Average Cost Model Research Articles

On the optimality of stepwise policies for managing capacity, inventory and backorders

We consider the problem of simultaneously managing capacity, inventory and backorders in a multi-mode production environment modelled via Brownian motion. The presence of more than two production modes adds an additional level of complexity: not just when to change modes, but also which mode to change to. We show that, under the two assumptions that demand is the overriding source of variability in the process and that the cost to change from one production mode to another is proportional to the difference in the production capacities, a policy that moves stepwise among the modes minimizes the long-run average cost. Examples demonstrate that if either assumption is violated no policy that moves stepwise among the modes may be optimal. To focus on the complexity of identifying when to change modes and which mode to change to, we restrict our model to simple convex holding and backorder costs and linear processing costs and costs for rejecting demand and idling capacity. We adopt the economic average cost model that allows the manager to reject demand or idle capacity at any time. We demonstrate that under our two assumptions we may impose an ordering assumption on the relative value functions that dramatically simplifies the classic Hamilton-Jacobi-Bellman equations. We show that under the economic average cost model a production mode that is initially unattractive may later become attractive as new modes are added. Our arguments are essentially constructive and lead to a practical algorithm for finding an optimal policy.

Calculation of the discount rate for the Russian market in present-day conditions

Subject. This article focuses on the consideration of the algorithm and methodological approaches to assessing the cost of capital. Objectives. The article aims to develop a practical algorithm for assessing the cost of capital and calculating the discount rate based on ruble risk-free assets and Russian financial statistics. Methods. For the study, we used the Weighted Average Capital Cost (WACC) and Capital Asset Pricing (CAPM) models. Results. The article offers a tested step-by-step algorithm for calculating the cost of capital and risk premium loading to it using domestic financial statistics. It also justifies the need to take non-systematic risks out and beyond the weighted average capital cost and offers a deterministic mechanism for their assessment. Conclusions and Relevance. The author-developed algorithm for estimating the cost of capital, as well as methodological recommendations for its use, can be used by domestic investors to make the necessary decisions, as well as by the financial services of Russian companies to build the economic policy of the company. Using the proposed approach may help obtain a more adequate assessment of the cost of capital of Russian companies for domestic investors, thereby improving their competitiveness.

Research on equipment financing decision based on three-level mechanism

Based on the analysis of the advantages and disadvantages of three-level financing mechanism, the equipment financing cost is divided into three parts: financing cost, storage cost and supply cost, and the average cost model of equipment financing is established. The equipment financing time is divided into three parts: financing time, storage time and supply time, and the average time model of equipment raising is established. Based on the time and cost of equipment raising, a model of equipment raising efficiency is established. By comparing the average cost, average time and efficiency of financing at all levels, we can determine the main responsibility of equipment financing.

The average-cost formulation of lot sizing models and inventory carrying charges: a technical note

It is generally recognised that the present-value criterion should be preferred to the average-cost formulation in developing lot sizing models. Despite the advantages of the present-value measure, average-cost lot sizing models are far more widely applied. Because of the nature of the average-cost formulation, inventory carrying costs are evaluated according to a look-back approach, relying on historical values. In this regard, a general misconception in the inventory management literature concerned with average-cost models is that the unit stockholding cost rate should be established considering fixed warehouse costs, which are costs that are, in the short term, independent of the inventory level. This paper develops arguments supporting our belief that inventory carrying charges used in lot sizing models should take into account only those costs varying with the inventory level in the warehouse, and that considering fixed warehouse costs leads to pitfalls when making inventory replenishment decisions. To this aim, we first present an analytical treatment based on the classical Economic Order Quantity (EOQ) model, as its full analytical tractability permits us to better discuss the problem we are interested in. Finally, we present numerical experiments to assess the effect of the correct procedure to establish the unit stockholding cost rate on inventory management decisions. These experiments are performed considering warehouse costs taken from some industrial case studies presented in the literature.

