Cost-plus pricing when joint costs are present

Companies using cost-plus pricing often produce products that entail joint cost allocation. A problem they have encountered is that, while product prices are a function of the full cost, joint cost allocation methods using net realizable values depend on the product prices. This paper shows that when all costs and production quantities are known (or can be budgeted), it is possible to simultaneously determine unique product prices and cost allocations using the net realizable value method.     

JOINT PRODUCT COST ALLOCATION IN THE CONTEXT OF COST-PLUS PRICING DETERMINATIONS WITH NON-UNIFORM MARKUPS

Companies that use cost-based pricing sometimes manufacture products that involve joint cost allocation. A problem with this is that, while product prices are a function of the full cost, joint cost allocation methods using net realizable values depend on the product prices. This paper demonstrates that when all costs and production quantities are known or can be budgeted, it is possible to simultaneously determine unique product prices (having non-uniform markup rates) and cost allocations using the net realizable value method.     

A Simple Algorithm for the Mathematical Programming Approach to Joint Cost Allocation for Decision Making (Demand-Adjusted-Sales-Value Algorithm)*

This paper investigates the mathematical programming (MP) approach for decision making and cost allocation in the context of joint products. Through analysis of the MP approach to marginal-value-based cost allocations, an algorithm is developed to show that the allocations contain two elements: an element that is specific to individual joint products due to differences in demand elasticities, and an element based on relative adjusted sales values. If demand elasticities are identical for all joint products, then the traditional sales value method will generate the same cost allocation as the MP method. The new algorithm, the demand-adjusted-sales-value algorithm (DASV), is especially helpful for solving the MP model with linear demand functions. The DASV algorithm provides an easy way to generate costs that are useful for optimal decision making.     

Allocating a fixed cost across the decision making units with two-stage network structures

A prominent issue in many organizations involves the fair allocation of a total fixed cost among a group of entities. This paper extends the traditional fixed cost allocation problem to situations where the decision making units (DMUs) have a two-stage network structure. To this end, this paper first uses the data envelopment analysis (DEA) methodology to determine the relative efficiency while taking the internal structure and possible allocated costs into account. It shows that each DMU can separately maximize its relative efficiency to one through determining a series of allocations and selecting a set of relative weights. Next, we demonstrate that there exists an efficient allocation set based on a set of common weights, using which all DMUs and their two sub-stages can be simultaneously efficient. However, there are alternative allocation plans in the efficient allocation set. According to this non-uniqueness problem, we further optimize the allocation plans by taking the size of operation units into account, such that the allocation result is proportional to current input usages and output productions from a size point of view. In addition, we suggest a min–max model and a feasible computation algorithm for it to generate the final allocation plan in a way that minimizes the deviation between the efficient allocations and size allocations. More importantly, by repeatedly minimizing the maximum deviation, our proposed method can guarantee a unique allocation plan for all DMUs and sub-stages. Finally, both a numerical example modified from previous literature and an empirical application of bank activities are used to demonstrate the efficacy and usefulness of the proposed approach.     

Simultaneous Determination of Joint Product Cost Allocations and Cost-Plus Prices*

Use of the net realizable value approach for joint manufacturing cost allocations requires knowledge of selling prices of joint products. However, joint product selling prices themselves are functions of the allocated costs under a cost-plus pricing policy. In this case, it is necessary to determine joint cost allocations and joint product prices simultaneously. This paper applies a nonlinear programming (NLP) approach to simultaneously determine the optimal joint production decision, joint product cost-plus prices, and joint cost allocations using the net realizable value method. The NLP solution provides not only the optimal joint production and pricing decisions, but also the necessary conditions for such optimal decisions.     

Optimal Abort Rules for Multiattempt Missions

Many real‐world systems use mission aborts to enhance their survivability. Specifically, a mission can be aborted when a certain malfunction condition is met and a risk of a system loss in the case of a mission continuation becomes too high. Usually, the rescue or recovery procedure is initiated upon the mission abort. Previous works have discussed a setting when only one attempt to complete a mission is allowed and this attempt can be aborted. However, missions with a possibility of multiple attempts can occur in different real‐world settings when accomplishing a mission is really important and the cost‐related and the time‐wise restrictions for this are not very severe. The probabilistic model for the multiattempt case is suggested and the tradeoff between the overall mission success probability (MSP) and a system loss probability is discussed. The corresponding optimization problems are formulated. For the considered illustrative example, a detailed sensitivity analysis is performed that shows specifically that even when the system's survival is not so important, mission aborting can be used to maximize the multiattempt MSP.     

