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

2023
Views:

100

Pages:

17
Author:

infestadayx

Multi-echelon Inventory Systems • Why? • Issues and decisions? • Models Why have a multi-echelon distribution system? • • • • Better service from regional locations Transportation economies Mixing functions Risk pooling over the manufacturing or procurement lead time • Differentiated stocking and service policies Design and Planning Issues • Number of echelons • Number and location of distribution centers • Stock location: what items to stock at each DC • Replenishment policies – inventory & transportation; who serves whom • Information systems Risk Pooling: Centralized Control • Assume periodic review, base-stock policies • Centralized control, with global information • Cross-dock operation – no inventory held at a “central distribution center” W1 Factory W2 W3 Decentralized system: r = 1, L Safety stock at each warehouse proportional to σ i L + 1 Total safety stock ≈ z 3 ∑σ i =1 Cycle stock? Pipeline stock? i L +1 W1 Factory W2 W3 Idealized system: r=1, L Total safety stock ≈ z 3 2 σ ∑ i L +1 i =1 Safety stock at each warehouse ≈ z σ i 3 ∑σ i =1 3 ∑σ i i =1 2 i L +1 Factory L1 L2 W1 W2 W3 Cross-dock system: r = 1, L = L1 + L2 Each period: • System replenishment order = d1 + d2 + d3 • Allocate stock receipts to balance inventories • Transship allocations Cross-dock System Safety stock at each warehouse: 2 ≈ z ⎛ ⎞ ⎜ σ ⎟ 3 j ⎜ 3 ⎟ L 1 ∑ σ i2 + ( L 2 + 1 ) σ ⎜ ⎟ i =1 σ ⎜∑ i⎟ ⎝ i =1 ⎠ 2 j Total safety stock: 2 ≈ z 3 ∑ j=1 ⎛ ⎞ ⎜ σ ⎟ 3 j ⎜ 3 ⎟ L 1 ∑ σ i2 + ( L 2 + 1 ) σ ⎜ ⎟ i =1 σ ∑ i ⎜ ⎟ ⎝ i =1 ⎠ 2 j Total safety stock Decentralized Idealized Cross-dock ≈ σ n L +1 ≈ σ n L +1 L1 ≈σn + L2 + 1 n n “identical” warehouses, each with standard deviation of demand = σ L1=0 L1=2 L1=5 L1=8 L1=10 Ideal n=1 166 166 166 166 166 166 n=2 332 316 292 265 245 235 n=3 497 466 415 357 312 287 n=5 829 766 661 536 433 371 n=10 1658 1517 1275 975 707 524 Safety stock L = 10, σ = 50, n warehouses with same σ Risk Pooling: Decentralized Control • Assume periodic review, base-stock policies • Decentralized control at warehouses, ordering on a central distribution center • Central distribution center holds inventory, and operates without global information • Central distribution center operates with high service level Factory W1 W2 W3 Independent warehouses r = 1 week L = 7 (production) + 1 (transportation) = 8 weeks E[D] = 500 / week σ[D] = 50 / week No CDC: How much safety stock? At each W: ≈ σ r + L = ( 50 ) 1 + 8 = 150 For n independent warehouses: ≈ nσ r + L = 150n = 450 for n = 3 Factory CDC W1 W2 W3 W: r = 1 week L = 1 week (transportation) CDC: r = 1 week L = 7 weeks (production) W: E[D] = 500 / week σ[D] = 50 / week CDC: How much safety stock? At each W: ≈ σ r + L = ( 50 ) 1 + 1 = 71 At CDC: ≈ σ n r + L = ( 50 ) 3 1 + 7 = 245 For system: ≈ nσ r + L + σ n r + L = (3)(50) 2 + ( 50 ) 3 1 + 7 = 212 + 245 = 457 # of Ws One-echelon Two-echelon n=1 150 212 n=2 300 342 n=3 450 457 n=4 600 566 n=5 750 671 Findings for Two-echelon Systems • For high demand low cost items – CDC should not buffer: e. g. 50% fill rate target at CDC; 99% fill rate target at Ws • For low demand high cost items – CDC should carry some safety stock, but usually less than normally assumed. Actual amount is very dependent on numbers. • For some low demand items – stock only at CDC and use premium transport, or provide slower service