OPTIMAL ALLOCATIONS OF JOINT (COMMON) COSTS: A PARAMETRIC PROGRAMMING APPROACH

A parametric programming model for allocating joint costs is described and illustrated. Given M mutually exclusive missions and P alternative systems for accomplishing such missions, the model first determines the optimal choice of systems for all missions simultaneously. It then allocates both joint and separable costs such that no mission receives a greater cost allocation than any other mission alternative that might be suboptimal for the mission but nonoptimal when all missions are simultaneously considered. Although the model initially assumes a mission priority ranking, this assumption is relaxed later on as alternative rankings are evaluated and cost allocation ranges under all priority rankings are evaluated.     

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.     

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.     

Manufacturing feature-based cost management system: a case study in Brazil

Feature costing is a topic of recent discussion related to cost management systems (CMSs) aimed at understanding how product features influence production process costs. It raises as a key issue in mass customisation environments where a single product model can present hundreds of menu options. In this study, we explore the concept of feature costing beyond the use of activity-based costing (ABC). We propose a CMS based on features and common elements as costing objects instead of products. In our model, we use the unit of production effort method to organise the direct manufacturing costs, ABC method to address the indirect cost and the standard methods to compute raw materials costs. We illustrate the method in the production of bus seats in a Brazilian manufacturing company. This study gives different perspectives to the international academic community on the use of a different CMS used by many Brazilian companies.     

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.     

联合订货区间值EOQ模型及变权Shapley值成本分摊方法

研究多个销售商企业组成联盟向一个供应商订购同种商品的联合订货问题。考虑到实际问题中很难预测到精确的需求，本文用区间表示单位时间需求量，研究允许缺货的销售商企业联合订货区间值EOQ模型，其中缺货完全回补。以联合订货平均成本最小为目标，结合连续有序加权集结算子求解出联合订货的周期、区间值订货量和区间值平均成本。定义变权Shapley值，给出区间值合作博弈的区间值变权Shapley值的求解方法，得出区间值变权Shapley值的表达式可直接利用相关联盟值的左、右端点计算得到。考虑联盟和局中人的相对重要性，结合需求率确定合成权重，提出基于区间值变权Shapley值的联合订货成本分摊方法。利用数值算例验证模型和方法的有效性。本文可为解决联合订货成本分摊问题提供决策参考。     

Cost Allocation in Manufacturing–Remanufacturing Operations

For firms remanufacturing their products, the total life‐cycle costs and revenues from new and remanufactured products determine their profitability. In many firms, manufacturing/sales and remanufacturing/remarketing operations are carried out in different divisions. Each division is responsible for only part of the product's life cycle. Practices regarding transfer pricing across divisions vary significantly among companies, affecting the life‐cycle profit performance of the product. In this research, we identify characteristics of transfer prices that achieve the firm‐wide optimal solution. To this end, we consider a manufacturer who also undertakes remanufacturing operations and we focus on price (quantity) decisions. We determine that a cost allocation mechanism that allocates a portion of the initial production cost to each of the two stages of the product life cycle should be used. We also conclude that cost allocation should be implemented as a fixed cost allocation, where charges to the remanufacturing division should be determined independently of the actual quantity of units remanufactured.     

The impact of the product mix on the value of flexibility

Product-mix flexibility is one of the major types of manufacturing flexibility, referring to the ability to produce a broad range of products or variants with presumed low changeover costs. The value of such a capability is important to establish for an industrial firm in order to ensure that the flexibility provided will be at the right level and used profitably rather than in excess of market requirements and consequently costly. We use option-pricing theory to analyse the impact of various product-mix issues on the value of flexibility. The real options model we use incorporates multiple products, capacity constraints as well as set-up costs. The issues treated here include the number of products, demand variability, correlation between products, and the relative demand distribution within the product mix. Thus, we are interested in the nature of the input data to analyse its effect on the value of flexibility. We also check the impact at different capacity levels. The results suggest that the value of flexibility (i) increases with an increasing number of products, (ii) decreases with increasing volatility of product demand, (iii) decreases the more positively correlated the demand is, and (iv) reduces for marginal capacity with increasing levels of capacity. Of these, the impact of positively correlated demand seems to be a major issue. However, the joint impact of the number of products and demand correlation showed some non-intuitive results.     

双渠道供应链中紧俏产品升级成本分担演化博弈分析

针对一个制造商和一个零售商所组成的双渠道供应链系统,本文运用演化博弈模型研究了供应链企业在紧俏产品升级成本分担中的产能分配问题,比较了无合作机制以及引入合作机制下供应链系统的演化稳定策略。研究发现：当无合作机制时,供应链系统根据不同的产能分配范围最终会稳定在以下3种策略上：(制造商投资,零售商不投资)、(制造商不投资,零售商投资)以及(制造商不投资,零售商不投资);当引入合作机制时,供应链系统在一定的产能分配范围内最终会稳定在双方共同投资的策略上。本文还通过算例分析了无合作机制时销售新产品的增加值以及产品升级成本对演化稳定策略的影响;产能分配比例,新产品批发价格对单方面投资概率的影响;引入合作机制下分享比例对共同投资为演化稳定策略时的影响。     

社交网络情境下基于同侪影响的产品线规划研究

依托社交网络优化产品线是实现“匹配消费者需求带动产品设计-制造-营销全流程协调发展”的重要途径,尽管已经引起实业界的重点关注,相应的学术研究却十分匮乏。鉴于此,本文基于同侪影响理论与前景理论,结合社交网络情境下消费者的产品需求、偏好及决策,构建涵盖产品线营销层面和设计层面的双层规划模型;然后结合智能手机产品线实例,运用嵌套灰狼算法对该双层规划模型进行求解验证。本研究旨在提出社交网络与产品线规划之间耦合作用的联合优化框架,为面向社交网络的产品线规划提供理论依据。     

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.     

Allocating Capacity with Demand Competition: Fixed Factor Allocation*

We consider a supply chain consisting of a supplier and two retailers. The supplier sells a single product to the retailers, who, in turn, retail the product to customers. The supplier has limited production capacity, and the retailers compete for the supplier's capacity and are duopolists engaged in Cournot competition for their customers. When the sum of the retailers' orders exceeds the supplier's capacity, the supplier allocates his capacity according to a preannounced allocation rule. We propose a new capacity allocation rule, fixed factor allocation, which incorporates the ideas of proportional and lexicographic allocations: it prioritizes retailers as in lexicographic allocation, but guarantees only a fixed proportion of the total available capacity to the prioritized retailer. We show that (1) the fixed factor allocation rule incorporates lexicographic and proportional allocations from the perspectives of the supplier and the supply chain; (2) under fixed factor allocation, the supply chain profit is not affected by the allocation factor when it is greater than a threshold; (3) the retailers share the supply chain profit with the supplier depending on the value of the allocation factor; and (4) the fixed factor allocation coordinates the supply chain when the market size is sufficiently large. We also compare fixed factor with proportional and lexicographic allocations, respectively. Furthermore, we demonstrate how the supplier can optimize his capacity level and wholesale price under fixed factor allocation.     

Managing Downstream Competition via Capacity Allocation

Consider a supply chain with one supplier and multiple retailers. The supplier produces a single product and sells it to the retailers, who in turn sell the product to consumers. The supplier has limited production capacity, and the retailers are engaged in a Cournot competition at the consumer/market level. When the sum of the retailer orders exceeds the capacity, the supplier allocates her capacity according to a pre‐announced allocation mechanism. Two mechanisms are considered: proportional allocation and lexicographic allocation. An extensive study of the two allocation mechanisms shows that the lexicographic mechanism has the ability to dampen the competition at the retail level, increasing the profits for both the supplier and the supply chain.     

不同货架空间分配顺序下农产品供应链优化问题研究

货架是超市和生鲜便利店的重要资源，不仅具有储存和展示农产品的功能，同时货架空间大小对农产品的销量具有重要影响。针对产品需求受货架空间与零售价格共同影响的两级农产品供应链，在考虑供应商主导和零售商主导的情况下，分别对零售商在销售季节来临前和来临后分配货架空间四种分散式农产品供应链的最优决策与利润进行了分析，并与一体化供应链的最优决策进行了比较。研究发现，不论是在供应商主导还是在零售商主导的农产品供应链中，零售商在销售季节来临前分配货架空间，相比在销售季节来临后分配货架空间，农产品的批发价格与零售价格更高，分配的货架空间更小，供应商和零售商均获得更少的利润，相应的农产品供应链整体利润更少。因此，零售商在销售季节来临后分配货架空间对农产品供应链更有利。相比一体化供应链，分散式供应链的零售价格更高，分配的货架空间更小，供应链整体利润小于一体化供应链的最优利润，本文给出了基于利润共享与成本共担的合同对分散式供应链进行协调。最后，通过数值算例研究了参数变化对最优决策和供应链利润的影响。     

关键链项目实时滚动监控方法研究

为提高项目的按时完工率，研究了一种实时滚动的动态缓冲监控方法。新方法充分考虑了项目不确定性的变化以及各活动之间的联系，基于活动的风险暴露度对缓冲总量进行分配，并根据缓冲量的实际消耗情况，将各监控点的缓冲监控剩余量按照活动风险权重因子进行实时滚动和再分配，对用于监控的缓冲量和监控基准点进行实时动态调整。仿真实验表明，该方法可以减少错误预警的产生和因此耗费的额外成本和时间，极大地提高项目的完工概率。     

基于Shapley值法的商务模式创新价值分享

商务模式的价值创造活动正逐步由个体企业的行为演变为主体企业、伙伴和客户的共同努力。只有以合理的价值分享为前提的价值获取才能保证商务模式创新的价值得以持续创造,保证商务模式创新的成功。基于Shapley值法对商务模式创新后的价值增值在主体企业和其他利益相关者之间进行分享,比较各个参与主体价值增值的大小,得到合理价值分享的条件。研究结果表明,对商务模式创新没有直接贡献的利益相关者也可能分享到创新的价值,但不同创新结果价值分享的对象和数量是不一样的,创新结果参数的变化会不同程度影响分享的价值,为了更好地提高各个利益相关者参与创新的积极性,有必要针对不同创新的结果调整分享的价值。     

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。     

Hierarchical Screening for Capacity Allocation in Supply Chains: The Role of Distributors

We consider a two‐stage principal–agent screening environment in a decentralized supply chain with retailers, distributors, and a supplier. The retailers possess private information regarding their local market profitabilities. The distributors can partially observe the retailers' profitabilities and are heterogeneous with regard to the precision of that information. The supplier determines the level of production, but knows neither the local market profitabilities nor the precision of the distributors' information. The supplier first allocates finished products to distributors, and the distributors then contract with local retailers with a capacity constraint. We find that due to the distributors' superior information, the quantity distortion on the retailers' side is mitigated, and the upstream information asymmetry subsequently affects the quantity allocation among the downstream retailers. The supplier may not benefit from contracting with the distributors. In addition, no distributor is excluded based on the heterogeneity of the information precision, even though some distributors do not have better information than the supplier. In the numerical examples, we further analyze how the local market heterogeneity and inventory costs affect the capacity allocation, the retailers' payoffs, and the supply chain profits. We document some counter‐intuitive quantity allocation rules that arise from the distributors' information advantage.     

Incentive Schemes for Semiconductor Capacity Allocation: A Game Theoretic Analysis

We study incentive issues that arise in semiconductor capacity planning and allocation. Motivated by our experience at a major U. S. semiconductor manufacturer, we model the capacity‐allocation problem in a game‐theoretic setting as follows: each product manager (PM) is responsible for a certain product line, while privately owning demand information through regular interaction with the customers. Capacity‐allocation is carried out by the corporate headquarters (HQ), which allocates manufacturing capacity to product lines based on demand information reported by the PMs. We show that PMs have an incentive to manipulate demand information to increase their expected allocation, and that a carefully designed coordination mechanism is essential for HQ to implement the optimal allocation. To this end, we design an incentive scheme through bonus payments and participation charges that elicits private demand information from the PMs. We show that the mechanism achieves budget‐balance and voluntary‐participation requirements simultaneously. The results provide important insights into the treatment of misaligned incentives in the context of semiconductor capacity‐allocation.     

Cost of Equity in Homeland Security Resource Allocation in the Face of a Strategic Attacker

Hundreds of billions of dollars have been spent in homeland security since September 11, 2001. Many mathematical models have been developed to study strategic interactions between governments (defenders) and terrorists (attackers). However, few studies have considered the tradeoff between equity and efficiency in homeland security resource allocation. In this article, we fill this gap by developing a novel model in which a government allocates defensive resources among multiple potential targets, while reserving a portion of defensive resources (represented by the equity coefficient) for equal distribution (according to geographical areas, population, density, etc.). Such a way to model equity is one of many alternatives, but was directly inspired by homeland security resource allocation practice. The government is faced with a strategic terrorist (adaptive adversary) whose attack probabilities are endogenously determined in the model. We study the effect of the equity coefficient on the optimal defensive resource allocations and the corresponding expected loss. We find that the cost of equity (in terms of increased expected loss) increases convexly in the equity coefficient. Furthermore, such cost is lower when: (a) government uses per‐valuation equity; (b) the cost‐effectiveness coefficient of defense increases; and (c) the total defense budget increases. Our model, results, and insights could be used to assist policy making.