Bipolar value-driven joint product costing

There exists a joint-cost allocation problem in the public sector, particularly highlighted by the cost-based national pricing of blood products in England, supposedly derived using volume-driven activity-based costing (ABC): an approach criticised by the implementation criteria propounded for ABC within the academic literature. In contrast, we believe that the contributions of quality-associated operations-based drivers, described within ABC, together with the net realisable value method, usually recommended as the optimal joint-cost allocation method, provide the beginnings of a solution. This paper sets out a methodological development from this platform that links allocation decisions with the issue of value. The bipolar nature of the model is based upon the combination of two types of allocation. One allocates joint costs according to the altered value of source material when competing non-joint alternative products exist. The other allocates joint costs according to product outcome values ascertained separately for the physical specification elements that comprise each of the range of joint products. The overall emphases are on academic context, model generalisation, the facilitation of cost-effective choices between joint products and non-joint alternatives, and possible future trends in the application of the method.     

Capacity Sharing and Cost Allocation among Independent Firms with Congestion

We analyze the benefit of production/service capacity sharing for a set of independent firms. Firms have the choice of either operating their own production/service facilities or investing in a facility that is shared. Facilities are modeled as queueing systems with finite service rates. Firms decide on capacity levels (the service rate) to minimize delay costs and capacity investment costs possibly subject to service‐level constraints on delay. If firms decide to operate a shared facility they must also decide on a scheme for sharing the capacity cost. We formulate the problem as a cooperative game and identify settings under which capacity sharing is beneficial and there is a cost allocation that is in the core under either the first‐come, first‐served policy or an optimal priority policy. We show that capacity sharing may not be beneficial in settings where firms have heterogeneous work contents and service variabilities. In such cases, we specify conditions under which capacity sharing may still be beneficial for a subset of the firms.     

An Empirical Investigation of Costs in Batching Decisions*

This paper examines the use of costs and cost functions to model lot‐sizing decisions in batch manufacturing. The cost functions used to model a wide variety of manufacturing systems are typically derived from average cost models of unconstrained inventory problems. The use of setups and average inventories as the basis for modeling the economics of a typical batch manufacturing cell is shown to be inadequate. An alternative physical model that focuses on lead times provides a model that more closely represents the underlying value of such a cell.     

Risk-Adjusted Mission Value: Trading Off Mission Risk for Mission Value

This article develops a decision-theoretic methodology for the risk-adjusted mission value (RAMV) for selecting between alternative missions in the presence of uncertainty in the outcomes of the missions. This methodology permits trading off mission risk for mission value, something that probabilistic risk analysis cannot do unless it explicitly incorporates both mission value and risk aversion of the project management. The methodology, in its complete implementation, is consistent with the decision theory known as expected utility theory, although it differs from conventional decision theory in that the probabilities and all but one of the utilities are not those of the decision maker. The article also introduces a new interpretation of risk aversion. The methodology is consistent with the elementary management concept concerning division of labor. An example is presented for selecting between discrete alternatives-four landing sites on Mars. A second example is presented for selecting among a set of continuous alternatives-a comet flyby distance. The methodology is developed within the context of scientific missions, but the methodology is equally applicable to any situation requiring outcome value judgments, probability judgments, and risk aversion judgments by different constituencies.     

Duality Approaches to Economic Lot‐Sizing Games

Sharing common production, resources, and services to reduce cost are important for not for profit operations due to limited and mission‐oriented budget and effective cost allocation mechanisms are essential for encouraging effective collaborations. In this study, we illustrate how rigorous methodologies can be developed to derive effective cost allocations to facilitate sustainable collaborations in not for profit operations by modeling the cost allocation problem arising from an economic lot‐sizing (ELS) setting as a cooperative game. Specifically, we consider the economic lot‐sizing (ELS) game with general concave ordering cost. In this cooperative game, multiple retailers form a coalition by placing joint orders to a single supplier in order to reduce ordering cost. When both the inventory holding cost and backlogging cost are linear functions, it can be shown that the core of this game is non‐empty. The main contribution of this study is to show that a core allocation can be computed in polynomial time under the assumption that all retailers have the same cost parameters. Our approach is based on linear programming (LP) duality. More specifically, we study an integer programming formulation for the ELS problem and show that its LP relaxation admits zero integrality gap, which makes it possible to analyze the ELS game by using LP duality. We show that there exists an optimal dual solution that defines an allocation in the core. An interesting feature of our approach is that it is not necessarily true that every optimal dual solution defines a core allocation. This is in contrast to the duality approach for other known cooperative games in the literature.     

