Approximation analysis of multi-class closed queueing maintenance networks with a parts inventory system and two-phase Coxian time distributions

We consider a maintenance network where a set of bases is supported by a replacement parts inventory system and a centrally located repair depot. The ordering policy for the parts is the (S, Q) inventory policy. We extended the previous results to the network, where processing times at each node follow a two-phase Coxian distribution. The proposed network was modeled as a multi-class closed queueing network with a synchronization station. To make the analysis of the network computationally tractable, we developed a two-phase approximation method. In the first phase of the method, the proposed network was analyzed with the previous algorithm based on a product-form approximation. In the second phase, a sub-network was again analyzed with the procedure of a product-form approximation method such that the state space of the sub-network was reduced. In the analysis of a sub-network, a recursive method was also used to solve balance equations by exploiting the special structure of the Markov chain. The new algorithm provided a good estimation of the performance measures of interest. In addition to being accurate, the new algorithm is simple and converges rapidly.     

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

A fixed interval ordering policy for joint optimization of age replacement and spare part provisioning

A new policy is presented for the joint optimization of age replacement and spare provisioning. The policy, referred to as a fixed interval ordering policy, is formulated by combining an age replacement policy with a periodic review ( t₀,q) type inventory policy, where t0 is the order interval and q is the order quantity. It is generally applicable to any operating system with either a single item or a number of identical items. A SLAM based simulation model has been developed to determine the optimal values of the decision variables by minimizing the total cost of replacement and inventory. The behaviour of the policy has been studied for a number of case problems specifically constructed by five-factor second-order rotatory design and the effects of different cost elements and item failure characterisics have been highlighted. The performance of the proposed policy has also been compared with that of the stocking policy which incorporates a continuous review ( s, S) type of inventory policy, where s is the stock reorder level and S is the maximum stock level. Simulation results clearly indicate that the optimal fixed interval ordering policy is less expensive than the optimal stocking policy when the system consists of a large number of operating units.     

Locating repair shops in a stochastic environment

In this paper, we consider a repair shop location problem with uncertainties in demand. New repair shops have to be opened at a number of locations. At these local repair shops, customers arrive with broken, but repairable, items. Customers go to the nearest open repair shop. Since they want to leave as soon as possible, an inventory of working items is kept at the repair shops. A customer immediately receives a working item from stock, provided that the stock is not empty. If a stockout occurs, the customer has to wait for a working item. The broken items are repaired in the shop and then put in stock. Sometimes, however, a broken item cannot be fixed at the local repair shop, and it has to be sent to a central repair shop. At the central repair shop the same policy with inventory and repair is used.     

A multi-server perishable inventory system with negative customer

In this paper, we consider a continuous review perishable inventory system with multi-server service facility. In such systems the demanded item is delivered to the customer only after performing some service, such as assembly of parts or installation, etc. Compared to many inventory models in which the inventory is depleted at the demand rate, however in this model, it is depleted, at the rate at which the service is completed. We assume that the arrivals of customers are according to a Markovian arrival process (MAP) and that the service time has exponential distribution. The ordering policy is based on (s, S) policy. The lead time is assumed to have exponential distribution. The customer who finds either all servers are busy or no item (excluding those in service) is in the stock, enters into an orbit of infinite size. These orbiting customers send requests at random time points for possible selection of their demands for service. The interval time between two successive request-time points is assumed to have exponential distribution. In addition to the regular customers, a second flow of negative customers following an independent MAP is also considered so that a negative customer will remove one of the customers from the orbit. The joint probability distribution of the number of busy servers, the inventory level and the number of customers in the orbit is obtained in the steady state. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

Simultaneous determination of the optimal production–inventory and product inspection policies for a deteriorating production system

In this paper, we attempt to find a method for the optimization of production–inventory and product inspection policies for deteriorating production systems. Taking advantage of the nature of a deteriorating production system, a strategy would be not to inspect the first s items of the batch. Therefore, an inspection policy which disregards the first s (DTF-s) items of the batch is proposed. Under the DTF-s policy, we do not inspect the first s produced items but inspect only those items from the (s+1)th till the end of the production run. The objective of this study was the joint determination of the production lot size and the inspection policy s, resulting in a minimization of the expected average cost per unit time. Based on this model, the underlying conditions necessary for the existence of an optimal policy are given. Two commonly used inspection strategies, no inspection and full inspection are discussed. Under both inspection strategies, an optimal production–inventory lot is bounded by the traditional economic quantity. The case of full inspection is shown to be an extension of previously reported results. The option of investing in the process of quality improvement is also discussed. Finally, numerical examples are given to illustrate the method and its advantages in the conclusion.Scope and purposeThis paper considers the relationship between production, inventory and inspection in a deteriorating production system which may transit from the “in-control” state to the “out-of-control” state after a period of operation. Once the transition to the “out-of-control” state has occurred, it is assumed that some percentage of the items produced are defective or of substandard quality. However, in many cases, defects in a defective item can only be identified by an inspection process which carries an inspection cost. Those inspected items which are found to be defective are reworked at some cost before being shipped. On the other hand, defective items which are not inspected will be passed to the customer, incurring a much larger warranty cost. In order to operate such a system economically, tradeoffs among production setup, inventory, inspection and defective cost must be analyzed. Deterioration of the production system is an inherent process in all manufacturing industries. An understanding of the relationship among production, inventory and inspection for such systems will help managers to maintain efficient and economic control of operations.     

