Modelling Bullwhip Effect in a Closed Loop Supply Chain with ARMA Demand

Abstract

The growing importance of environmental concerns and focus on recycling has encouraged our research efforts to study the bullwhip effect on Closed Loop Supply Chain (CLSC). This article attempts to measure bullwhip effect in a six echelon CLSC with recycling as a reprocessing option for materials like paper and plastics (perhaps the first time in CLSC literature). The proposed model considers the effect of two critical parameters of CLSC: quality of recyclable raw material (in terms of its yield) and degree of segregation at source. It is assumed that the echelons in CLSC employ an Order-Up-To (OUT) inventory policy with Minimum Mean Square Error (MMSE) forecasting scheme, and that the demand forecast is performed via a first order Auto Regressive Moving Average model (ARMA [1, 1]). The model developed is employed to investigate the impact of Auto Regressive (AR) and Moving Average (MA) parameter, yield of recycled material, degree of segregation at source and the lead-time on the bullwhip effect. The model enables the CLSC managers to anticipate the downstream demand. In order to avoid order-process instability, a careful selection of Auto Regressive (AR) and the MA parameters is advised. Sensitivity analysis on replenishment lead-times provides managerial insights for effective design of recycling—distribution system, with constant accumulated lead-time. Further, the analysis reveals that increased degree of segregation at the source reduces the bullwhip effect.