University:
Massachusetts Institute of Technology
Course:
15.992 | S-Lab: Laboratory for Sustainable Business
Academic year:

2023
Views:

134

Pages:

38
Author:

botohanl8j

Variability The Bull Whip Effect A Vicious Cycle Build-to-Order, Lean, JIT, … Managing Variability: A different view of inventory 1 Example Procter & Gamble: Pampers Smooth consumer demand Fluctuating sales at retail stores Highly variable demand on distributors Wild swings in demand on manufacturing Greatest swings in demand on suppliers 2 Illustration Consumer Sales at Retailer Consumer demand 1000 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 13 15 11 9 5 7 3 0 1 100 Retailer's Orders to Distributor 1000 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 9 11 7 5 0 3 100 1 Retailer Order 900 3 Illustration Retailer's Orders to Distributor 1000 Retailer Order 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 9 11 7 5 3 0 1 100 Distributor's Orders to P&G 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 11 9 7 5 0 3 100 1 Distributor Order 1000 4 Illustration Distributor’s Orders to P&G Distributor Order 1000 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 9 11 7 5 3 0 1 100 P&G's Orders with 3M 1000 900 800 600 500 400 300 200 40 37 34 31 28 25 22 19 16 13 7 4 0 10 100 1 P&G Order 700 5 Illustration Consumer Sales at Retailer Consumer demand 1000 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 13 15 11 9 5 7 3 0 1 100 P&G's Orders with 3M 1000 900 800 600 500 400 300 200 40 37 34 31 28 25 22 19 16 10 7 4 0 13 100 1 P&G Order 700 6 What Are the Effects? What problems, costs, challenges does this create for the players in the supply chain? What problems does this create for the product in the market place? 7 Forecasting More variability Poorer forecasts Less reliable supply 8 Causes of Bullwhip Today Product Proliferation/Mass Customization More varieties of products Build-to-Order Prohibits pooling orders to smooth requirements Lean Prevents pooling releases to smooth demand on the supply chain 9 Why Lean (Just-In-Time)? Reduces inventory Capital requirements Etc Reduces handling Direct-to-Line Improves Quality See problems quickly Increases launch speed 10 Why Not Lean? Capacity Changes in requirements create upstream inventory Changes in requirements raise transport costs Reliability Distant suppliers subject to disruption 11 Release Variability Daily Receipt 1400 1200 1000 800 600 400 200 0 01-Apr-02 06-Apr-02 11-Apr-02 16-Apr-02 21-Apr-02 26-Apr-02 Managing Variability Capacity Buffer Inventory Buffer Time Buffer 13 Required rate of conveyances Freight Cost Capacity Utilized Capacity Time 14 Required rate of conveyances Expediting Expedited Service Lower Capacity Utilized Capacity Time 15 Ideal Supply Chain Same requirements every day No excess capacity No inventory No service failures Minimum Cost 16 Buffer Inventory with Constant Supply Volume Variation in Demand Variation in Buffer Time 17 A Financial Model From Revenues Cash Expenses Cash Acct 18 A Financial Model From Revenues Cash Expenses Invest Sell Assets Cash Acct 19 Controls Invest enough to bring it to here When Cash balance reaches here 20 Controls Sell assets to bring it to here When Cash balance falls to here 21 Controls T t b 22 Trade-offs Opportunity cost of Cash Balance Transaction costs of investing and selling assets Set the controls, T, t and b to balance these costs 23 Inventory Analogy Cash Expenses From Revenue Sell Assets Invest Excess Daily Production reqs. Constant supplies Expedited order Curtailed order 24 Trade-offs Cost of holding Inventory Supply chain costs of expediting and curtailing orders Set the controls, T, t and b to balance these costs Opportunity cost of Cash Balance Transaction costs of investing and selling assets 25 The Traditional Model 1 1-(p1+ q1) p1 p2 2 … 1 0 q1 q2 pk k … qk … M 1 A Markov Model 26 Challenges Data intensive: pi’s and qi’s Computationally intensive Alternative Brownian motion Inventory behaves like a random walk Model of a particle in space Two parameters: mean and variance Advanced calculus methods make it “easy” to work with 27 Release Variability Daily Receipt 1400 68% of time usage is between 0 and 800 1200 1000 800 σ = 412 600 400 µ = 367 200 0 01-Apr-02 06-Apr-02 11-Apr-02 16-Apr-02 21-Apr-02 26-Apr-02 The EOQ as a Special Case Average usage rate µ Variance in usage σ2 Nominal release rate λ < µ Since we order less than we consume, inventory drifts downward How much should we “expedite” when it reaches 0? 29 Trade offs Expediting disrupts the supply chain Fixed cost F for each time we expedite Variable cost f for each item in the order holding cost h for inventory Larger orders mean less frequent but larger disruptions and more inventory 30 EOQ as Special Case Order Q Time between orders is Q/(µ – λ) Order frequency is (µ – λ)/Q Average Inventory is Q/2 + σ2/2(µ – λ) Average Cost is Expediting Cost: Inventory Cost: (F+fQ)(µ – λ)/Q h(Q/2 + σ2/2(µ – λ)) 31 The Total Cost Formula hQ/2 + F(µ – λ)/Q + hσ2/2(µ – λ) + f(µ – λ) EOQ: Transaction EOQ: Inventory Constant that doesn’t depend on Q The best Q balances inventory and ordering costs: hQ/2 = F(µ – λ)/Q Q2 = 2F(µ – λ)/h Q = √2F(µ – λ)/h 32 Fixed Expediting Quantity Find the best nominal release rate λ to get the right frequency of expediting 33 The Total Cost Formula hQ/2 + hσ2/2r + fr + Fr/Q EOQ: Transaction EOQ: Inventory Constant that doesn’t depend on r The best drift rate r = µ − λ balances inventory and ordering costs: hσ2/2r = fr + Fr/Q r2 = hσ2Q/2(F+fQ) r = √hσ2Q/2(F+fQ) 34 Two-sided Version If inventory grows too large, curtail shipments What’s too large? How much should we curtail? If expediting is expensive create a positive drift order more than you need curtail shipments when inventory is too high 35 Differences Constant Stream of Releases punctuated by Expediting and Curtailing If supplier can see inventory, can anticipate expedited and curtailed orders Have to set a lower bound > 0 to protect against disruptions – safety stock 36 246 239 232 225 218 211 204 197 190 183 176 169 162 155 148 141 134 127 120 113 106 99 92 85 78 71 64 57 50 43 36 29 22 15 8 1 Example: Shipments 300 250 200 150 100 50 0 37 Example: Inventory 1000 900 800 700 600 500 400 300 200 100 0 38