EOQ with independent endogenous supply disruptions

We consider an inventory installation, controlled by the periodic review base stock (S, T) policy and facing a fixed-rate deterministic demand which, if unsatisfied, is backordered. The supply process is unreliable, so supply deliveries may fail according to an independent Bernoulli process; we refer to such failures reflecting the supply service quality and being internal to the supply chain, as endogenous disruptions. We seek to jointly determine the two policy variables, so to minimize long-run average cost. While an approximate model for this problem was recently analyzed, we present an exact analysis, valid for two common accounting schemes for inventory cost evaluation: continuous and end-of-cycle costing. After developing a unified (and exact) average cost model for both costing schemes, the cost for each scheme is analyzed. In both cases, the optimal policy variables and cost prevail in closed-form, having an identical structure to those of EOQ (with backorders). In fact, under continuous costing, the optimal solution reduces to EOQ for perfect supply. Analytical properties, demonstrating the impact of deteriorating supply quality on the optimal policy, are established. Moreover, computations reveal the cost impact of deploying heuristics that either ignore supply disruptions or rely on inaccurate costing information.

A Decision-making Method for Active Remanufacturing Time Based on Environmental and Economic Indicators

Optimal status and performance of the used parts can often make the difference between successful and unsuccessful remanufacturing for construction machinery. However, a used parts is remanufactured at an unreasonable time, there is a greater degree of resource waste and diseconomy. In this paper, a new method for determining the optimum active remanufacturing time is proposed, which considers both environmental and economic indicators. As an example, the life cycle assessment method was adopted for assessing the environmental impact of an oil cylinder over its entire service life, and an average annual cost model was established. Considering both the environmental index and the cost index, an optimization process was performed and the optimum active remanufacturing time for the oil cylinder was determined to be after 6.58 years of operation.

To Kill the U-Shaped Production Theory

This paper changes the traditional view of the U-shaped average cost model. It also changes the view about fixed cost. A fixed cost, which comes with a fixed capital, may increase the initial value of the total average cost, but its positive impact on output and profit is more significant. The U-shaped AC curve or its cascade is refuted.

Optimal Maintenance Modeling for Systems with Multiple Non-Identical Units Using Extended DSSP Method

In the optimal maintenance modeling, all possible maintenance activities and their corresponding probabilities play a key role in modeling. For a system with multiple non-identical units, its maintenance requirements are very complicated, and it is time-consuming, even omission may occur when enumerating them with various combinations of units and even with different maintenance actions for them. Deterioration state space partition (DSSP) method is an efficient approach to analyze all possible maintenance requirements at each maintenance decision point and deduce their corresponding probabilities for maintenance modeling of multi-unit systems. In this paper, an extended DSSP method is developed for systems with multiple non-identical units considering opportunistic, preventive and corrective maintenance activities for each unit. In this method, different maintenance types are distinguished in each maintenance requirement. A new representation of the possible maintenance requirements and their corresponding probabilities is derived according to the partition results based on the joint probability density function of the maintained system deterioration state. Furthermore, focusing on a two-unit system with a non-periodical inspected condition-based opportunistic preventive-maintenance strategy; a long-term average cost model is established using the proposed method to determine its optimal maintenance parameters jointly, in which “hard failure” and non-negligible maintenance time are considered. Numerical experiments indicate that the extended DSSP method is valid for opportunistic maintenance modeling of multi-unit systems.

Tearing the Kinked Demand Apart: The Contradictory U-Shaped Cost Theory

This paper proves that the u-shaped average cost model derives contradictory results. It also shows that the two demand curves for an oligopolistic firm have the same intercept, to disprove the traditional kinked demand model. The correct approach to describe price war is to follow Bertrand. This paper makes use of the theory developed by Hotelling (1929) and others to model price war and to derive a stable Bertrand equilibrium.

The discounted (R,Q) inventory model—The Shrewd Accountant's Heuristic

The discounted continuous-review (R,Q) inventory model with continuous and stochastic demand is investigated. New optimality conditions are derived, clarifying the difference to the average-cost case, also graphically. Supported by depreciation theory, applied to the value of a setup, the results suggest an insightful and very precise approximation – The Shrewd Accountant's Heuristic – based on a new average-cost model. It deepens and extends the work of Hadley (1964). Three examples are worked out in detail and the model is generalized to Poisson demand and to stochastic lead-times.