On the Limitations of Redundancies in the Improvement of System Reliability

Some program managers share a common belief that adding a redundant component to a system reduces the probability of failure by half. This is true only if the failures of the redundant components are independent events, which is rarely the case. For example, the redundant components may be subjected to the same external loads. There is, however, in general a decrease in the failure probability of the system. Nonetheless, the redundant element comes at a cost, even if it is less than that of developing the first one when both are based on the same design. Identical parts save the most in terms of design costs, but are subjected to common failure modes from possible design errors that limit the effectiveness of the redundancy. In the development of critical systems, managers thus need to decide if the costs of a parallel system are justified by the increase in the system's reliability. NASA, for example, has used redundant spacecraft to increase the chances of mission success, which worked well in the cases of the Viking and Voyager missions. These two successes, however, do not guarantee future ones. We present here a risk analysis framework accounting for dependencies to support the decision to launch at the same time a twin mission of identical spacecraft, given incremental costs and risk-reduction benefits of the second one. We illustrate this analytical approach with the case of the Mars Exploration Rovers launched by NASA in 2003, for which we had performed this assessment in 2001.     

Priority Rules for Multi‐Task Due‐Date Scheduling under Varying Processing Costs

We study the scheduling of multiple tasks under varying processing costs and derive a priority rule for optimal scheduling policies. Each task has a due date, and a non‐completion penalty cost is incurred if the task is not completely processed before its due date. We assume that the task arrival process is stochastic and the processing rate is capacitated. Our work is motivated by both traditional and emerging application domains, such as construction industry and freelance consulting industry. We establish the optimality of Shorter Slack time and Longer remaining Processing time (SSLP) principle that determines the priority among active tasks. Based on the derived structural properties, we also propose an effective cost‐balancing heuristic policy and demonstrate the efficacy of the proposed policy through extensive numerical experiments. We believe our results provide operators/managers valuable insights on how to devise effective service scheduling policies under varying costs.     

基于厂商理论的区域产业边界和最优要素配置结构

区域经济发展核心是产业结构优化升级和资源的优化配置。在全球经济结构亟待优化升级和要素资源呈现不同层次紧缺的大背景下,如何合理配置和引导区域资源配置,优化产业发展方向,确定包括新兴产业在内的产业发展战略,是每一个地区新形势下面临的重要问题。一方面,在经济全球化和零边际成本趋势驱动下,区域产业发展不再局限于区域内部资源禀赋,资源流动性加强,区域产业发展的选择更加广泛和灵活;另一方面,资源日益短缺和经济快速发展推动了劳动力成本和资本成本上升,产业的生产要素配置也随之变化。基于厂商理论,将区域作为市场经济中的生产主体,在考虑区域交易成本和生产要素成本的基础上,构建区域产业边界模型和产业的最佳要素配置结构模型,开创了资源和商品全球化趋势下的产业升级战略的研究范式,探索了成本约束下的产业生产要素优化配置模式,为经济新常态下的区域产业升级战略和资源配置研究提供理论指引,为区域制定个性化的产业发展战略提供实践依据,同时对零边际成本社会趋势下的产业格局进行了初步的探索。研究得出:产业边界能够在一定程度下反映区域产业长期演化趋势,在完全市场经济下产业边界是产业发展的最优规模;区域产业的要素配置格局取决于产...     

Supply Performance in Multi‐Echelon Inventory Systems with Intermediate Product Demand: A Perspective on Allocation

In this article, we study the performance of multi‐echelon inventory systems with intermediate, external product demand in one or more upper echelons. This type of problem is of general interest in inventory theory and of particular importance in supply chain systems with both end‐product demand and spare parts (subassemblies) demand. The multi‐echelon inventory system considered here is a combination of assembly and serial stages with direct demand from more than one node. The aspect of multiple sources of demands leads to interesting inventory allocation problems. The demand and capacity at each node are considered stochastic in nature. A fixed supply and manufacturing lead time is used between the stages. We develop mathematical models for these multi‐echelon systems, which describe the inventory dynamics and allow simulation of the system. A simulation‐based inventory optimization approach is developed to search for the best base‐stock levels for these systems. The gradient estimation technique of perturbation analysis is used to derive sample‐path estimators. We consider four allocation schemes: lexicographic with priority to intermediate demand, lexiographic with priority to downstream demand, predetermined proportional allocation, and proportional allocation. Based on the numerical results we find that no single allocation policy is appropriate under all conditions. Depending on the combinations of variability and utilization we identify conditions under which use of certain allocation polices across the supply chain result in lower costs. Further, we determine how selection of an inappropriate allocation policy in the presence of scarce on‐hand inventory could result in downstream nodes facing acute shortages. Consequently we provide insight on why good allocation policies work well under differing sets of operating conditions.     

