Average Cost Approach Research Articles

Non-cooperative game-based electricity pricing method for data centers

Data centers are characterized by high energy consumption, with operating costs being extremely sensitive to electricity prices. Therefore, modern data centers are often equipped with microgrids for power supply, which adjust their operational strategies based on the given electricity prices to minimize costs. However, existing research has overlooked the flexible pricing potential of electricity retailers, prompting this study to propose a non-cooperative game theory-based optimization method for data center electricity procurement negotiation. A two-layer optimization model is established for data center electricity pricing. The upper layer focuses on electricity price optimization, modeling price negotiation as a Stackelberg game and adopting a weighted average cost approach to describe the electricity procurement prices. The lower layer addresses data center operational optimization, formulated as a nonlinear programming problem. To enable rapid solution convergence, a hybrid problem-solving method combining a genetic algorithm and branch-and-cut algorithm is proposed. Finally, a simulation is conducted using a data center located in California, United States, to validate the proposed method. The results demonstrate that the proposed method can reduce data center operational costs by 3% and increase the revenue for electricity retailers by 17%, achieving a win–win outcome.

Is the Achievement of “Good Status” for German Surface Waters Disproportionately Expensive?—Comparing Two Approaches to Assess Disproportionately High Costs in the Context of the European Water Framework Directive

Currently only 8.2% of German surface water bodies have reached the goal of the European Water Framework Directive to bring all water into a “good status”. For all water bodies that presumably will not achieve the objective by 2027, the member states have to justify an exemption by 2021, for example, by arguing that the costs of achieving “good status“ would be “disproportionately high”. In this paper, two approaches for assessing cost-disproportionality of surface water bodies are empirically tested and compared on a set of real-world data from a German federal state. In the first approach, called average cost approach, costs are considered as being disproportionately high if they are significantly higher than what would be a “relatively normal effort”. The core idea of the second, the benchmark approach, is to take the past public expenditures on water management as a basis for comparison. Both approaches include generated utility for determination of a water-body-specific disproportionality threshold. While the benchmarking approach needs less data, the empirical tests indicate that both approaches yield comparable results and are suitable to support authorities in the decision as to which water bodies are to be considered disproportionately expensive such that exemptions are justified.

Allocating runway costs using a user-pay and average-cost approach: application to Taiwanese airports

This paper develops a mechanism to allocate the costs of providing landing services at airports to different types of aircraft. Costs are classified into assignable and non-assignable items. The former is allocated by the user-pay principle, using traffic level as a key determining factor, and the latter is allocated by an average-cost approach. Land costs are included in the non-assignable category under some scenarios for analysis. The mechanism is validated at two major Taiwanese airports, Taipei Songshan Airport (TSA) and Taiwan Taoyuan International Airport (TPE), both are located in the Taipei Metropolitan area. Research results indicate that landing charges based on these allocated costs reflect the true costs of providing takeoff and landing services better than the weight-based charges. For example, the greatest landing fees charged to B747-400 at many airports based on the maximum takeoff weight is not supported by the user-pay principle. The results also provide a guideline to decide the minimum charge of each landing. Hence, it is believed that the mechanism has the potential to be applied to other airports worldwide.

Abstract 166: The Role of Ambulatory Blood Pressure Monitoring in Pediatric Hypertension Confirmation: A Cost and Efficacy analysis

