Expected System Cost Research Articles

Shared information in a serial inventory system

In this study, a supply chain model consisting of a single product, one supplier and one retailer is considered. Transportation times are constant and demands at the retailer are assumed to be generated by a stationary Poisson process. Demands not covered immediately from inventory are backordered. The retailer carries inventory and replenishes stock according to a (Q, R) policy. The supplier has online information about the demand at the retailer and uses this information to replenish its stock. The order size at the supplier is a multiple integer to the retailer’s order size. Considering order costs for the retailer and the supplier, we derive the exact cost function for this inventory system. Then, using a search method, the optimal solution for the exact value of the expected system costs is found. Furthermore, for utilising information in the supplier’s decision making, we resort to solve several numerical examples.

Optimal Replacement Schedule in a Deteriorating Production System With Deterministic, Random Lead Time for Replacement

This study investigates the replacement schedule for a production system with a non-repairable key module that deteriorates over time, and is subject to random failure. We examine the case where replacing the key module requires lead time for preparing such replacement. Our aim is to determine the cost-minimizing schedule point that signals the point in time when the preparation of key module replacement shall start. We propose two models with deterministic lead time, and two models with random lead time in response to whether or not a prespecified quality level shall be met during a system operating cycle. The numerical results demonstrate that longer expected lead time advances the optimal schedule points, and increases the expected system costs per unit time in all models, while a higher variation of lead time advances the optimal schedule points, and increases the expected system costs per unit time in the models with random lead time. The numerical results also reveal that, relaxing the constraint of meeting a prespecified quality level, even in the presence of penalty, may be more economical than having this constraint. Our findings shed light on system maintenance with uncertainties in the activities required prior to component replacement.

A Cost Analysis of Systems Subject to Random Field Environments and Reliability

We present a generalized cost model subject to random field environments with considerations of cost to remove failures during testing and warranty periods, and penalty cost due to the system failures. We also determine the optimal release time policies that minimize the expected system cost. Many scientific contributions have been developed in software reliability modeling, while none has studied the manufacturing or industrial system reliability growth yet, considering also the differences between testing and operating environments. The application of the proposed model, in comparison to the nonhomogenous Poisson process Goel-Okumoto model, to an industrial application is discussed to illustrate how the proposed model can be used in practice.

An EMQ model in an imperfect production process

The intention of this article is to develop a framework of production policy (resumption and non-resumption) in order to find out optimal safety stock, optimal production rate and production lot size. It encompasses specific versions of the concept of quality and inventory model, stochastic machine breakdown and its correcting and regular repair paths with safety stocks. This framework hopefully serves to simplify answers to the important questions: How much safety stocks, production rate and production lot size are required to minimise the total expected system cost. The optimal production rate, production lot size, production run time and safety stocks are determined numerically and the joint effect of process deterioration, machine breakdown and its repair (correcting and preventive) on the optimal decision is investigated for a numerical example. Such an investigation should also yield logistics directions for the design of products and their manufacturing processes.

Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals

In many production/distribution systems, materials flow in fixed lot sizes (e.g., in full truckloads or full containers) and under regular schedules (e.g., delivery every week). In this paper, we study a multiechelon serial system with batch ordering and fixed replenishment intervals. We derive the optimal inventory control policy, provide a distribution-function solution for its optimal control parameters, and present an efficient algorithm for computing those parameters. Further, we show that the optimal expected system cost is minimized when the ordering times for all stages are synchronized. In contrast to the known approach in the literature that develops a lower bound for the average cost of a given period for the classical serial system, we develop a lower bound for the average total cost over an appropriately defined cycle and then construct a policy that reaches the lower bound. We also discuss its extension to the nonlinear shortage cost case (i.e., the nonlinear cost case). This paper generalizes several recent results on the analysis of multiechelon systems.

