Fair transfer price and inventory holding policies in two-enterprise supply chains

Abstract

A key issue in supply chain optimisation involving multiple enterprises is the determination of policies that optimise the performance of the supply chain as a whole while ensuring adequate rewards for each participant.

In this paper, we present a mathematical programming formulation for fair, optimised profit distribution between echelons in a general multi-enterprise supply chain. The proposed formulation is based on an approach applying the Nash bargaining solution for finding optimal multi-partner profit levels subject to given minimum echelon profit requirements.

The overall problem is first formulated as a mixed integer non-linear programming (MINLP) model. A spatial and binary variable branch-and-bound algorithm is then applied to the above problem based on exact and approximate linearisations of the bilinear terms involved in the model, while at each node of the search tree, a mixed integer linear programming (MILP) problem is solved. The solution comprises inter-firm transfer prices, production and inventory levels, flows of products between echelons, and sales profiles.

The applicability of the proposed approach is demonstrated by a number of illustrative examples based on industrial processes.

Introduction

During the last decade, there has been a strong emphasis in industry towards supply chain improvements. The implementation of Just-In-Time systems and Business Process Reengineering have achieved huge savings for supply chains. Companies have managed to reduce costs associated with production, inventory, transportation and administration. This process has primarily focused on profit generation on a single-company level. There has been a general lack of focus on the multi-enterprise supply chain optimisation which constitutes a complex, hierarchical problem.

Any model in which manufacturing and distribution are coordinated should be responsive in order to face changing customer demand and be adaptive in terms of customer preferences. The various stakeholders in a multi-enterprise supply chain demand predictability and stable creation of wealth. Responsiveness, reliability, adaptivity and predictable profit generation are ultimate objectives for building the supply chain model.

A number of different approaches for supply chain modelling and optimisation have been investigated since the late 1980s. One of the first thorough attempts was given by Cohen and Lee (1989) who propose a model to determine resource deployment within a global supply chain network, and solve different scenarios utilising the GAMS (Brooke et al., 1988) optimisation system. They also discuss several strategies or “policy options” for plant utilisation, supply and distribution. The overall mixed integer linear programming (MILP) model is quite extensive containing terms such as taxes paid in different countries and offset requirements (e.g. minimum gain entry level of manufacturing in a country).

Arntzen et al. (1995) conclude, after developing a very large MILP model, called the Global Supply Chain Model: “We also wonder how anyone can rely on heuristic solution methods in this area”. The program minimises cost or distribution times, meeting estimated demand, local restrictions, offset trade and maximum capacity. The model was implemented in restructuring the Digital Equipment Corporation and it is claimed to have saved the company over $1.2 billion as of 1995 (D'Amours et al., 1999).

D'Amours et al. (1999) are among the few authors discussing multi-enterprise collaboration from a modelling perspective. They propose a network approach in which firms are selected and scheduled with the objective of fulfilling demand of one product on time at minimum cost for a supply chain including manufacture, storage, distribution and customer broker. The manufacture, storage and customer are nodes in the network while the transportation costs are associated with the flows between nodes. Their results show that a collaborative approach is more profitable than other alternatives, but the impact of information shared in a networked organisation is yet to be fully understood. Based on their results, they also advise that inter-organisational systems should be implemented to provide for electronic data interchange.

In the late 1990s, many authors attest to new supply chain paradigms evolving. Bartezzaghi (1999) argues for more strategically flexible production models which can handle high degrees of complexity and incorporate novel product development with reduced delivery times as the primary objective. He suggests a more integrated and collaborative business approach with a delegation of core processes, thus combining local and global information to obtain multi-focused, flexible processes.

Lehtinen (1999) quantifies partnership collaboration. In her study, a doubled cooperation rate within the manufacturing industry has been proved in the last 10 years and 20% of the subcontractors now handle 80% of the orders. She maintains that the delivery performance is the best order-winning criterion rather than, for example, product quality.

Spekman et al. (1998) regard partnership activities as involving risk-sharing, collaborative design development, and achieving highly efficient processes. They point to the success stories of General Motor's Saturn project and the Toyota philosophy in distinguishing between the superficial cooperation of many other car manufacturers and GM and Toyota's more closely integrated collaborative production processes. They argue that most companies today are well motivated to maintain long-term relationships, continuous information sharing and fair play in order to obtain supply chain integration, joint planning and technology sharing which is perceived to result in a more competitive supply chain performance.

Dowlatshahi (1999) emphasises that a fully integrated partnership supply chain network tends to focus on strategic planning than on the price-based issues in the interface of buyers and suppliers in the network and the price of goods is determined on contracts instead of free market price. Flexibility, service, and total cost of the overall network are measured as major performance objectives. Partnerships convey the benefits of vertical integration without the inherent risks of a single enterprise ownership. There has been little research performed to study the actual performance implications of partnerships (Heide and Stump, 1995). An ability to measure and predict the performance of the supply chain is believed to strengthen a stable relationship between partners.

Lummus and Vokurka (1999) notice that many companies already have implemented systems for electronic data interchange or information exchange via the Internet. A strong move towards customised products and flexible customer service will further boost this development.

Transfer pricing is a term that has previously been utilised to denote an intra-company selling cost, primarily used as a performance measure of specific subdivisions. We find it useful to extend the terminology as to include the whole supply chain and thereby cover the inter-company price mechanisms. Howe and Cox (1994) claim that the transfer price applies to the local organisational level thus enforcing market pressure into the organisation. Their results emphasise that local decision-making within the supply chain can be quite harmful if it is not linked to global evaluation of the performance.