Background: With the goal of averting future cardiovascular disease, the Affordable Care Act of 2010 mandates population-wide identification of children with high blood pressure (BP). Since children are prone to white coat (reactive) hypertension and masked hypertension, ambulatory blood pressure monitoring (ABPM) may be a cost-effective confirmatory test and therefore of high relevance to this mandate. Using actual patient data we evaluated the role of ABPM in patients referred to specialty clinic for evaluation of elevated blood pressure. Methods: From an unselected group of consecutive referral patients all receiving ABPM (n=58), we collected ABPM results, clinic auscultative BP and subsequent work-up patterns. Pre-elevated (90-95% referenced to age-sex-height) and elevated (>95%) clinic BP (CBP) were defined per NHLBI 2011 integrated guidelines. ABPM stratified patients into a) normal (mean 24 systolic BP (SBP) < 95%; SBP load <25%);b) pre-elevated (mean 24 SBP 25%); and c)elevated (mean 24 hour SBP >95%; SBP load >25%). ABPM was treated as the gold standard. We then compared 3 high BP confirmation strategies: 1. Average CBP alone to stratify into normal, pre-elevated, or elevated BP; 2. CBP followed by ABPM for CBP > 90%ile, using CBP and ABPM to stratify; 3. ABPM alone to stratify. The scenarios were compared by a) proportion elevated BP children appropriately identified; b) charges incurred. Charges included NHLBI 2011 recommended evaluation for elevated BP, extended secondary etiology work-up when indicated, target organ damage assessment in all pre-elevated, and screening for co-morbidities in obese pre-elevated patients. Rates of secondary etiology work-up and proportion obese were derived from the clinical cohort. We used an average cost approach with charges gleaned from our institution rate book. Results: CBP alone, CBP + ABPM, and ABPM alone identified 33.3% (3/9), 44.4% (4/9), and 100% (9/9) hypertensive cases respectively. Cost per hypertensive patient identified in each scenario was $28,994; $14,312; and $11,336 respectively. Conclusion: Given pediatric high BP is uncommon with many false positives and negatives, ABPM as a universal confirmatory test identifies more true hypertensives at a lower average cost.

Cumulative staircase considerations for dynamic lotsizing when backlogging is allowed

The dynamic lotsizing problem concerns the determination of optimal batch quantities, when given required amounts appear at discrete points in time. The standard formulation assumes that no shortages are allowed and that replenishments are made instantaneously.For the case when no shortage is allowed, previously it has been demonstrated that the inner-corner condition for an optimal production plan in continuous time reduces the number of possible replenishment times to a finite set of given points at which either a replenishment is made, or not. The problem is thus turned into choosing from a set of zero/one decisions with 2n−1 alternatives, of which at least one solution must be optimal, where n is the number of requirement events. Recently, the instantaneous replenishment assumption has been replaced by allowing for a finite production rate, which turned the inner-corner condition into a condition of tangency between the cumulative demand staircase and cumulative production.In this paper we investigate relationships between optimal cumulative production and cumulative demand, when backlogging is permitted. The production rate is assumed constant and cumulative production will then be a set of consecutive ramps. Cumulative demand is a given staircase function. The net present value (NPV) principle is applied, assuming a fixed setup cost for each ramp, a unit production cost for each item produced and a unit revenue for each item sold at the time it is delivered.Among other results, it is shown that optimal cumulative production necessarily intersects the demand staircase. Instead of having 2n−1 production staircases as candidates for optimality, there are 2n−1 production structures as candidates. These are made up of sequences of batches, of which the set of batches may be optimised individually. Also is shown that the NPV of each batch has a unique timing maximum and behaves initially in a concave way and ends as convex.Results for the average cost approach are obtained from a zeroth/first order approximation of the objective function (NPV).

Dynamic lotsizing with a finite production rate

The dynamic lotsizing problem concerns the determination of optimally produced/delivered batch quantities, when demand, which is to be satisfied, is distributed over time in different amounts at different times. The standard formulation assumes that these batches are provided instantaneously, i.e. that the production rate is infinite.Using a cumulative geometrical representation for demand and production, it has previously been demonstrated that the inner-corner condition for an optimal production plan reduces the number of possible optimal replenishment times to a finite set of given points, at which replenishments can be made. The problem is thereby turned into choosing from a set of zero/one decisions, whether or not to replenish each time there is a demand. If n is the number of demand events, this provides 2n−1 alternatives, of which at least one solution must be optimal. This condition applies, whether an Average Cost approach or the Net Present Value principle is applied, and the condition is valid in continuous time, and therefore in discrete time.In the current paper, the assumption of an infinite production rate is relaxed, and consequences for the inner-corner condition are investigated. It is then shown that the inner-corner condition needs to be modified to a tangency condition between cumulative requirements and cumulative production.Also, we have confirmed the additional restriction for feasibility in the finite production case (provided by Hill, 1997), namely the production rate restriction. Furthermore, in the NPV case, one further necessary condition for optimality, the distance restriction concerning the proximity between adjacent production intervals, has been derived. In an example this condition has shown to reduce the number of candidate solutions for optimality still further. An algorithm leading to the optimal solution is presented.