A condition- and age-based replacement model using delay time modelling

To make realistic maintenance decisions, it is important that maintenance managers make their preventive replacement decisions based on observations of the condition of their equipment. This study addresses a condition- and age-based replacement decision problem using the complete history of measured condition observations to minimize long-run average cost, maximize long-run average availability, or both. A stochastic filtering process (SFP) is used to estimate the residual lifetime distribution conditional on the history of observed condition information. A long-run average cost model and a long-run average availability model are analysed in order to determine the theorems necessary for calculating the optimum replacement time. To minimize the cost and maximize availability, a multiobjective decision frontier is proposed that will help maintenance managers deal with trade-offs between the two objectives. Finally, numerical examples are presented for each scenario to show the effectiveness of the methods proposed.

A Strongly Polynomial Algorithm for Controlled Queues

We consider the problem of computing optimal policies of finite-state finite-action Markov decision processes (MDPs). A reduction to a continuum of constrained MDPs (CMDPs) is presented such that the optimal policies for these CMDPs constitute a path in a graph defined over the deterministic policies. This path contains, in particular, an optimal policy of the original MDP. We present an algorithm based on this new approach that finds this path, and thus an optimal policy. In the general case, this path might be exponentially long in the number of states and actions. We prove that the length of this path is polynomial if the MDP satisfies a coupling property. Thus we obtain a strongly polynomial algorithm for MDP s that satisfies the coupling property. We prove that discrete time versions of controlled M/M/1 queues induce MDP s that satisfy the coupling property. The only previously known polynomial algorithm for controlled M/M/1 queues in the expected average cost model is based on linear programming (and is not known to be strongly polynomial). Our algorithm works both for the discounted and expected average cost models, and the running time does not depend on the discount factor.

A drug cost model for injuries due to road traffic accidents.

This study aimed to develop a drug cost model for injuries due to road traffic accidents for patients receiving treatment at a regional hospital in Thailand. The study was designed as a retrospective, descriptive analysis. The cases were all from road traffic accidents receiving treatment at a public regional hospital in the fiscal year 2004. Three thousand seven hundred and twenty-three road accident patients were included in the study. The mean drug cost per case was USD18.20 (SD=73.49, median=2.36). The fitted drug cost model had an adjusted R (2) of 0.449. The positive significant predictor variables of drug costs were prolonged length of stay, age over 30 years old, male, Universal Health Coverage Scheme, time of accident during 18:00-24:00 o'clock, and motorcycle comparing to bus. To forecast the drug budget for 2006, there were two approaches identified, the mean drug cost and the predicted average drug cost. The predicted average drug cost was calculated based on the forecasted values of statistically significant (p<0.05) predictor variables included in the fitted model; predicted total drug cost was USD44,334. Alternatively, based on the mean cost, predicted total drug cost in 2006 was USD63,408. This was 43% higher than the figure based on the predicted cost approach. The planned budget of drug cost based on the mean cost and predicted average cost were meaningfully different. The application of a predicted average cost model could result in a more accurate budget planning than that of a mean statistic approach.

Determining Economic Manufacturing Quantity for an unreliable manufacturing system in discrete time setting

The paper considers an Economic Manufacturing Quantity (EMQ) problem for a failure-prone manufacturing system in which the production facility may fail at most once during a production cycle. In a discrete time framework, we formulate the model under general-failure and -repair (corrective) time distributions based on the Net Present Value (NPV) approach. As a special case, the model with general failure and constant repair times is considered. The traditional long-run average cost model is obtained from the NPV model by taking limitation on the discount rate. The criteria for the existence of a local optimal solution are derived for the NPV as well as the long-run average cost models. With numerical examples, the optimal production policies are determined and sensitivity of some model-parameters are examined. A comparison of the outcome of the proposed model with the one obtained by time discretisation in the corresponding continuous time model is also made.

