Cost Allocation Problem Research Articles

Fixed cost allocation based on a data envelopment analysis aggressive game approach

The literature on organizational strategy and production operations suggests that establishing a shared platform would be beneficial for addressing competition and mitigating risks. However, the creation of a common platform inevitably incurs expenditures and costs, prompting the natural question of how to equitably distribute the total fixed cost among all participating units. While the fixed cost allocation (FCA) problem has been explored in the context of data envelopment analysis (DEA), this paper addresses a distinct decentralized environment wherein there is no central decision-maker, and each individual decision-making unit (DMU) pursues a self-interested strategy to minimize its allocated cost share. In tackling the challenge of proposing an acceptable allocation plan within this decentralized setting, we initially improve the non-egoistic principle by considering the perspective of operational size. This improvement mandates that each DMU bears the maximum fixed cost per unit of operational size in its own allocation proposal. The improved non-egoistic principle implicitly addresses the platform constraint and fairness concerns, while each DMU remains committed to maximizing other DMUs’ cost shares and minimizing their own performance efficiency. Additionally, we introduce an aggressive game process to amalgamate all DMUs’ allocation proposals into the DEA efficiency analysis. A DEA aggressive game approach and its corresponding computational algorithm are developed to facilitate consensus and determine the final FCA plan. Mathematically, we prove that all average post-allocation efficiencies, incorporating fixed costs, converge to the same aggressive game cross-efficiency for each DMU in the iterative algorithm. To the best of our knowledge, this paper represents the first study that employs an aggressive strategy in the FCA problem to minimize efficiency scores, while existing literature predominantly focuses on maximizing or maintaining efficiency scores. Finally, we apply the proposed approach to a classical numerical example and an empirical study involving nine independent truck fleets to showcase its characteristics and efficacy.

Cost allocation and airport problems

We consider the problem of dividing the cost of a facility when agents can be ordered in terms of the needs they have for it, and accommodating an agent with a certain need allows accommodating all agents with lower needs at no extra cost. This problem is known as the “airport problem”, the facility being the runway. We review the literature devoted to its study, and formulate a number of open questions.

Cooperation in spare parts systems with penalty cost per unit backlogged

Inventory pooling is well known to reduce inventory costs and improve customer service. Although potential benefits are well understood, one important prerequisite to form a stable coalition between independent companies, who like to cooperate to benefit from inventory pooling, is agreeing on a cost allocation such that no group of companies would better off leaving the coalition. Existence of such stable allocations would depend on the scenarios that these companies are cooperating in.In this paper, we study cooperation between a group of companies, who keep spare parts to maintain their expensive equipment, by pooling their inventory in several practically motivated scenarios. To address the cost allocation problem, we borrow concepts from cooperative game theory and examine the core of the resulting cooperative games in each scenario. We especially focus on systems with high penalty cost per unit backlogged, which is modelled as a well known (S−1,S) inventory system with backlogging.We study cooperation under four scenarios, namely cooperation under penalty cost, cooperation with joint capacity investment, cooperation under service level constraints and cooperation by inventory pooling. The first three scenarios consider cooperation by investing into a central pool of inventory optimally, whereas in the last scenario, companies cooperate by pooling their available inventory only. In most of the scenarios, we show the existence of stable cost allocations by identifying a core allocation, which is easy to compute and, in some, a population monotonic allocation (PMAS). In other scenarios, we present examples explaining why finding a stable allocation might not be possible by showing the core of the resulting games can be empty. To establish these results, we also derive several interesting properties (e.g. subhomogeneity of degree one) of the main performance measure (i.e., average number of backorders).

Cost allocation problems on highways with grouped users

One of the practical applications of cooperative transferable utility games involves determining the fee structure for users of a given facility, whose construction or maintenance costs need to be recouped. In this context, certain efficiency and equity criteria guide the considered solutions. This paper analyzes how to allocate the fixed costs of a highway among its users through tolls, considering that different classes of vehicles or travelers utilize the service. For this purpose, we make use of generalized highway games with a priori unions that represent distinct user groups, such as frequent travelers or truckers, who, due to enhanced bargaining power, often secure reductions in their fares in real-world scenarios. In particular, the Owen value, the coalitional Tijs value, and a new value termed the Shapley–Tijs value are axiomatically characterized. Additionally, straightforward formulations for calculating these values are provided. Finally, the proposed methodology is applied to actual traffic data from the AP-9 highway in Spain.

