Transfer pricing of a service department facing random demand

• Published in: International journal of production economics 1996-12, Vol.46 (1), p.351-358
• Main Author: Johansen, Søren Glud
• Format: Article
• Language: English
• Subjects: Algorithms; Customer services; Demand; Economic models; Economic theory; Production planning; Random demand; Service department; Studies; Transfer pricing
• ISSN: 0925-5273; 1873-7579
• DOI: 10.1016/0925-5273(95)00050-X

Most service departments have occasionally idle capacity and occasionally saturated capacity. The reason for these phenomena is that a service department faces a random demand for the service it renders. How shall its transfer pricing be influenced by this randomness? We discuss this question by analyzing an abstract model of a service department. The model depicts a service department as an M/D/1 queueing system with an upper limit UL on the time in the system. Potential input to the system is operating departments' requests for service which arise according to a Poisson process. All requests for service take the same amount of time. The net benefit (defined as the benefit minus any direct costs) of satisfying a request is uniformly distributed and is known at the time the request materializes. If the net benefit is larger than the net transfer price (defined as the transfer price minus any direct costs) and the delivery time does not exceed UL then the request is submitted to the service department. We develop two algorithms to find the optimal transfer pricing and the best simple transfer price, respectively. Numerical computations indicate that the expected net benefits earned per unit time by employing the solutions found by the two algorithms differ by at most 3%. We also investigate the relationship between the best simple net transfer price and the cost of service capacity.