Zhe George Zhang

Optimal preventive maintenance and repair policies for multi-state systems

This paper studies the optimal preventive maintenance (PM) policies for multi-state systems. The scheduled PMs can be either imperfect or perfect type. The improved effective age is utilized to model the effect of an imperfect PM. The system is considered as in a failure state (unacceptable state) once its performance level falls below a given customer demand level. If the system fails before a scheduled PM, it is repaired and becomes operational again. We consider three types of major, minimal, and imperfect repair actions, respectively. The deterioration of the system is assumed to follow a non-homogeneous continuous time Markov process (NHCTMP) with finite state space. A recursive approach is proposed to efficiently compute the time-dependent distribution of the multi-state system. For each repair type, we find the optimal PM schedule that minimizes the average cost rate. The main implication of our results is that in determining the optimal scheduled PM, choosing the right repair type will significantly improve the efficiency of the system maintenance. Thus PM and repair decisions must be made jointly to achieve the best performance.

Extended Optimal Replacement Policy for a Two-Unit System With Shock Damage Interaction

In this paper, we consider a system consisting of two major units, A and B, each subject to two types of shocks that occur according to a non-homogeneous Poisson process. A type II shock causes a complete system failure which is corrected by a replacement; and a type I shock causes a unit A minor failure, which is rectified by a minimal repair. The shock type probability is age-dependent. Each unit A minor failure results in a random amount of damage to unit B. Such a damage to unit B can be accumulated to a specified level of the complete system failure. Moreover, unit B with a cumulative damage of level z may become minor failed with probability π(z) at each unit A minor failure, and fixed by a minimal repair. We consider a more general replacement policy where the system is replaced at age T, or the Nth type I shock, or first type II shock, or when the total damage to unit B exceeds a specified level, whichever occurs first. We determine the optimal policy of T* and N* to minimize the s-expected cost per unit time. We present some numerical examples, and show that our model is the generalization of many previous maintenance models in the literature.

Extended preventive replacement policy for a two-unit system subject to damage shocks

We consider a system consisting of two units (A and B), which is subject to two types of shocks (I and II) that occur according to a non-homogeneous Poisson process. The probabilities of these two shock types are age-dependent. Each type-I shock causes a minor failure of unit A, which can be corrected by a minimal repair. Meanwhile, this type of shock results in a certain amount of damage to unit B. These damages to unit B are accumulated to trigger a preventive replacement (PM) or a corrective replacement (CM) action. In addition, a minor failure for unit B with the cumulative damage of z will occur with probability at a type-I shock instant. Type-II shock is a major one that causes system replacement. We consider a two-dimensional PM policy, which prescribes that the system is preventively replaced at age T, or at the time when the total damage to unit B exceeds a prespecified level Z (but less than the failure level K where K > Z) or is replaced correctively at first type-II shock or when the total damage to unit B exceeds a failure level K, whichever occurs first. Thus, both PM and CM actions may be performed in our model. To minimise the expected cost per unit time, the optimal policy (, ) is derived analytically and determined numerically. We also show that our model is a generalisation of many previous maintenance models in the literature.

An algorithmic analysis of multi-server vacation model with service interruptions

Motivated by the trade-off between reliability and utilization level of a stochastic service system, we considers a Markovian multi-server vacation queueing system with c unreliable servers. In such a system, some servers may not be available due to either planned stoppage (vacations) or unplanned service interruptions (server failures). The vacations are controlled by a threshold policy. With this policy, at a service completion instant, if d (=

Equilibrium in vacation queueing system with complementary services

This paper studies a queue with server vacations where customers need complementary services. The main service provider or the queue server may become absent for a random period of time called a vacation. More specifically, the server adopts a multiple vacation policy which means that the server keeps taking vacations until at least a customer waiting at the vacation completion instant. The secondary service provider offers an instantaneous service (no delay or no queue). The two services are complementary and a customer must receive both services if he or she joins the system. We investigate the equilibriums of such a system in a time-based fee model under competition and monopoly cases, respectively. Furthermore, a fixed or flat fee model is also analysed.