ChatGPT 등 인공지능 모델 출현에 따른 원가관리회계 교육에서의 조화 가능성 탐색

[Purpose] This study aims at providing suggestions and implications on cost accounting education under the circumstances of generative artificial intelligence language models such as ChatGPT, Bing, and Bard.
 [Methodology] First, this study evaluates how well the model can provide solutions for the cost accounting exam questions. Second, this paper modifies prompts in order to get the desired answers from the AI model.
 [Findings] The artificial intelligence model can solve the questions such as explaining the main concepts of cost accounting and developing managerial accounting schemes like BSC. The models also provide the correct answers for simple questions on calculating cost with a simple process. However, there are limits on multi-level cost allocation problems.
 [Implications] This paper introduces examples that ChatGPT can provide answers to cost accounting questions. Based on the initial draft that ChatGPT generated, students can validate or revise their initial draft. In addition, prompt engineering activities can be introduced with cost accounting topics as illustrated in this study.

Cost allocation in energy distribution networks

This paper presents a cost allocation problem arising from energy distribution and proposes cost allocation rules that depend on the distribution network and consumer demands. To determine relevant rules, we adopt a normative approach and compare two principles: (i) the connection principle and (ii) the uniformity principle. The Connection rule is proposed in accordance with (i), while the Uniform rule is developed in line with (ii). However, (i) and (ii) are incompatible. To make a trade-off between them, we propose a family of Mixed rules. Each rule is axiomatically characterized. Then, we demonstrate that the Connection rule coincides with the multi-choice Shapley value of a specific multi-choice game derived from the original problem. Moreover, the Connection rule is in the Core of this game. Similarly, we show that the Uniform rule and the Mixed rules coincide with other solution concepts from multi-choice games.

An adaptive optimization consensus mechanism for group decision making using the Shapley allocation scheme

Adaptive consensus mechanism adopts differentiating consensus improvement strategies according to different consensus levels, which is reasonable and efficient for reaching consensus in group decision making. However, previous adaptive consensus methods adopt the feedback iteration mechanism, which has drawbacks such as time-consuming, over-consensus adjustment, and failure of consensus-reaching. Therefore, this paper studies the adaptive consensus mechanism by optimization models to avoid the above issues of the feedback iteration mechanism. In our approach, corresponding optimization models are constructed to identify non-consensus judgments, non-consensus alternatives, and non-consensus decision makers, respectively. Meanwhile, the related total minimum consensus adjustments are ascertained. Since the uniqueness of the consensus adjustment scheme cannot be ensured according to the built models, we regard it as a cost allocation problem in cooperative games, and define three types of consensus adjustment cooperative games. After that, the Shapley function, a well-known single payoff index, is adopted to allocate total consensus adjustments in different cases. Additionally, we employ the optimization model to determine the modified values of non-consensus judgments by minimizing the number of adjustment judgments. Finally, numerical study and comparison are made.

APPLICATION OF THE H&S MODEL FOR THE ADVANCED EXERGY ANALYSIS OF AN ORGANIC RANKINE CYCLE

In order to carry out the advanced exergy analysis of a system, an exergoeconomic-based approach is required. The Specific Exergy Costing method is chosen for this. Thus, there is a gap in the literature regarding the application of other approaches. An alternative is the H&S Model, which was originally proposed to solve the cost allocation problem in power cycles. Therefore, the objective of the present paper is to verify whether the H&S Model is able to be adapted for the purpose of performing advanced exergy analysis. The power cycle taken as a case study is an organic Rankine cycle, which is fed with waste heat and uses R-245fa as the working fluid. Both conventional and advanced exergy analyses are done for a base case. In addition, a parametric analysis is performed to check the consistency of the H&S Model. Regarding the results of the case study, the conventional exergy analysis indicated that the evaporator should be the priority to improve the cycle. On the other hand, the advanced exergy analysis showed that the greatest amount of the avoidable exergy destruction was also endogenous and associated with the expander. The results also showed that the adaptation of the H&S Model is possible when considering the base case. It has also been shown that such an adaptation is consistent when taking into account the parametric analysis.

Cost Sharing in Insurance Communities: A Hybrid Approach Based on Multiple-Choice Objective Programming and Cooperative Games

At present, utilizing the insurance community is a common method to deal with investment risks along the Belt and Road; however, there is no clear method or mechanism to deal with the decision-making optimization and cost allocation of the insurance community participants. We propose a hybrid approach to solve this problem. First, we construct an underwriting decision optimization model for the insurance community using the multi-choice goal programming method, which generates the cost characteristic function based on a cooperative alliance. Second, we use the cooperative game method combined with the modified Shapley value method to take risk factors into consideration, which allows us to optimize the cost allocation among members of the insurance community. Finally, our simulation analysis results show that the multi-choice goal programming method can optimize the insurance community’s underwriting decisions. Specifically, the total underwriting cost is lower than the sum of the underwriting costs under the insurance company’s single-action strategy, and the total underwriting scale is as large as possible. Compared with the classical Shapley value method, the modified Shapley value method can better reflect differences in the underwriting risks of different regions, encouraging governments to take measures to reduce underwriting risks. To conclude, we propose some suggestions based on our research findings. The possible contributions of this paper are as follows: our research provides a hybrid optimization method based on multiple-choice objective programming and cooperative games to solve the cost allocation problem facing the insurance community, and it has some reference value for improving the cost-sharing system of the insurance community.

