Analysis of a two-stage telecommunication supply chain with technology dependent demand

Abstract

We analyze a two-stage telecommunication supply chain consisting of one operator and one vendor under a multiple period setting. The operator faces a stochastic market demand which depends on technology investment level. The decision variables for the operator are the initial technology investment level and the capacity of the network for each period. The capacity that the operator installs in one period also remains available in subsequent periods. The operator can increase or decrease the available capacity at each period. For this model, an algorithm to find the centralized optimal solution is proposed. A profit sharing contract where firms share both the revenue and operating costs generated throughout the periods along with initial technology investment is suggested. Also a coordinating quantity discount contract where the discount on the price depends on the total installed capacity is designed. The case where the vendor decides on the technology investment level and the operator decides on the capacity of the network is also analyzed and it is shown that this game has a unique Nash equilibrium.

Introduction

Telecommunications is a heterogeneous industry where the business logic has changed significantly during the last decade. Liberalisation on a global scale and mobile services changed the landscape in the sector. Factors like outsourcing of manufacturing and research and development (R&D) functions to suppliers, fierce technological competition and shorter life-cycle technologies contribute to an increased need for improved coordination in the telecom supply chain (Laffont and Tirole, 2000, Agrell et al., 2004).

Telecom supply chains contain actors of different nature: some are vendors that are producers of technology and physical products (like handsets, base stations, switches etc.) while the operators concentrate on installing a capacity to provide service to the customers.

The telecom sector is a fast developing sector through the introduction of new technologies and services. New services such as GPRS in GSM or ‘video on demand’ for digital subscriber lines are introduced to increase the customer demand. The increase in demand usually requires an increase in capacity at the operator’s end. From the capacity point of view there are two types of operator. The traditional operator who usually operates a circuit switch type network with strictly determined capacity (i.e. 10.000 lines means the operator cannot give a service to the 10.001st subscriber). The fixed line network or the GSM network are two examples. Other operators (such as WLAN operators) have capacities that are calculated under certain assumptions and using rejection probabilities. The notion of ‘capacity’ used in this paper corresponds to the total number of lines for the former type of operator for which we assume that the average revenue per line is constant. For the latter type of operator we presume that the operator calculates her capacity according to busy hour traffic and an increase in total usage of subscribers affects both the busy hour usage and the total daily usage (which in turn effects the revenue) with the same proportion. The model presented in this paper is relevant to both types of operator but probably more so to the former type where capacity definition is more straightforward.¹ Our analysis does not focus on the definition of capacity but rather on the effect of technology investment on a given capacity along with operations.

This paper analyzes the interactions between a telecom vendor and an operator where the vendor supplies the necessary equipment so that the operator installs a capacity to serve uncertain end customer demand. We assume that the demand is effort dependent and random. We envision a technology investment that serves as an effort to influence the demand. Although there may be examples of unsuccessful technology investments in reality, we concentrate on those cases where technology investment strictly increases the demand. As an example, the operator invests in the R&D activities of a new technology (like GPRS) with the hope that, when introduced, the new technology is going to increase total usage and the revenue.

Fig. 1 summarizes the situation as modelled in this paper. The operator installs a network to face the stochastic demand of subscribers. The usage of the network resources fills up the capacity of the network and the revenue generated per unit capacity used is assumed to be constant. The operator is charged an operation cost per unit capacity she has installed. There is no back logging option as is sometimes customary in supply chain models. The unsatisfied demand is lost and incurs a penalty for the operator due to lost profit and lower customer satisfaction. There is no possibility to salvage unused capacity. The equipment used to build up capacity is manufactured by the vendor and transferred to the operator. The capacity decision is usually given long before the beginning of each period. The telecom industry widely utilizes periodic capacity planning. Typical planning period can range from a quarter of a year up to one year. The lead time for replenishment of equipment is usually not more than a month and is neglected in our models. There is an opportunity to make a technology investment. By investing in new technologies and services the operator can increase the demand. This variable somewhat resembles the sales effort in marketing and supply chain models.

There are two sets of decisions. The technology investment level is decided in the first period only. The network capacity can change in every period for a finite planning horizon. This is in tune with the current industry standard where the effects of a newly introduced technology is observed over several periods. We first assume that both of the decisions are made by the operator which is in tune with the common telecom industry structure. However, we also analyze a model where the technology investment level is decided by the vendor and capacity decisions are given by the operator in Section 3. The model is analyzed both from a centralized and a decentralized point of view. In the centralized model, a single agent controls the entire supply chain to maximize overall supply chain profit whereas in the decentralized model, the players make choices with the objective of maximizing their own profits.