Optimal lotsizing within MRP Theory

MRP Theory combines the use of Input–Output Analysis and Laplace transforms, enabling the development of a theoretical background for multi-level, multi-stage production-inventory systems together with their economic evaluation, in particular applying the Net Present Value principle (NPV). In this paper we concentrate our attention on the question of optimal lotsizing decisions within the MRP Theory framework. MRP Theory has mainly dealt with assembly structures by which items produced downstream (on a higher level in the product structure) contain one or more sub-items on lower levels, but at each stage, the assembly activity produces only one type of output. This enables the input matrix, after enumerating all items suitably, to be organised as a triangular matrix, with non-zero elements only appearing below its main diagonal. The introduction of a diagonal lead time matrix capturing the advanced timing when required inputs are needed, enables compact expressions to be obtained, explaining the development of key variables such as available inventory and backlogs in the frequency domain. Central in this theory is the generalised input matrix showing when and how much the internal (dependent) demand amounts to for any production plan. Previously has been demonstrated that in a one-product case, inner-corner conditions for an optimum production plan in continuous time reduce the number of possible replenishment times to a finite set of given points at which either a replenishment is made, or not. The dynamic lotsizing problem is thus turned into choosing from a set of zero-one decisions with 2 m−1 alternatives, of which one (or possibly several equivalent) solution(s) must be optimal, where m is the number of requirement (demand) events. Given these points in time and the corresponding staircase function describing cumulative demand, the optimal plan may be obtained, for instance by employing the Triple Algorithm of dynamic lotsizing. This applies either an Average Cost approach, or the Net Present Value principle is applied. In this paper, we extend this analysis to a general multi-item system of the assembly type. Among other issues, it is shown how the number of internal demand events depends on product structure and number of external demand events. Also the inner-corner condition is proven still to be valid in this somewhat more complex situation, when demand for lower-level items no longer is given from the outset, but instead depends on decisions concerning production of items on higher levels in the product structure. A simple dynamic program procedure is provided offering a solution to maximising the NPV for any general assembly system. To solve for the optimal production plan, the Triple Algorithm may be applied to each stage.

Setting the holding cost rates in a two-product system with remanufacturing

This paper analyzes a two-product system with joint manufacturing and remanufacturing. In such a system the end-product stock contains both manufactured and remanufactured products, while the remanufacturable stock may contain products of different quality. Due to its complex structure, the valuation of inventories at the various stocking points is ambiguous. For two cases regarding quality differentiation we determine holding cost rates such that the outcomes of a net present value approach and an average cost approach are approximately equivalent. We show how the correct holding cost rates deviate from traditional valuation methodology and demonstrate its impact on operational performance.

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.

Economic evaluation of disassembly processes in remanufacturing systems

A model to deal with the disassembly processes in remanufacturing systems is presented with focus being on evaluating their economic consequences. More specifically, the model assists decisions such as to which degree and for the sake of which components should the returned items be disassembled. Consequently, using the economic values of recoverable items, the inventory holding costs of these items are obtained. This information is further used to determine the inventory control policy. To access such economic values, the above average cost approach is compared with the net present value method. The latter is often considered a more ‘correct’ way in remanufacturing systems from the viewpoint of inventory control. The results from the economic evaluation model are intended to aid companies in systematically evaluating current as well as projected remanufacturing systems.

On the non-optimality of the average cost approach for inventory models with remanufacturing

When analyzing average cost (AC) inventory models, it is common use to add the discount rate times the capital tied up in a product, to the out-of-pocket holding cost rate. This way, capital costs are (roughly) included. In this paper we show that such a method may not always be appropriate for reverse logistics inventory models with both remanufacturing and disposal of returned products.

Some basic problems in inventory theory: The financial perspective

The analysis of the standard EOQ problem from a financial perspective is proposed. The case of mixed financing (equity and debt) is considered and the results are compared with those stemming from the Average cost approach. It is shown that no prediction about the result can be made. We solve completely the problem of finding the best financing policy. As the financial framework suggests to consider an infinity of inventory cycles, we investigate the effects on the solution of a more realistic finite truncation of the chain. We show that the finite chain solution is always smaller than the infinite chain one.

Capital structure and inventory management:: The temporary sale price problem

The paper discusses the use of adjusted present value techniques in a problem of inventory management, the temporary sale price problem, in the presence of equity or debt financing. While traditional net present value approaches produce results very similar to those of the average cost approach, our consideration of the capital structure of the firm opens the way to theoretically and numerically different inventory policies.

