-time-based dispatching policy. The model discussed here takes into the account of the inventory cost, the transportation cost, the dispatching cost and the re-order cost. Since a new inventory cycle begins whenever there is a dispatching of products, the long-run average costs of the model can be obtained by using the renewal theory. We also derive a closed form solution of the optimal dispatching policy.

Maintenance models for a continuously degrading system

This paper considers on-condition maintenance of a continuously degrading system, in which the intermaintenance time and the maintenance time depend on the condition of the system at which maintenance is carried out. Without assuming any underlying statistical distribution of the time to failure, models are established to maximize the system average availability when the expected intermaintenance time and the expected maintenance time are (i) deterministic or (ii) contain random components. Optimal solutions on the condition of the system at which maintenance should be performed and the number of times of maintenance action to be carried out are obtained. Numerical searching procedures are proposed, and illustrative examples are given.

Optimal Production and Pricing Policies in a Combined Make-to-Order/Make-to-Stock System

In this paper, we consider a production system which is capable to produce two types of products. The first type of products is make-to-order, while the second type is make-to-stock whose demand is satisfied by the on-hand inventory. The demand arrival rates of both types of products are price-sensitive. The excess demand that cannot be satisfied immediately is either backlogged or lost. The system costs include the holding costs of product inventories and shortage costs of unsatisfied demand. The objective is to maximise the total discounted profit over an infinite planning horizon by coordinating the production process and pricing decisions. By analysing the properties of objective functions, we characterise the optimal control policy by two switch curves and the optimal price is also given for different ordering and inventory levels. We also explore the monotonicity of both switch curves which will reduce the computation effort. Numerical experiments are conducted to demonstrate the use of the switch curves in managing the production system and illustrate that compared with the static pricing policy, the optimal integrated price and inventory control policy can result in a significant profit improvement in the make-to-order/make-to-stock system that is much higher than in a single-product system.

An EPQ Model for Deteriorating Production System and Items with Rework

This paper investigates the economic production quantity model jointly considering product deterioration and a deteriorating production system with rework. In this imperfect deteriorating production system, not only does the machine produce defective product but also the machine is subjected to quality deterioration. To be more specific, the defective rate increases at certain time intervals. The defects produced are stored until the end of normal production process. Then they are reworked with extra cost to restore their quality and regarded as perfect product. The main objective is to minimize the total cost per unit product by determining the optimal combination of production run time and backlog quantity. Numerical experiments are carried out to illustrate the behavior of the inventory and show the impact of different parameters on the model. Discussion and conclusions are made at the end of the paper.

Hidden Markov models for inventory systems with deteriorating items

In this paper, we propose to apply hidden Markov model (HMM) in modelling an inventory system for deteriorating items. Each item in the inventory has certain chance to deteriorate in a fixed period of time. We propose models for both cases of deterministic and stochastic demands. With the information provided by customers, the inventory levels in the system, which are unknown, can be estimated. Numerical examples are provided to demonstrate the effectiveness of the proposed models.

An EOQ model for imperfect quality items with multiple quality characteristic screening and shortage backordering

In this paper, we propose an inventory model where items are inspected through multiple screening processes on varies quality characteristics before delivery to customers. Each screening process on a single quality characteristic has independent screening rate and defective percentage. Defective items screened out are stored and then returned to supplier. Shortage backordering are also allowed in the model. Two approaches are used to obtain the closed-form optimal order size and the maximum backordering quantity. Numerical examples are also provided to demonstrate the use of the model. [Received 16 February 2013; Revised 8 July 2013; Revised 16 November 2013; Accepted 27 January 2014]

A fast algorithm for the spread of HIV in a system of prisons

In this paper, we propose a continuous time model for modelling the spread of HIV in a network of prisons. We give some sufficient conditions for the equilibrium points of the system to be stable. We also develop an efficient algorithm based on Newtons method and the Sherman-Morrison-Woodbury formula for computing the equilibrium values of the infectives in each prison.

A Two-echelon Model for Inventory and Returns

We consider an Markovian model for a two-echelon inventory/return system. The system consists of a supply plant with infinite capacity and a central warehouse for inventory and returns. There is also a number of local warehouses which are also able to re-manufacture products. To obtain a high service level of handling inventory and returns, lateral transshipment of demands is allowed among the local warehouses.