非瞬时补货下改良品联合采购决策

联合采购往往使订货批量成倍增加,从而更易享受供应商提供的价格折扣,因此联合采购受到零售商们的青睐。考虑由单供应商与多零售商组成的二级改良品供应链中,供应商对零售商提供非瞬时补货,分别建立零售商独立采购与联合采购的单位时间成本函数,求解出两种采购模式的最小单位时间成本并对之进行比较,得到联合采购优于独立采购的必要条件。同时,以联合采购的联盟成本作为分摊对象,应用多人合作博弈理论,将联合采购的成本分摊问题构造成多人合作博弈问题,给出最小核心法的成本分摊思路。通过数值算例演示成本分摊过程,给出净改良率对订货参数及成本参数的敏感性分析,并对四种成本分摊算法的分摊结果作出比较。     

电子商务环境下合作采购效益分析

合作采购是一种重要的企业间电子商务应用模式,成功实施合作采购需要供应链成员的积极参与。本文针对供应商采取的两种批发价定价策略,比较分析了协调成本对买主间合作采购动力及其总体采购成本的影响。其结果表明,只要协调成本较小,买主便具有合作采购动力,且无论供应商采取固定价格策略还是采取数量折扣策略,都存在一个协调成本临界值,当协调成本小于该临界值时,合作采购将同时减少买主与供应商的总体成本;当协调成本大于该临界值时,则总有一方的总体成本在合作采购中增加。     

Self‐Selecting Priority Queues with Burr Distributed Waiting Costs

Service providers, in the presence of congestion and heterogeneity of customer waiting costs, often introduce a fee‐based premier option using which the customers self‐segment themselves. Examples of this practice are found in health care, amusement parks, government (consular services), and transportation. Using a single‐server queuing system with customer waiting costs modeled as a Burr Distribution, we perform a detailed analysis to (i) determine the conditions (fees, cost structure, etc.) under which this strategy is profitable for the service provider, (ii) quantify the benefits accrued by the premier customers; and (iii) evaluate the resulting impact on the other customers. We show that such self‐selecting priority systems can be pareto‐improving in the sense that they are beneficial to everyone. These benefits are larger when the variance in the customer waiting costs is high and the system utilization is high. We use income data from the poorest and richest areas (identified by zipcode) in the United States along with the countrywide income distribution to illustrate our results. Numerical results indicate that planning for a 20–40% enrollment in the high‐priority option is robust in ensuring that all the stakeholders benefit from the proposed strategy.     

The Impact of Revenue‐Maximizing Priority Pricing on Customer Delay Costs

Speed is an increasingly important determinant of which suppliers will be given customers' business and is defined as the time between when an order is placed by the customer and when the product is delivered, or as the amount of time customers must wait before they receive their desired service. In either case, the speed a customer experiences can be enhanced by giving priority to that particular customer. Such a prioritization scheme will necessarily reduce the speed experienced by lower‐priority customers, but this can lead to a better outcome when different customers place different values on speed. We model a single resource (e.g., a manufacturer) that processes jobs from customers who have heterogeneous waiting costs. We analyze the price that maximizes priority revenue for the resource owner (i.e., supplier, manufacturer) under different assumptions regarding customer behavior. We discover that a revenue‐maximizing supplier facing self‐interested customers (i.e., those that independently minimize their own expected costs) charges a price that also minimizes the expected total delay costs across all customers and that this outcome does not result when customers coordinate to submit priority orders at a level that seeks to minimize their aggregate costs of priority fees and delays. Thus, the customers are better off collectively (as is the supplier) when the supplier and customers act independently in their own best interests. Finally, as the number of priority classes increases, both the priority revenues and the overall customer delay costs improve, but at a decreasing rate.     

A coordination mechanism with fair cost allocation for divergent multi-echelon inventory systems

In this paper we study the coordination of inventory control in divergent multi-echelon inventory systems under periodic review and decentralized control. Under decentralized control the installations decide upon replenishment policies that minimize their individual inventory costs. In general these policies do not coincide with the optimal policies of the system under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. We present a simple coordination mechanism that removes this cost inefficiency. The upstream installations increases its base stock level while the downstream installations compensate their supplier for increased costs and provide it with additional side payments. We show that this mechanism coordinates the system; the global optimal policy of the system is the unique Nash equilibrium of the corresponding strategic game. Furthermore, the mechanism results in a fair allocation of the costs; all installations enjoy cost savings.