© Hajime Mizuyama Production & Operations Management #2 @AGU Lec.13: Supply Chain Management #1 • How to conceptualize supply chain • Bullwhip effect • Supply chain simulation 

© Hajime Mizuyama Course Schedule #2 Date Contents Dynamic scheduling and control (1): Dynamic scheduling environment, discrete-event simulation (DES), and online job shop scheduling Dynamic scheduling and control (2): Discrete-time simulation (DTS), black-box optimization, and reinforcement learning Scheduling games and mechanisms (1): Game theoretical scheduling environment, and price of anarchy (POA) Scheduling games and mechanisms (2): Mechanism design, VCG mechanism, and scheduling auction Supply chain management (1): Bullwhip effect, and supply chain simulation Supply chain management (2): Double marginalization, and game theoretical analysis Summary and review 

© Hajime Mizuyama Supply Chain • A series of business entities, such as parts manufacturer, product manufacturer, wholesaler, retailer, etc., which produces and delivers products to customers. What is Supply Chain? Process parts Assemble products Deliver products Deliver products Retail inventory Wholesale inventory Maker inventory Supplier inventory Material inventory Customers Order Order Order Order 

© Hajime Mizuyama Supply Chain • A series of business entities, such as parts manufacturer, product manufacturer, wholesaler, retailer, etc., which produces and delivers products to customers. • It is often conceptualized as a network of inventories. How to Conceptualize Supply Chain? Stage 1 Order Order Order Order Delivery Delivery Delivery Delivery Stage 2 Stage 3 Stage 4 Stage 5 𝐼! 𝐼" 𝐼# 𝐼$ 𝐼% 

© Hajime Mizuyama Echelon stock of stage 3 Echelon Stock of Stage 𝒊 • All items kept in any of the inventories at stage 𝑖 or smaller. Echelon Stocks Stage 1 Order Order Order Order Delivery Delivery Delivery Delivery Stage 2 Stage 3 Stage 4 Stage 5 Inventory Level: 𝐼! " = 𝐼# + 𝐼$ + ⋯ + 𝐼! Lead-time (to the final demand): 𝐿𝑇! " = 𝐿𝑇# + 𝐿𝑇$ + ⋯ + 𝐿𝑇! ( Holding costs: ℎ! " = ℎ! − ℎ!%# ) 𝐼! 𝐼" 𝐼# 𝐼$ 𝐼% 

© Hajime Mizuyama • A central decision maker is required to manage all the inventory stages making up a supply chain in a unified manner, for example, based on the concept of echelon stocks. • However, in most supply chains, the inventory at each stage is controlled by a different business entity. That is, the inventories need to be controlled in a decentralized manner. • This decentralized aspect of supply chains brings about various issues, such as: – Bullwhip effect – Double marginalization Decentralized Aspect of Supply Chains 

© Hajime Mizuyama Bullwhip Effect • It is a phenomenon where the more upstream an inventory stage is in a supply chain, the higher the variation of the demand for that stage. What is Bullwhip Effect? Process parts Assemble products Deliver products Deliver products Retail inventory Wholesale inventory Maker inventory Supplier inventory Material inventory Customers Order Order Order Order 

© Hajime Mizuyama • The demand forecast may be too sensitive to small fluctuation of the demand. • The fluctuation is amplified over the lead-time, when calculating the order quantity. • Order batching, or other lot sizing policy, may translate a large order quantity even larger and a small one even smaller. • Volume discount, or other sales promotion measures, may lead to ordering more items than necessary. • Behavioral and human factors, such as panic ordering after shortage, risk-averse attitude, etc. Potential Causes of Bullwhip Effect 

© Hajime Mizuyama DTS Model: Outline • Each stage 𝑖 (∈ {1, ⋯ , 𝑖"#$ }) is operated in a periodic ordering system using exponential smoothing for demand forecasting. • If shortage occurs, it is backordered, that is, the ordered items will be shipped after the next replenishment. • Ordering and transportation lead-times are separately considered. Stage 𝑖 − 1 Demand: 𝑦!,# Order: 𝑞!,# Supply Replenishment Stage 𝑖 Stage 𝑖 + 1 Ordering cycle: 1 (every period) Ordering lead-time: 𝐿𝑇$ Transportation lead-time: 𝐿𝑇% Smoothing parameter of average: 𝑆𝑃& variance: 𝑆𝑃' Safety stock coefficient: 𝐾() 𝑠!,# 𝑟!,# Forecast: . 𝑦!, 𝜎! * Available stock: 𝐼! = 𝑂𝐻! − 𝐵𝑂! + 𝑂𝑂! (= On hand – Backorder + On order ) 