An algorithm to find the first-best scenario (centralized solution) is proposed. Revenue sharing and quantity discount contracts are proposed to coordinate the supply chain. The mathematical model of the proposed contracts are given in detail for non-stationary unit costs. In order to evaluate the performance of the contract, a representative numerical example is developed and analyzed. A sensitivity analysis is conducted on the first best solution to understand the behavior of the system with respect to different parameters.

We also consider a model where the vendor makes the technology investment decision. We show that a unique Nash equilibrium exists under a revenue sharing contract.

The contributions of this paper can be summarized as follows: (i) a service sector firm rather than a traditional replaceable product retailer is considered in a multi-period newsvendor setting, (ii) an algorithm to find the multi-period centralized solution is proposed, and (iii) multi-period revenue sharing and quantity discount contracts are suggested as coordinating contracts for the telecom supply chain.

Most of the operations literature on contract design models the problem such that contract parameters are exogenously determined rather than treating these parameters as part of the model (Cachon, 2003). We follow the same suit in this paper and assume that contract parameters are not endogenous to our model.

Cachon (2003) gives an in-depth review of supply chain contracts. Models with effort dependent demand are reviewed among many other forms of settings and contracts. Effort dependent demand has been considered mostly in the sense of sales effort in marketing and operations literature. Jeuland and Shugan (1983) explore the problems inherent in channel coordination. They try to find answers to the benefits of channel coordination, the causes of lack of coordination and ways to improve channel efficiency until it is coordinated. They work on a model with sales effort dependent demand and propose a quantity discount contract scheme to coordinate the channel. In Chu and Desai (1995), the supplier can also exert costly effort to increase demand (customer satisfaction assistance), e.g., brand building advertising, but the impact of effort occurs only with a lag: they have a two period model and period one effort by the supplier increases only the second period demand. They also enrich the retailer’s effort model to include two types of effort, effort to increase short term (i.e., current period) sales and long term effort to increase long term customer satisfaction and demand (i.e., second period sales). They allow the supplier to compensate the retailer by paying a portion of his effort cost and/or by paying the retailer based on the outcome of his effort. They show that both the manufacturer and the retailer are better-off using both techniques.

Taylor (2002) examines a newsvendor model with effort dependent demand. He demonstrates that although the sales rebate contract does not coordinate on its own, it can coordinate the channel if it is combined with a buy-back contract. One of our contracts is analogous to this one but we develop it in a multi-period setting. Cachon and Lariviere (2005) study revenue sharing contracts explicitly to identify their strengths and limitations. In our multiple-period model, we propose contract parameters that need to be adjusted for each period.

Netessine and Rudi (2004) analyze the interaction between a wholesaler and a single retailer for drop-shipping supply chains in a multi-period environment. In drop-shipping model the wholesaler takes the inventory risks while the retailer organizes marketing activities where demand she is facing is effort dependent and stochastic. They examine three distinct drop-shipping models: with wholesaler leader, with retailer leader and with a wholesaler and a retailer having equal power. They compare results with the coordinated and traditional cases. They find that both channel members prefer the drop-shipping agreement over the traditional agreement for a wide range of problem parameters. They work out a model that is closely related to ours. In fact, if we had a single-period model it would be exactly as in their case without the lost sales penalty. We differ from this work by our multiple period setting and the type of contracts we propose.

Agrell et al. (2004) consider a three stage telecom supply chain in a two-period investment-production game. They also model the effects of information asymmetry between the agents which we do not consider. Their assumptions about the investment and its effects are different from ours as well.

Our model differs from many effort dependent demand models mainly due to multiple periods where capacity (change) decisions are more meaningful. In multi-period models with inventory decisions the retailer applies a base stock policy to satisfy the periodic random demand (Porteus, 2002). But in our model the operator sells a service rather than a replaceable product and each period has to adjust the contract parameters so that coordination can be achieved.

The rest of the paper is organized as follows: In Section 2 we develop the model, give basic assumptions, provide a centralized solution and discuss two types of contracts for the decentralized system. We illustrate the centralized solution using a numerical example. as well as optimal profits are analyzed and two coordinating contracts are proposed. In Section 3, we modify the model by letting the vendor make the initial investment decision. We show that a unique Nash equilibrium exists under a revenue sharing contract. Finally, Section 4 states concluding remarks and possible directions for future research. Longer proofs are given separately in Appendix A.