Efficiency Versus Robustness of Markets – Why Improving Market Efficiency Should Not Be the Only Objective of Market Regulation

The efficiency of capital markets has been questioned almost as long as the efficient market hypothesis had been worked out. Numerous critics have been formulated against this hypothesis, questioning notably the behavioural assumptions underlying the efficient market hypothesis. The present contribution does not focus on the behavioural assumptions but rather looks at the implications of focusing purely on the objective of market efficiency when considering market design questions. Hence it aims at discussing the following, possibly rather fundamental issue: Is the objective of efficiency, which has guided most of the market reforms in the last decades, sufficient? Or has it to be complemented by the objective of robustness? Mathematical and engineering control theory has developed the concept of robust control (e.g. Zhou and Doyle, 1998) and it has been shown that there is always a trade-off between the efficiency of a control system and its robustness (cf. e.g. Safonov, 1981, Doyle et al., 1988). The efficiency of the system describes its reactions to disturbance signals. The lower the integral loss function over the so-called transfer or sensitivity function, the less a system is affected by disturbances such as demand fluctuations, and the more efficient is the control. The economic equivalent clearly is the maximisation of welfare, which results in an efficient economic system. Robustness by contrast is defined as stability of the control system in the presence of model uncertainty (deviations in the model parameters or misperceptions of the underlying system). These concepts are applied to the financial markets in their interaction with the real economy. The financial markets being understood as the controllers of real world activity through investments, the implications of misperceptions in the financial sphere are analysed both theoretically and in an application example. From the theory it may readily derived that financial markets providing efficient, i.e. welfare-optimal solutions, must have limitations with respect to robustness. Also in the application example it turns out that in the presence of potential misperception a reduction of irreversible cost shares in investments may lead to an increase in overall expected system costs. Hence improvements in (conventional) market efficiency may be counter-productive by facilitating misallocation of capital as a consequence of misperceptions in the financial markets. This leads to the conclusion that a sole focus on the efficiency objective in market design is problematic and some of the recent turmoil in financial markets may be explained by the lack of consideration given to robustness issues.

Optimal solution for a two-level inventory system with information exchange leading to a more computationally efficient search

In this paper we consider a two-level inventory system with one warehouse and one retailer with information exchange. The retailer applies fixed order size continuous review policy. The supplier starts with m initial batches of the same order size of the retailer, and places an order to an outside source immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s. Transportation times are constant and the retailer faces independent Poisson demand. In a recent paper it was pointed out that the optimal supplier policy in this inventory system is an open question. To obtain the optimal policy for this system, first we find the optimal solution for the exact value of the expected system costs by using a search method. Second to make the numerical computations required by the search process more efficient, we obtain an upper bound for the value of m; and s. For revealing the computational efficiency of the above suggested upper bounds we resort to solving several numerical examples and compare the general upper bounds for the values of m and s with the modified upper bounds obtained in this paper.

Optimal and Near-Optimal Decisions for Procurement and Allocation of a Critical Resource with a Stochastic Consumption Rate

Management of critical resources having uncertain consumption rates is perhaps the most common challenge encountered by businesses in discharging their numerous functions, e.g., inventory distribution, marketing, finance, production, personnel, etc. It involves making two key decisions optimally: (1) How much of each critical resource must be procured (replenishment quantity decision), and, having procured, (2) How much of each resource should be allocated among the competing entities (allocation decision). The finance/inventory literature thus far has addressed the allocation decision in an optimal fashion using certain ranking algorithms. However, the optimal replenishment decisions have not yet been addressed optimally except under a restrictive assumption called the allocation assumption. Using the illustration of a periodic-review, stochastic-demand, fixed-route, centralized, multi-echelon distribution system in this paper, we propose a non-ranking allocation policy that is faster than those existing in the literature and also develop an optimal replenishment algorithm that is independent of the allocation assumption. Furthermore, we allow our distribution system a greater flexibility than that allowed in the literature thus far--we explicitly permit fixed delivery routes, arbitrary demand distribution parameters, non-identical delivery leadtimes simultaneously with a positive order leadtime. The major empirical contribution of this work is to demonstrate, through an extensive simulation study, that computationally efficient heuristic, called the hybrid heuristic, performs close to optimal, even for the systems with high demand uncertainty. Intriguingly, the bottom line finding of our computational experiments is that while the probability of violation of the allocation assumption itself is very sensitive to the system demand uncertainty, it is relatively insensitive to the expected system inventory costs in the vicinity of the optimal region. We also develop hand- computable theoretical lower and upper bounds on system replenishment quantity and expected system cost per period that require a single Normal distribution table look-up.