An update-based step-wise optimal cache replacement for wireless data access

Many network applications requires access to most up-to-date information. An update event makes the corresponding cached data item obsolete, and cache hits due to obsolete data items become simply useless to those applications. Frequently accessed but infrequently updated data items should get higher preference while caching, and infrequently accessed but frequently updated items should have lower preference. Such items may not be cached at all or should be evicted from the cache to accommodate items with higher preference. In wireless networks, remote data access is typically more expensive than in wired networks. Hence, an efficient caching scheme considers both data access and update patterns can better reduce data transmissions in wireless networks. In this paper, we propose a step-wise optimal update-based replacement policy, called the Update-based Step-wise Optimal (USO) policy, for wireless data networks to optimize transmission cost by increasing effective hit ratio. Our cache replacement policy is based on the idea of giving preference to frequently accessed but infrequently updated data, and is supported by an analytical model with quantitative analysis. We also present results from our extensive simulations. We demonstrate that (1) the analytical model is validated by the simulation results and (2) the proposed scheme outperforms the Least Frequently Used (LFU) scheme in terms of effective hit ratio and communication cost.     

Computing (r, Q) policy for an inventory system with limited sharable resource

This paper deals with inventory systems with limited resource for a single item or multiple items under continuous review (r, Q) policies. For the single-item system with a stochastic demand and limited resource, it is shown that an existing algorithm can be applied to find an optimal (r, Q) policy that minimizes the expected system costs. For the multi-item system with stochastic demands and limited resource commonly shared among all items, an optimization problem is formulated for finding optimal (r, Q) policies for all items, which minimize the expected system costs. Bounds on the parameters (i.e., r and Q) of the optimal policies and bounds on the minimum expected system costs are obtained. Based on the bounds, an algorithm is developed for finding an optimal or near-optimal solution. A method is proposed for evaluating the quality of the solution. It is shown that the algorithm proposed in this paper finds a solution that is (i) optimal/near-optimal and/or (ii) significantly better than the optimal solution with unlimited resource.     

A mathematical model on EPQ for stochastic demand in an imperfect production system

In the paper, we develop an EPQ (economic production quantity) inventory model to determine the optimal buffer inventory for stochastic demand in the market during preventive maintenance or repair of a manufacturing facility with an EPQ (economic production quantity) model in an imperfect production system. Preventive maintenance, an essential element of the just-in-time structure, may cause shortage which is reduced by buffer inventory. The products are sold with the free minimal repair warranty (FRW) policy. The production system may undergo “out-of-control” state from “in-control” state, after a certain time that follows a probability density function. The defective (non-conforming) items in “in-control” or “out-of-control” state are reworked at a cost just after the regular production time. Finally, an expected cost function regarding the inventory cost, unit production cost, preventive maintenance cost and shortage cost is minimized analytically. We develop another case where the buffer inventory as well as the production rate are decision variables and the expected unit cost considering the above cost functions is optimized also. The numerical examples are provided to illustrate the behaviour and application of the model. Sensitivity analysis of the model with respect to key parameters of the system is carried out.     

Queueing analysis of a server node in transaction processing middleware systems

Quantitative performance modeling of complex information systems is of immense importance for designing enterprise e-business infrastructures and applications. In this paper, we present a traffic model of a server node in a typical transaction processing middleware system as well as a quantitative framework to model and analyze its performance. A multi-class open queueing network model is presented in which multi-class jobs are admitted to a number of server processes sharing hardware resources including the CPU and the disk. We have developed a viable approximation method, which decomposes the dependent components into their independent counterparts while preserving their relevant characteristics. We have conducted queueing-theoretic delay analyses and verified the approach using simulation. Results demonstrate the strength of our approach in predicting delays, elapsed times and other system performance measures.     