© Hajime Mizuyama 1. Receive replenishment from the upstream stage 2. Receive demand from the downstream stage (or the market) and ship out corresponding items from the inventory 3. Update demand forecast through exponential smoothing 4. Update the safety stock level and then the order up to level for periodic ordering system 5. Place order to the upstream stage DTS Model: Operation Flow of Each Stage 𝑖 in Every Period 𝑡 

© Hajime Mizuyama 1. Receive replenishment from the upstream stage 𝑟%,' = 𝑠(%)*),(',-.+,*) 𝑂𝐻% = 𝑂𝐻% + 𝑟%,' 𝑂𝑂% = 𝑂𝑂% − 𝑟%,' 2. Receive demand from the downstream stage (or the market) and ship out corresponding items from the inventory 𝑦%,' = 𝑞(%,*),(',-.,) 𝑠%,' = min(𝑦%,' + 𝐵𝑂% , 𝑂𝐻% ) 𝑂𝐻% = 𝑂𝐻% − 𝑠%,' 𝐵𝑂% = 𝑦%,' + 𝐵𝑂% − 𝑠%,' DTS Model: Operation Flow of Each Stage 𝑖 in Every Period 𝑡 For the final stage, this is the market demand 𝑑', which we model as follows: 𝑑' = 𝐵𝐴𝑆𝐸 + 𝐶𝑉 > 𝑑',* + 𝜀' 𝜀' ~𝑁(0, 𝑆𝐷/) 

© Hajime Mizuyama 3. Update demand forecast through exponential smoothing D 𝑦% = D 𝑦% + 𝑆𝑃0 > (𝑦%,' − D 𝑦% ) 𝜎% / = 𝜎% / + 𝑆𝑃1 > 𝑦%,' − D 𝑦% / − 𝜎% / 4. Update the safety stock level and then the order up to level for periodic ordering system 𝑆𝑆% = 𝐾22 > 𝜎% > 𝐿𝑇3 + 𝐿𝑇. + 1 𝑅𝑃% = D 𝑦% > 𝐿𝑇3 + 𝐿𝑇. + 1 + 𝑆𝑆% DTS Model: Operation Flow of Each Stage 𝑖 in Every Period 𝑡 

© Hajime Mizuyama 5. Place order to the upstream stage 𝐼% = 𝑂𝐻% − 𝐵𝑂% + 𝑂𝑂% 𝑄% = 𝑅𝑃% − 𝐼% 𝑞%,' = max(0, 𝑄% ) Overall frow of simulation for 𝑡 = 1 to 𝑡"#$ do for 𝑖 = 1 to 𝑖"#$ do The operation flow of stage 𝑖 in period 𝑡 od od DTS Model: Operation Flow of Each Stage 𝑖 in Every Period 𝑡 

© Hajime Mizuyama Example Result 𝐿𝑇$ = 𝐿𝑇% = 2, 𝑆𝑃& = 𝑆𝑃' = 0.3, 𝐾(( = 1.65, 𝐵𝐴𝑆𝐸 = 100, 𝑆𝐷 = 5, 𝐶𝑉 = 0.5 

© Hajime Mizuyama Impact of Lead-Times 𝐿𝑇$ = 1 = 3 = 2 𝐿𝑇% = 1 𝐿𝑇% = 2 𝐿𝑇% = 3 

© Hajime Mizuyama Impact of Smoothing Parameters 𝑆𝑃& = 0.1 = 0.5 = 0.3 𝑆𝑃' = 0.1 𝑆𝑃' = 0.3 𝑆𝑃' = 0.5 

© Hajime Mizuyama • Information sharing and lead-time reduction • Education and training • Business structural measures – Retailer-supplier partnerships (RSP) • Continuous replenishment program (CRP) • Vender managed inventory (VMI) – Third party logistics (3PL) – Vertical integration How to Mitigate Bullwhip Effect 

© Hajime Mizuyama • The influence of human factors and behavioral aspects on the bullwhip effect is difficult to analyze and understand with computer simulation alone. • Serious gaming and participatory simulations are often utilized for studying such effects as well as training and educating people how to address the bullwhip effect. Beer Game (or Beer Distribution Game) John D. Sterman: Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making Experiment, Management Science, Vol.35, No.3, pp.321-339 (1989). Supply Chain Serious Game 

© Hajime Mizuyama Supplemental material providing a sample Python code for the simulation model used in this lecture is available from the following link. Push “Open in Colab” button, then you can test it in Google Colaboratory environment. https://github.com/j54854/myColab/blob/main/pom2_13.ipynb Sample Code for Supply Chain Simulation Model