Balanced externalities and the proportional allocation of nonseparable contributions

This paper provides axiomatic characterizations of the proportional allocation of nonseparable contributions (PANSC) value for TU games, being the solution which allocates the total worth proportional to the separable contributions of the players. First, we show that the PANSC value is the only one satisfying efficiency and weak balanced externalities, the last axiom requiring that every player’s payoff is the same fraction of the total externality inflicted on the other players with her presence. This is a weakening of balanced externalities studied in the context of queueing problems to characterize the Shapley value. Our second characterization is obtained by investigating the dual relation between the PANSC value and the proportional division value, showing that the PANSC value is the only one satisfying complement consistency and dual proportional standardness. In addition, we discuss the relation between the PANSC value and two methods widely used in cost allocation problems: the separable costs remaining benefits method and the alternative cost avoided method.

Allocating a fixed cost as a reduction of outputs in a non-cooperative decision-making environment: A data envelopment analysis approach

The fixed cost generated from constructing a common platform by all units needs to be allocated among these units in a reasonable way in many management practices. As market information is often incomplete, data envelopment analysis (DEA) approaches have been successfully used in fixed cost allocation problems. The fixed cost was treated as an input measure in previous studies. However, it has no effect on the original inputs and outputs when making the allocation decision after an operating cycle. In this case, it can be regarded as a reduction of outputs rather than an input. This paper developed a new DEA approach based fixed cost allocation model in a decentralized decision-making environment that treats the fixed cost as a reduction of outputs. Unlike the existing approaches addressing efficiencies, the proposed model considers the cost itself in the allocation process. An iterative procedure is then presented to derive the average game cost allocation scheme. A classical numerical example from the prior literature is given to show the applicability of the proposed model. The simulation results show that the developed approach can obtain a unique allocation scheme.

Cost and emission allocation for joint replenishment systems subject to carbon constraints

We consider joint replenishment among multiple retailers subject to various types of carbon constraints. In particular, we consider four types of carbon constraints: carbon tax, strict carbon cap, carbon cap-and-offset, and carbon cap-and-price. Under each carbon policy, we first identify the optimal joint ordering policy. Then, we study the cost allocation problem in the framework of cooperative game theory. For the joint replenishment game with carbon tax, we show that a simple proportional rule belongs to the core of the corresponding game. For the joint replenishment games with strict carbon cap, carbon cap-and-offset, and cap-and-price wherein the penalty rate is larger than the reward rate, we show that the cost allocation rules based on the Lagrangian multipliers belong to the core of the corresponding games. Interestingly, for the joint replenishment game with cap-and-price wherein the penalty rate is less than the reward rate, we show that the corresponding joint replenishment game may not satisfy subadditivity and may have an empty core. This implies that joint replenishment is not feasible in this situation. In addition, we further discuss carbon emission allocation game under the strict carbon cap policy. We show that the carbon emission game does not necessarily satisfy subadditivity, and therefore, we propose an algorithm to generate an optimal coalition structure.

Cost-allocation problems for fuzzy agents in a fixed-tree network

Cost-allocation problems in a fixed network are concerned with distributing the costs for use by a group of clients who cooperate in order to reduce such costs. We work only with tree networks and we assume that a minimum cost spanning tree network has already been constructed and now we are interested in the maintenance costs. The classic problem supposes that each agent stays for the entire time in the same node of the network. This paper introduces cost-allocation problems in a fixed-tree network with a set of agents whose activity over the nodes is fuzzy. Agent’s needs to pay for each period of time may differ. Moreover, the agents do not always remain in the same node for each period. We propose the extension of a very well-known solution for these problems: Bird’s rule.

Two-stage Minimum Cost Spanning Tree Game under Fuzzy Optimistic Coalition

This paper discusses the problem of cost allocation when players have different levels of optimism based on the two-stage minimum spanning tree game, and uses Choquet integral to calculate the characteristic function of fuzzy optimistic coalition and fuzzy pessimistic coalition. It is proved that the subgame of the two-stage clear optimistic coalition minimum cost spanning tree game is also a convex game. Finally, an example is used to prove that the two-stage fuzzy pessimistic coalition minimum cost spanning tree game has a dynamical instability solution.

