Quantifying the Bullwhip Effect of Multi-echelon System with Stochastic Dependent Lead Time

Abstract

Considering a multi-echelon system, the bullwhip effect is recognized as a significant factor with regards to the inventory management. This paper focuses on the effect of stochastic dependent lead time on the bullwhip effect. Simulation based approach is used to quantify the bullwhip effect with different demand and lead time distributions. The experiment results show that the dependent lead time has much effect on the 2 nd echelon (from the downstream to the upstream) and bullwhip effect decrease significantly if the variance of this echelon decreases.

Mitigation of Bullwhip Effect in Closed-Loop Supply Chain Based on Fuzzy Robust Control Approach

“…However, uncertainties and lead times are two important factors leading to BE. erefore, many scholars studied the BE caused by uncertainties or lead times; for example, by simulationbased approach, Do et al [10] quantified the BE with different demands and stochastic lead times; for a two-echelon serial supply chain, Agrawal et al [11] compared the effects of lead time reduction and information sharing on the mitigation of the BE; using the statistical method, Kim et al [12] considered the stochastic lead time and provided expressions for quantifying the BE both with information sharing and without information sharing; Modak and Kelle [13] used a hybrid all-unit quantity discount along a franchise fee contract to mitigate the BE in the dual-channel supply chain with the delivery time and stochastic demand; Li and Liu [14] explored the mitigation of the BE in the supply chain with uncertainties and the vendor order placement lead time.…”

“…Fuzzy membership functions 10. Complexityz(k) � c h1 + Δc h1 x 1 (k) + c h2 + Δc h2 x 2 (k) + c h3 + Δc h3 x 4 (k) + c r + Δc r u 3 (k) + u 3 k − τ 3 +(η + Δη)x 4 (k) + c m + Δc m u 3 (k) + u 3 k − τ 3 + c t + Δc t u 4 (k) + u 4 k − τ c mt + Δc mt (η + Δη)x 4 (k) + c q + Δc q (μ + Δμ)x 3 (k) + c d + Δc d (λ + Δλ)x 4 (k) + c s + Δc s u 2 (k) + u 2 k − τ 2(34)…”