A net present value approach to safety stocks in planned production

In a number of recent papers, the Laplace transform together with input-output analysis has been applied for the sake of formulating a basic theoretical description of material requirements planning (MRP). The transform approach has had a threefold use; on the one hand, it has been useful for describing time developments of the relevant production, demand and inventory properties in a compact way including effects of order flows and lead times. Second, the transform also captures stochastic properties by functioning as a generating function, and, third, the transform is easily applied for assessing the resulting cash flows when adopting the net present value (NPV) principle (or the annuity stream principle which is a variation of NPV). Input-output analysis, in particular the input matrix, is applied for describing multi-level product structures, which has made the analysis concise and distinct. In this paper we extend the analysis of determining optimal safety stock levels for a sequence of planned production decisions (a one-level MRP system) by applying the annuity stream as a criterion to a simple model instead of the average cost approach previously used.

Negotiating Development Charges in Ontario: Average Cost versus Marginal Cost Pricing of Services

This article attempts to determine how the interplay of stakeholders in a larger economic and political context influences the design of development charge regimes in particular jurisdictions. As a vehicle for this exploration, the authors pose the question: Why do so many municipalities adopt average cost approaches to calculating development charges when it is widely assumed that a marginal cost approach is superior from an infrastructure and land-use efficiency perspective? The question is addressed through a case study method, which focuses on the creation of development charge regimes in Ontario, Canada, and in particular on eight 'focus' municipalities within the Greater Toronto Area. The article begins by presenting the 'pragmatic' explanations for adopting an average cost approach offered by finance officials and consultants. These explanations present the average cost method as the outcome of the deliberate application of basic principles of efficiency, equity, administrative simplicity and public acceptability. We proceed by showing that such explanations are incomplete or incoherent in important ways and turn to more 'critical' explanations, which require an understanding of developer-municipal conflict over the principles involved in the design of development charges. This leads us to an account of the emergence of development charges in Ontario and the evolving debate between municipalities and developers over who should pay for the infrastructure needed to support growth. This account reveals that there has been a gradual shift in municipal infrastructure financing practices from a marginal cost or 'site-specific' approach, favoured by developers, to an average cost or 'municipality-wide' approach, favoured by municipalities. Associated with this trend has been an evolution from negotiated charges to formulaic charges. In the conclusions, a number of factors underlying this evolution are identified.

Initial order quantities in a multistage production system with backlogging

The problem considered is that of determining optimal initial order quantities and backlogged amounts in a multistage serial production system with lost sales allowed. Items are processed into end products at finite rates within each production stage and thereafter delivered into an inventory of end products. Before each entire batch of end products is completed, any demand appearing from the start of the production period cannot be met when there is a lack of initial inventory. In order to reduce lost sales, smaller batches and/or larger backlogs than the stationary ones may be preferred, but this would incur additional costs. The net present value principle is applied to evaluate the performance of the system. This procedure automatically takes capital costs and the effects of lost sales and backlogging into account. The optimal decision policy developed by dynamic programming determines the optimal sequences of order quantities and backlogs over time and provides conditions for whether or not the process starts in a transient phase to be followed by a stationary phase. Under certain circumstances batch sizes will increase and backlogged amounts decrease during the former phase, after which both remain constant during the subsequent stationary phase. The model incorporates backlogging costs both per unit backlogged and per unit and time unit. Properties of the stationary solution are derived. An interior solution will normally be obtained also, with positive backlogging costs per unit in contrast to corresponding results when applying the traditional average cost approach. Numerical examples illustrating different basic cases are provided.

The Impact of Lapse Rates on Life Insurance Prices: Comment

Professor Belth is, uncomfortably for the actuarial profession, close to the truth in pointing to an absence of specific published analyses of the impact of lapse rates on prices.1 The only mild rebuttal that I can offer without going rather far into the past is to draw attention to a discussion of the subject by Neil W. Macintyre, F.S.A.2 Mr. Macintyre's is particularly of interest because it recognizes the existence of two different premises upon which calculations of the cost of lapsation may be based. These two are labeled by Mr. Macintyre the average cost approach and the marginal cost approach, respectively. Professor Belth uses only the first of these. The aim of this communication is to suggest several ways in which Professor Belth might, if he wishes, write a sequel to his present paper which would in my opinion throw considerably clearer light upon the subject than he thus far has succeeded in doing. My suggestions are as follows: