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.     

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.     

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。     

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。     

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.     

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.     

Investigating the effect of product variants,and demand distributions on the optimal demand supply network setup

In today's marketplace, consumers are looking for product variety and low prices. In this paper, we investigate how product variation and demand distributions affect demand supply network optimality in a real-life based setting. The research methodology was based on a novel Petri net formulation, which employs reachability analysis to demand supply network optimisation. We found that in our case study localised final assembly is justified with one or two product variants, but a centralised production should be favoured with three or more product variants. We also noted the sensitivity of this result to transport cost/inventory carrying cost tradeoff.     

Economic efficiency when prices are not fixed: disentangling quantity and price efficiency

This paper proposes an approach to compute cost efficiency in contexts where units can adjust input quantities and to some degree prices so that through their joint determination they can minimise the aggregate cost of the outputs they secure. The model developed is based on the data envelopment analysis (DEA) framework and can accommodate situations where the degree of influence over prices ranges from minimal to considerable. When units cannot influence prices at all the model proposed reduces to the standard cost efficiency DEA model for the case where prices are taken as exogenous. In addition to the cost efficiency model, we introduce an additive decomposition of potential cost savings into a quantity and a price component, based on Bennet indicators.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

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.     

Product Positioning and Pricing Under Production Cost Considerations*

A framework in a competitive environment is proposed that incorporates production cost and economies of scale in the problem of positioning a product for a market segment. The model facilitates the existence of a Nash equilibrium in prices and product positions. As such, firms can simultaneously choose prices and product positions for the segment. This result improves the traditional theory on equilibria points in prices and product positions where firms choose their product positions first and then set their prices. A sensitivity analysis demonstrates the effects of changes in the unit savings derived from economies of scale or the cost of furnishing a product with its attributes by one firm on the product positions, prices, and profits of all competing firms. More important, the paper examines the effect on prices and profits of competing firms when one of the firms repositions its product closer to the segment's ideal point. It is shown that under certain conditions, the profit of a firm may actually decrease as it redesigns its product closer to the segment's ideal point. These conditions assist management to identify the product design beyond which enhancements of the product would lead to lower profits because of increasing production costs. It is also shown that the price of this firm increases. Past research supports the idea that positioning a brand closer to the ideal point, given fixed product positions of competing firms, would lead to greater buyer preferences and eventually higher profits. The price and profits of the competing firm may increase or decrease. Conditions are derived under which a movement towards the segment's ideal point by one firm would lead to higher profits by the competing firm.     

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.     

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.     

The Impact of Manufacturers' Wholesale Prices on a Retailer's Shelf‐Space and Pricing Decisions*

This article examines shelf‐space allocation and pricing decisions in the marketing channel as the results of a static game played à la Stackelberg between two manufacturers of competing brands and one retailer. The competing manufacturers act as leaders that play a simultaneous and noncooperative game. They fix their transfer prices by taking into account the shelf‐space allocation and price‐markup decisions of their common exclusive dealer. The results indicate that the wholesale prices of brands are strongly linked to their share of the shelf. The main results of our numerical simulations may be summarized as follows: first, the lower the unit cost and/or the greater the price elasticity, the greater the shelf space allocated to that brand. Second, the higher the shelf‐space elasticity, the lower are the wholesale prices and the profits of all channel members.     

考虑策略型消费者行为的零售商订货及忠诚计划联合决策研究

顾客忠诚计划是零售商的重要销售策略之一. 本文针对两期折扣问题中零售商的订货和积分回馈计划投入的联合决策问题,基于完全理性假设,并结合问题的实际情况,考虑了全价期单期以及全价期和折扣期两期的积分回馈计划,构建了基于这两种积分回馈计划下的策略型消费者决策模型. 分析了不同积分回馈计划对策略型消费者行为的影响,进而讨论了零售商在不同决策下的收益情况,探索了零售商订货和积分回馈计划联合决策的制定. 研究发现：(1)积分回馈计划会对策略型消费者行为产生影响,从而影响零售商的决策和收益;(2)订货和忠诚计划制定的联合决策有利于零售商提高收益;(3)对于单位成本低的商品,面向全价期的积分回馈计划的最优收益提升较大;(4)对于商品价值与实际价格差异较小的商品,积分回馈计划对最优收益的提升作用较大. 具体而言,如果商品单位成本小于等于折扣价,则面向全价期的积分回馈计划的最优收益提升较大,反之,则面向全价期和折扣期的积分回馈计划的最优收益提升较大.     

Assortment Planning for Vertically Differentiated Products

We consider the problem of a retailer managing a category of vertically differentiated products. The retailer has to pay a fixed cost for each product included in the assortment and a variable cost per product sold. Quality levels, fixed, and variable costs are exogenously determined. Customers differ in their valuation of quality and choose the product (if any) that maximizes their utility. First, we consider a setting in which the selling prices are also fixed. We find that the optimal set of products to offer depends on the distribution of customer valuations and might include dominated products, that is, products which are less attractive than at least one other product, on every possible dimension. We develop an efficient algorithm to identify an optimal assortment. Second, we consider a setting in which the retailer also determines the selling prices. We show that in this case the optimal assortment does not include any dominated product and does not vary with the distribution of customer valuations when there is no fixed cost. We develop several efficient algorithms to identify an optimal assortment and optimally price the products. We also test the applicability of our methods with realistic data for two product categories.     

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。     

A COMMENT ON THE COST OF NEW ISSUES OF COMMON STOCK

According to the constant growth model and perceived finance theory, the cost of new external equity exceeds the cost of retained earnings due to flotation costs and underpricing. Carlson and Dietz [1] have recently argued that the constant growth model is operationally inadequate whenever the net proceeds from the issuance of a new share differ from book value. Specifically, they contend that the cost of new external equity is less than the cost of retained earnings whenever the net proceeds from a new share exceed book value. We show that these conclusions stem from an error in interpretation and therefore that the constant growth model is valid regardless of the relationship between market prices and book value.     

存在网络外部性下的两阶段圆周模型

本文分析了存在网络外部性下的两阶段圆周模型。网络外部性的存在使厂商有动机降低产品价格以获得更大的市场份额,模型的子博弈精炼纳什均衡表明消费者剩余和社会净福利水平得到改进,同时行业内产品的差异程度偏少。特别地,在强网络外部性下,垄断结构能使社会净福利最大化。     

考虑信用销售的改良品联合采购决策

信用销售能够提升生产企业竞争力、扩大经营规模,帮助销售企业缓解资金压力,对供应链的运作效率有较大影响,成为供应链管理研究的重要课题之一。考虑在单一供应商和多个零售商组成的二级改良品供应链中,供应商提供延迟支付作为信用销售手段,分别建立零售商独立采购和联合采购的最小单位时间总成本函数,通过比较最小单位时间总成本函数得到联合采购优于独立采购的条件。将改良品联合采购的成本分配问题构造为改良品联合采购博弈,给出博弈具有的基本性质,并设计一种基于博弈核心的成本分配方法。通过数值算例和敏感性分析验证了文中所构建模型的正确性。