Production inventory with service time and interruptions

This paper considers an (s,S) production inventory system with positive service time, with time for producing each item following Erlang distribution. Customers arrive according to a Poisson process. A customer who arrives when there is no inventory in the system is considered lost. On the other hand, a customer who finds a busy server with at least one inventory in the system joins a queue of infinite capacity. When the inventory level falls to s, production process is switched on, and it is switched off when the inventory level reaches back to S. Service time to each customer also follows an Erlang distribution. The service of a customer may be interrupted, where the time for such a phenomenon follows an exponential distribution, whenever it occurs. An interrupted service, after repair, resumes from where it was stopped. The correction/repair time follows an exponential distribution. We assume that the service of a single customer may encounter any number of interruptions and that the customer being served waits there until his service is completed. Moreover, at a time the server is subject to at most one interruption. We also assume that no inventory is lost due to a service interruption. Like the service process, the production process also is subject to interruptions, where the duration to an interruption follows an exponential distribution. However, in contrast to the service interruption, in the case of interruption to production process, we assume that the item being processed is lost because of interruption. That is, the production process, on being interrupted, restarts from the beginning, after repair. The repair time of an interrupted production process follows exponential distribution. Few of the last service phases are assumed to be protected in the sense that the service will not be interrupted while being in these phases. The same is assumed for the production process also.

The model is analysed as a level-independent quasi-birth–death process. We apply a novel method to obtain an explicit expression for the necessary and sufficient condition for the stability of the system under study. This method works even if we assume general phase-type distributions for the production as well as the service processes, and hence can be used to characterise the stability of inventory systems where the assumption of disallowing the customers to join the system, when there is a shortage of inventory has been made. Under stability, we apply matrix analytic methods to compute the system state distribution. In consequence to that, several system performance measures have been derived, and their dependence on the system parameters has been studied numerically.     

Warranty servicing for discretely degrading items with non-zero repair time under renewing warranty

This paper considers a repair-replacement strategy for a special class of discretely degrading and repairable products under renewing free replacement warranty. Each product may experience N different working states with different exponential hazard functions, before the warranty contract expires. Once the item enters working state i (i = 1, 2, … , N), it can either fail or move to any of the subsequent working states with different probabilities, given that a transition has been made. In the former case, the best rectification action, replacement or minimal repair, regarding the failure status, i.e., the product degradation level at the failure time and the remaining warranty time, should be conducted to put the item into operation. It is assumed that replacement of the faulty item occurs instantly and the product warranty is renewed, but non-zero repair time has been included in the model. We derive the optimal replacement-repair policy to minimize the manufacturer’s expected warranty servicing cost per item sold. The Adomian decomposition method is used to find an analytic approximate solution for a special case with two working states. For N > 2, a simulation based optimization method has been developed to analyze the expected warranty cost. Some numerical examples in each section are given to clearly demonstrate the application of this model.     

A mathematical model to minimize the inventory and transportation costs in the logistics systems

In this paper we consider a logistics system for parts manufacturer distribution center(depot) to supply the parts to the parent company. And we formulate the mathematical model to minimize the sum of inventory holding costs at the depot, and the transportation and inventory costs at parts manufacturer.

We apply the model to an actual automobile parts manufacturer to demonstrate the effectiveness of the proposed model.     

Throughput analysis for order picking system with multiple pickers and aisle congestion considerations

Most of previous studies in picker-to-parts warehousing systems investigated only single-picker operations and are therefore adequate to evaluate order picking efficiency by travel distance as aisle congestion never takes place in such systems. In real world applications, the congestion inevitably occurs when a system has multiple pickers working together within the same region. This paper presents an approximation method based on a GI/G/1 closed queueing network by using self-correcting approximation technique algorithm to evaluate the throughput time of an order picking system with multiple pickers and aisle congestion considerations for different routing policies. The results generated by the proposed method are compared and validated via simulation model using eM-plant simulator for different sizes of warehouses. The results indicate that the approximation method appears to be sufficiently accurate for practical purposes. The sensitivity analysis of the throughput time with respect to order sizes, number of pickers and number of aisles are conducted and the performance of different item storage policies are also evaluated using the proposed approximation model.     

Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy

In this paper, we consider a replacement model with minimal repair based on a cumulative repair-cost limit policy, where the information of all repair costs is used to decide whether the system is repaired or replaced. As a failure occurs, the system experiences one of the two types of failures: a type-I failure (repairable) with probability q, rectified by a minimal repair; or a type-II failure (non-repairable) with probability p (=1 − q) that calls for a replacement. Under such a policy, the system is replaced anticipatively at the nth type-I failure, or at the kth type-I failure (k < n) at which the accumulated repair cost exceeds the pre-determined threshold, or any type-II failure, whichever occurs first. The object of this paper is to find the optimal number of minimal repairs before replacement that minimizes the long-run expected cost per unit time of this polish. Our model is a generalization of several classical models in maintenance literature, and a numerical example is presented for illustration.     

Extended optimal replacement policy for a system subject to non-homogeneous pure birth shocks

This article studies the optimal replacement policy with general repairs for an operating system subject to shocks occurring to a non-homogeneous pure birth process (NHPBP). A shock causes that the system experiences one of two types of failures: type-I failure (minor failure) is rectified by a general repair, or type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a bivariate replacement policy (n, T) under which the system is replaced at planned life age T, or at the nth type-I failure, or at any type-II failure, whichever occurs first. The optimal replacement schedule which minimizes the expected cost rate model is derived analytically and discussed numerically.     

Item dwell time in project inventories: A field experiment

This paper describes the use of item dwell-time measurement in the context of capital investment projects. It contributes to the research on product-centric control and intelligent products by empirically demonstrating the value of item dwell-time alerts in the context of project delivery. The paper shows how item dwell-time measurement can be implemented in the field, and compares item dwell-time alerts to conventional measures of inventory turnover and inventory value in four telecommunications infrastructure projects. We find that when individual items cannot be used interchangeably at project sites, conventional inventory measures do not provide sufficiently timely and accurate information about emerging problems in project inventories. These findings are especially important in situations in which supply chain managers can find alternative uses for materials at other sites or in other projects. Timely reallocation of materials prevents the accumulation of slow-moving items that weigh on project performance by increasing obsolescence and inventory holding costs.     

Composite recommendations: from items to packages

Classical recommender systems provide users with a list of recommendations where each recommendation consists of a single item, e.g., a book or DVD. However, several applications can benefit from a system capable of recommending packages of items, in the form of sets. Sample applications include travel planning with a limited budget (price or time) and twitter users wanting to select worthwhile tweeters to follow, given that they can deal with only a bounded number of tweets. In these contexts, there is a need for a system that can recommend the top-k packages for the user to choose from. Motivated by these applications, we consider composite recommendations, where each recommendation comprises a set of items. Each item has both a value (rating) and a cost associated with it, and the user specifies a maximum total cost (budget) for any recommended set of items. Our composite recommender system has access to one or more component recommender systems focusing on different domains, as well as to information sources which can provide the cost associated with each item. Because the problem of decidingwhether there is a recommendation (package)whose cost is under a given budget and whose value exceeds some threshold is NP-complete, we devise several approximation algorithms for generating the top-k packages as recommendations. We analyze the efficiency as well as approximation quality of these algorithms. Finally, using two real and two synthetic datasets, we subject our algorithms to thorough experimentation and empirical analysis. Our findings attest to the efficiency and quality of our approximation algorithms for the top-k packages compared to exact algorithms.     

Higher-order distributional properties in closed queueing networks

In many real-life computer and networking applications, the distributions of service times, or times between arrivals of requests, or both, can deviate significantly from the memoryless negative exponential distribution that underpins the product-form solution for queueing networks. Frequently, the coefficient of variation of the distributions encountered is well in excess of one, which would be its value for the exponential. For closed queueing networks with non-exponential servers there is no known general exact solution, and most, if not all, approximation methods attempt to account for the general service time distributions through their first two moments.We consider two simple closed queueing networks which we solve exactly using semi-numerical methods. These networks depart from the structure leading to a product-form solution only to the extent that the service time at a single node is non-exponential. We show that not only the coefficients of variation but also higher-order distributional properties can have an important effect on such customary steady-state performance measures as the mean number of customers at a resource or the resource utilization level in a closed network.Additionally, we examine the state that a request finds upon its arrival at a server, which is directly tied to the resulting quality of service. Although the well-known Arrival Theorem holds exactly only for product-form networks of queues, some approximation methods assume that it can be applied to a reasonable degree also in other closed queueing networks. We investigate the validity of this assumption in the two closed queueing models considered. Our results show that, even in the case when there is a single non-exponential server in the network, the state found upon arrival may be highly sensitive to higher-order properties of the service time distribution, beyond its mean and coefficient of variation.This dependence of mean numbers of customers at a server on higher-order distributional properties is in stark contrast with the situation in the familiar open M/G/1 queue. Thus, our results put into question virtually all traditional approximate solutions, which concentrate on the first two moments of service time distributions.