Pfeiffer (1999) describes transfer pricing in a supply chain consisting of procurement, manufacturing and selling units of one single company. His theoretical model handles one commodity at each node and does not include any capacity constraints. He proposes a transfer price system governed by the headquarters, which fixes a specific transfer price level. Each node optimises its own decisions independently to maximise a given profit function, according to the price level fixed by the headquarters. After the decentralised optimisation, headquarters evaluates and collects the overall results obtained and chooses a new transfer price which leads to a higher overall profitability. This algorithm stops when the overall profit function is maximised. In common with the model proposed in this paper, Pfeiffer uses the transfer price as a value measure of the goods stored. As would be expected, his conclusion is that the stock level and the intensity (output/time) in the process system should be chosen to be minimal, thus minimising inventory and production costs subject to production requirements.

As mentioned above, supply chains evolve to have more open processes and information sharing. Moad (1997) argues that the interfaces between companies are becoming more like permeable membranes in which information flows rather than fixed, discrete links between suppliers and customers. The direction is towards a single, extended enterprise that includes suppliers and customers, in which electronic commerce plays a very important role. Moad states that a recent figure for the cost of planning of production levels, sourcing of raw materials, inventory handling and delivering products to market is 14% in a typical appliance manufacturer industry.

Lindsey II et al. (1996) show that as the degree of private information decreases, i.e. more information is available to both parties, the amount of mutually acceptable price levels decreases also. They point out that in the bargaining process the parties show their beliefs and knowledge through their bidding behaviour. The surplus payoff that one party can attain depends on his level of private information.

In general, there has been a high concentration of articles on supply chain partnerships, albeit not much about how such systems may be optimised. As this paper shows, methods can be applied to optimise the whole supply chain but a naive optimisation of the overall supply chain normally leads to unsatisfactory profit distributions amongst the participating enterprises. Game theory provides us with the concept of fair profit sharing among partners. By utilising the mechanism of variable transfer prices and the Nash bargaining solution, we can achieve a Pareto optimal (within a pre-specified margin) solution for all participating partners in a general supply chain.

For multi-enterprise problem formulations, it is generally difficult to apply optimisation when modelling more than one objective function at the same time, since it is not clear how utility (e.g. money) should be distributed among the participating parties. Some popular approaches in the literature have been Pareto approaches, game theoretical approaches, neural networks, and the analytical hierarchy process. In this paper, for comparison we first simply maximise the total profit of the whole supply chain (i.e. treating the supply chain as a single level profit centre). When the overall system is optimised in this fashion there is no mechanism to allow profits to be apportioned fairly to all participants. Indeed, solutions to this class of problems usually exhibit very uneven profit distributions and are therefore impractical. They do however give an indication of the best possible total profit attainable in the supply chain. Our goal is then to extend this class of model to achieve solutions of similar quality overall but with equitable profit distributions. In order to achieve a more fair split of the profits, we then apply the Nash bargaining solution (Nash, 1950), which maximises the product of the deviations of the achievable profit levels of each profit centre by the status quo profit levels.

In this paper, we make use of the term “transfer pricing” even though more than one company is concerned (contrary to Vaysman, 1998) to underline the nature of the supply chain as one profit generating entity. Vaysman recognises the way the managerial decisions are influenced by transfer pricing, but the production planning implications of this influence are not modelled. One could argue about the way the proposed model uses administered transfer pricing; top management in both firms agree on utilising the Nash bargaining model as a set of rules to improve from the currently best solution obtainable. After that there is no room for negotiation. Thus, the combined effect of coordinated planning results in improved profits.

Vaysman states that one reason for applying transfer pricing in the first place is that “some divisional information is known only to divisional managers”. Therefore, it is argued that a full-information approach cannot incorporate transfer pricing. Our proposal is that whereas this argument certainly has its merits, this paper does not necessarily require that information be shared between the parties but rather that the production information be handed to an external (e.g. academic) agent.

Baldenius et al. (1999) discuss the managerial aspects of a transfer pricing system and compare cost-based transfer pricing with negotiated transfer pricing. An important issue here is that if each division bears the full cost of its investment the future trend will be to adjust further investments downwards since only a share of the added surplus from the investment will be received by the division. They specify a model in which management is centralised and where “head office” specifies generic rules of rights and obligations of the divisions. The divisions have symmetric but imperfect knowledge of the state variables. With respect to the view of the enterprise (in this paper the supply chain) they have a similar reasoning to what the relationships between the divisions are. From the point of view of this paper, the firms have information about their production processes but they do not know what production patterns will be utilised in the future horizon. Contrary to Baldenius et al., the model proposed here does not consider future investments but is an operational planning model on the medium scale horizon.

We present a mixed-integer programming approach to determine the most appropriate transfer price level for goods transferred from production to distribution centres as well as production levels, timings and quantities of goods delivered. The overall problem can be formulated as a mixed integer non-linear programming (MINLP) model. For its solution, a special global optimisation procedure is applied. The advantage of deterministic, constrained global optimisation schemes is that they can be guaranteed to reach the global optimum within a finite amount of iterations. There are several approaches of deterministic global optimisation including branch-and-bound, cutting plane and decomposition methods. Here, we consider a spatial and binary variable branch-and-bound algorithm which is applied based on exact and approximate linearisations of the bilinear terms involved in the model, while at each node of the search tree an MILP problem is solved.

The paper is organised as follows. In Section 2, we describe the problem and our objectives. In Section 3, we explain why we use the Nash bargaining solution and how we model it, including McCormick approximations (McCormick, 1976) and our spatial branch-and-bound algorithm. Then, in Section 4, we describe and evaluate our computational experiments. Some concluding remarks are drawn in Section 5. Finally, in Appendix A, we describe the model including constraints and linearisations.