Analysis of a hybrid warranty policy for discrete-time operating products

This article considers a warranty policy consisting of a renewable free-replacement period and a rebate period for products operating in discrete time. Under such a Hybrid Warranty Policy (HWP), if a product fails during the first N periods (from period 1 to period N), it is replaced with either a new or a repaired unit for free (or at the manufacturers expense) and the policy is renewed; if it fails in the next W − N periods (from period N + 1 to period W), then the manufacturer refunds a pre-specified proportion of the sales price to the buyer. A pure rebate warranty policy and a pure renewable replacement policy can be considered as special cases of the HWP. With the HWP, customer service and warranty cost can be traded off. The conditions under which the HWP is more cost-effective are derived from the perspective of the manufacturer or seller. Some structural properties of the HWP are examined. Furthermore, how to choose between using new and repaired products to replace failed products is discussed. A numerical example is presented to demonstrate the computation of the optimal N*, the decision variable of the HWP, and a sensitivity analysis is performed to gain some managerial insights for practitioners.

Analysis of Price Competition in Two-Tier Service Systems

This article focusses on the issue of price competition of two private service providers (SPs) in a market with a free public SP. The two private SPs, differentiated by service quality and capacity, choose the optimal prices to maximize their own profits. It has been shown that such a price competition between the private SPs in a market with a public SP reaches a pure Nash equilibrium. Such a system with both private and public SPs is called a two-tier service system. We investigate the impact on the social welfare of the two-tier service system of the competition and collaboration between the two private SPs. In addition, we also examine the impact of the public SP’s competitive advantage on customer service and the private SP’s pricing strategies and their performance. Numerical examples are presented to generate managerial insights for practitioners.

Improving Operational Efficiency for a Two-Way Highway Toll Station

Abstract This paper addresses the over congestion issue at a real highway toll station and proposes the optimal design and operation policy to improve the overall system performance — minimizing both customer waiting and toll station’s operational costs. Based on the empirical data of Liuzhong Highway Tianshui Road toll station (LHTR-station), the real-time arrival rates of the traffic flows in both directions have been characterized via statistical analysis. Using an M/D/1 queuing model and stationary independent period-by-period (SIPP) and peak-hour approximations for the time-varying arrival rates, (i.e. two hours per period and 12 periods a day), we develop the optimal staffing levels in both directions of highway toll station. Then, the optimal staffing schedules are developed for different scenarios, for example, four-hour working a day, six-hour working a day, eight-hour working a day, and four-hour working and two-hour resting and four-hour working a day. The operating costs are compared for different schedules used in practice. Finally, using the empirical data of LHTR-station, we evaluate the performance improvement with the schedules suggested by our analysis. It has been found that the operation efficiency for LHTR-station can be improved significantly. This paper shows the value of using the operations research models innovatively to solve real-world problems.

A note on workload control for an under-utilized server of M/G/1 system

In this note, we study the issue of adjusting the workload of an under-utilized server in a queueing system. Using an M/G/1 model with server vacations of two types, we can effectively control the workload level of the server. The server vacations are time periods that the server does not serve the queue. Type 1 vacations represent durations of supplementary non-queue jobs assigned to the server. Type 2 vacations represent the non-productive period for the server such as idle time. With a two threshold policy, we demonstrated that the servers workload can be effectively controlled. A simple procedure for determining the conditionally optimal policy is proposed. Numerical examples are presented to illustrate the use of the procedure.

Equilibrium Mixed Strategies in a Discrete-Time Markovian Queue Under Multiple and Single Vacation Policies

Abstract We study the Nash equilibrium behavior of customers in a discrete-time single-server queue under multiple vacation policy or single vacation policy. Every arriving customer either joins the queue or balks based on his or her service utility. Using a Quasi-Birth-Death Processes (QBD) model, we obtain the stationary distribution of the queue length via the Matrix-Geometric Solution method. We analyze the equilibrium mixed threshold strategies under two different vacation policies. By presenting numerical examples, we examine the impacts of system parameters on the equilibrium customer behavior and compare the single and multiple vacation policies in terms of the social welfare.