The analysis of bullwhip effect in a HMMS-type supply chain

The aim of the paper is to investigate the well-known bullwhip effect of supply chains. Control theoretic analysis of bullwhip effect is extensively analyzed in the literature with the Laplace transform. This paper tries to examine the effect for an extended Holt–Modigliani–Muth–Simon model. A two-stage supply chain (supplier–manufacturer) is studied with quadratic costs functional. It is assumed that both firms minimize the relevant costs. The order of the manufacturer is delayed with a known constant. Two cases are examined: supplier and manufacturer minimize the relevant costs decentralized, and a centralized decision rule. The question is answered, how to decrease the bullwhip effect.