A two-echelon allocation model and the value of information under correlated forecasts and demands

In this article we explore the effects of incorporating forecasts explicitly in a two-echelon allocation model which consists of a central depot and several retailers. In particular, we investigate the possible benefits on the system costs and inventory levels. The depot does not hold any inventory and the demand is observed only at the retailers. Under a general correlated demand-forecast structure we obtain the approximate system-wide order-up-to level and the expected system cost. In order to assess the value of information provided by keeping track of the forecasts, we construct a comparable inventory system operating under a standard demand model. We demonstrate that the standard demand model results in higher order-up-to levels and higher system costs.

On the optimal design of N-version software systems subject to constraints

Software size and complexity continue to grow and find new applications, such as safety assurance systems for nuclear power generators, electronic transfer systems for banking, and manned spacecraft. To achieve ultrareliability in computing, it is necessary to adopt the strategy of defensive programming based on redundancy. Redundant versions, however, require additional resources, e.g., additional costs in terms of programming effort, time needed for design and testing, and hardware requirements. This article addresses the optimization issue for the cost of N-version programming (NVP) and majority systems. The optimization problems are formulated and solved for the minimum expected cost of NVP and majority systems subject to the desired reliability level. The problems of maximizing the reliability of the NVP and majority systems subject to a constraint on expected system cost are also obtained. Numerical examples are provided to illustrate the results.

Optimal production policy for a single-product single-machine problem with intermediate machine inspection allowed

This paper considers a single-product single-machine production problem where, once the machine is setup for production operation over an interval of time, the operation quality inspection is periodically carried out at equal time intervals, since the machine is subject to operation quality defect occurring in an exponential time distribution. Once such a quality defect starts to occur, the machine keeps producing a fixed rate of imperfect items which may incur various management costs. If the machine operation is checked as being out of quality at the end of an inspection interval, the operation is stopped to do the machine restoration work for getting the next interval operation started at the original condition, and no demand is supplied until the operation is resumed. Such a machine restoration work mostly includes the machine restoration work itself and an after-service type of repair work on out-of-quality items, which requires a constant amount of time mostly for the item repair work. The paper considers various costs including lost-sales, customer goodwill loss, inventory cost, and after-service repair cost, and determines both the optimal production operation interval and the optimal number of intermediate inspections over the interval which minimizes the average expected system cost per unit time. Numerical problems are solved for illustration.

Optimal number of redundant channels for a digital communication system

Abstract In many critical applications of digital systems, fault tolerance has been an essential architectural attribute for achieving high reliability. This paper considers the problem of determining the optimal number of redundant channels in a digital communication system. The expected system cost is obtained. We determine the number of redundant channels minimizing the expected system cost. A numerical example illustrates the techniques.

A Location-Allocation Model for a Two-Echelon Repair-Inventory System

Abstract In this paper a model is developed for determining physical location of a repair and stockage facility at the first echelon together with optimal allocation of recoverable spares to each location in a two-echelon repair-inventory system to minimize the total expected system cost. An illustrative example is included to indicate the application of the model and the iterative methodology developed.

Implications of certain assumptions in database performance evauation

The assumptions of uniformity and independence of attribute values in a file, uniformity of queries, constant number of records per block, and random placement of qualifying records among the blocks of a file are frequently used in database performance evaluation studies. In this paper we show that these assumptions often result in predicting only an upper bound of the expected system cost. We then discuss the implications of nonrandom placement, nonuniformity, and dependencies of attribute values on database design and database performance evaluation.

Monte Carlo Determination of Stock Redistribution

A model was designed for the purpose of studying stock distribution policies in an inventory system consisting of a number of demand points distributed through space. The model is limited to items that are not centrally repaired and that are procured only once for the life of the item, since both centralized repair and recurrent procurement offer opportunities to correct an imbalance in the distribution of stock among bases at little or no cost to the system. Assuming then an initial distribution of stock among bases, an analytical solution to the redistribution of stock between a pair of bases is obtained in each time period of the model, in terms of (1) the cost of transportation, (2) the stock on hand, depletion penalty, and demand probability function at each of the bases, and (3) a controlled variable βt representing the per cent of the transportation cost to be charged in the tth period in the analytical solution. The expected system costs associated with alternative β functions are then determined by Monte Carlo methods, with each function beginning at a value between zero and one in the first period, and rising to one in the last period. The methodology is extended to include the redistribution decision among three or more bases.