A bivariate process model for maintenance and inspection planning

The paper describes decision making about monitoring and maintenance of systems described by a general stochastic process. The system is monitored and preventive and corrective maintenance actions are carried out in response to the observed system state. The decision process is simplified by using an associated process as well as the underlying state as decision variables. The bivariate approach allows a wide class of models to be considered including long term memory within a simple probability structure. Both average cost and life-cycle cost models are used as the basis for decision making. The models generalize age replacement and other simple maintenance strategies. The approach can deal with failures that prevent the system functioning further, failures defined by regulation, or by economic considerations. The unified framework developed allows the inclusion of covariates and imperfect inspection or repair.

Exact formulation of stochastic EMQ model for an unreliable production system

The purpose of this paper is to present an exact formulation of stochastic EMQ model for an unreliable production system under a general framework in which the time to machine failure, corrective (emergency) and preventive (regular) repair times are assumed to be random variables. For exact financial implications of the lot-sizing decisions, the EMQ model is formulated based on the net present value (NPV) approach. Then, by taking limitation on the discount rate, the traditional long-run average cost model is obtained. The criteria for the existence and uniqueness of the optimal production time in both the models are derived under general failure and specific repair time distributions. Numerical examples are devoted to find the optimal production policies of the developed models and examine the sensitivity of the parameters involved. Computational results show that the optimal decision based on the NPV approach is superior to that based on the long-run average cost approach, though the performance level strongly depends on the pertinent failure and repair time distributions.

Optimal lot sizing for an unreliable production system based on net present value approach

The paper considers the net present value (NPV) approach to determine the economic manufacturing quantities for an unreliable production system over an infinite planning horizon. The NPV of the expected total cost is obtained under general failure time and general repair time distributions and its asymptotic characteristics are examined by perturbation of the instantaneous discount rate. The criteria for the existence and uniqueness of the optimal production time (lot size) are derived under exponential failure and constant/zero repair time. The performance of the NPV model is compared with the traditional long-run average cost model in terms of the NPV of the expected total cost based on the optimal decisions of the two models. From numerical experiments, it is observed that the decision based on the average cost can be 10% worse than the decision based on the NPV depending upon the machine failure rate.

An NPV and AC analysis of a stochastic inventory system with joint manufacturing and remanufacturing

While the net present value (NPV) approach is widely accepted as the right framework for studying production and inventory control systems, average cost (AC) models are more widely used. For the well-known EOQ model, it can be verified that (under certain conditions) the AC approach gives near optimal results. This paper investigates whether the same holds for two-source systems with joint manufacturing and remanufacturing. It appears that the performance of the AC approach stands or falls with the right choice of the holding cost parameters. Through the analysis of a deterministic model, a theoretical basis is provided for choosing the parameters. Then, given this set of holding cost parameters, the performance of the AC approach is tested in a stochastic model.

A reverse logistics valuation method for inventory control

We propose a method for valuing new, recoverable, and recovered assemblies (products, components, parts, etc.) in production systems with reverse logistics. Values of assemblies influence their opportunity holding cost rates and are hence essential for comparing inventory strategies in average cost models. We argue that the proposed method is 'correct' from a discounted cash flow (DCF) point of view. We refer to some previous results on valuing assemblies in systems without disassembly of returned products that seem to confirm this. Furthermore, we test the method for a specific example with disassembly of returned products. The simulation results indicate that the method indeed leads to (nearly) DCF optimal inventory strategies.

An Instruction-Level Power Analysis Model with Data Dependency

Power constraints are becoming a critical design issue in the field of portable microprocessor systems. The impact of software on overall system power is becoming increasingly important as more and more digital applications are implemented as embedded systems, part of which are hardware (ASICs) and part software in which a specific application is executed on a processor. In this paper, a data-dependent instruction-level power analysis model is presented. It is compared with the average cost model proposed by Tiwari et al. [1] in both estimation accuracy and characterisation time. The data-dependent model can be generalised to be applied to generic RISC processor. Application of the data-dependent model we propose sensibly reduces errors in estimating software power consumption per clock cycle which is lower than 10%, in the case of the ST20-C2P core.