Axiomatization of the counting rule for cost-sharing with possibly redundant items.

For cost allocation problems with an existing set of indivisible public resources with heterogeneous individual needs and non-rivalry access, an axiomatization is provided for the allocation rule that proportionally charges agents for a given resource with respect to their counting liability indices. The main result we obtain holds in the class of cost allocation rules that are additive in cost and simply combines a new independence property together with the well-known axioms of consistency and independence of supplementary items.

Allocating a fixed cost across decision-making units with undesirable outputs: A bargaining game approach

Allocating a fixed cost among a set of peer decision-making units (DMUs) is one of the most important applications of data envelopment analysis. However, almost all existing studies have addressed the fixed cost allocation (FCA) problem within a traditional framework while ignoring the existence of undesirable outputs. Undesirable outputs are neither scarce in various production activities in real world applications nor trivial in efficiency evaluation and subsequent decision making. Motivated by this observation, this article attempts to explicitly extend the traditional FCA problem to situations in which DMUs are necessarily involved with undesirable outputs. To this end, we first investigate the efficiency evaluation of DMUs considering undesirable outputs based on the joint weak disposability assumption. Then, flexible FCA schemes are considered to revisit the efficiency evaluation process. The results show that feasible allocation schemes exist such that all DMUs can be simultaneously efficient. Furthermore, we define the comprehensive satisfaction degree and develop a satisfaction degree bargaining game approach to determine a unique FCA scheme. Finally, the proposed approach is tested with an empirical study of banking activities based on real conditions.

A bankruptcy approach to solve the fixed cost allocation problem in transport systems

A bankruptcy approach to solve the fixed cost allocation problem in transport systems

Fixed cost allocation considering the input-output scale based on DEA approach

As independent and decentralized entities often share common resources, it is necessary to allocate common costs across these subunits. When there is a lack of specific price information, data envelopment analysis (DEA) approaches have been successfully used to resolve fixed cost allocation problems. To this end, this paper develops a fixed cost allocation scheme based on decision-making unit (DMU) input–output scales that considers both the input consumption and output production scales. The allocation scheme is derived from a one-dimensional case to a general case, in which the input–output scale is calculated based on a common set of weights (CSW) determined using a DEA approach. The proposed method is demonstrated using a classical numerical example from the prior literature and an empirical application that has been applied in previous studies, from which it is found that the fixed cost allocation scheme is more acceptable to the involved DMUs.

Network Connectivity Game

We investigate the cost allocation strategy associated with the problem of providing service /communication between all pairs of network nodes. There is a cost associated with each link and the communication between any pair of nodes can be delivered via paths connecting those nodes. The example of a cost efficient solution which could provide service for all node pairs is a (non-rooted) minimum cost spanning tree. The cost of such a solution should be distributed among users who might have conflicting interests. The objective of this paper is to formulate the above cost allocation problem as a cooperative game, to be referred to as a Network Connectivity (NC) game, and develop a stable and efficient cost allocation scheme. The NC game is related to the Minimum Cost Spanning Tree games and to the Shortest Path games. The profound difference is that in those games the service is delivered from some common source node to the rest of the network, while in the NC game there is no source and the service is established through the two-way interaction among all pairs of participating nodes. We formulate Network Connectivity (NC) game and construct an efficient cost allocation algorithm which finds some points in the core of the NC game. Finally, we discuss the Egalitarian Network Cost Allocation (ENCA) rule and demonstrate that it finds an additional core point.

Allocating fixed costs using multi-coalition epsilon equilibrium

In this paper, a multi-coalition fixed cost allocation (MCFCA) is considered. The problem is solved using epsilon equilibrium (also called ε-Nash equilibrium) concept and data envelopment analysis framework. The MCFCA epsilon equilibrium involves tradeoffs between satisfying objectives of cooperative coalitions and conflicts arising from inter-coalitions objectives. First, it is shown that a simple single objective fixed cost allocation problem is an easy problem to solve and multiple solutions satisfying traditional Nash equilibrium can be trivially obtained. Second, the MCFCA problem is proposed by using different coalitions’ objective criteria highlighted in previous studies. Third, the MCFCA problem is solved using a genetic algorithm (GA) procedure. Several real-world datasets from different domains are used to test the procedure and two different types of GA fitness functions – raw and scaled – are used. The results indicate that different fitness functions perturb solutions around the epsilon equilibrium so that multiple statistically similar solutions can be obtained to aid subjective managerial solution selection among multiple similar solutions.