Stability and Monotonicity Requirements

Abstract

This chapter examines how gain and the anticipation level of commitment-based policies affect the stability and monotonicity of homogeneous supply chains; i.e., chains where suppliers use the same policy: F _j ≡ F,H _j ≡ H. Stability and monotonicity are desirable properties, but separate issues. Instability can lead to the bullwhip effect, and lack of monotonicity to order cancellations. Therefore, they are studied separately. Section 4.1 defines the two forms of stability considered in these notes, “stability in the small” and “stability in the large”, and their connection with the bullwhip effect. Sec. 4.2 develops a stability test, which is illustrated with several examples in Sec. 4.3. A monotonicity test for order-based policies is then presented in Sec. 4.4. Together, Sections 4.1-4 show that historical policies (without commitments) and positive gains are problematic, both, from the standpoint of stability and monotonicity. Since as a rule, suppliers prefer policies with positive gain, this explains the prevalence of the bullwhip effect. The last section of the chapter (Sec. 4.5) extends the results to queuing systems.