Transportation Management Fundamental Concepts

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Operational
Tactical
Strategic
Decisions made at different times
Strategic – longer scope and less data available (yr+) Tactical – shorter scope w/ planning data (week to yr) Operational – very short scope real data (daily)
ijkl L
∑ ∑ ∑X
l=1
≤ Vk Z k ; for all K
X ijk ≥ 0 , for all I, J, K Z k = {0,1} , for all K
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Facility Location Cost Trade-Offs
0
2
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Number of Warehouses Freight Cost Inventory Cost Facility Costs Total Costs
Inventory Carrying Cost for SKUi @ DCj Inventory Carrying Cost % Fill rate adjustment by SKU by Customer Std Dev of Supplier Lead time Average Demand
ICCij = COGi x ICC%ij x SSij
Transportation Management
Network & Hubs
Chris Caplice ESD.260/15.770/1.260 Logistics Systems Dec 2006
Distribution System Approach
Distribution System
Number and location of transshipment points Routes and schedules of vehicles Routes and schedules of items flowing
V P W W C C
V P W C C
V
V P W C
V P W C C C
V
W C C
W
C C
C
C
C
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The Network Design Problem
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A “Simple” MILP Formulation
Minimize: Subject to:
∑ ∑ ∑ ∑C
i=1 j=1 k=1 l=1 ijkl
I
∑X
k=1 I J
ijk
∑∑ X
i=1 j=1 J
≤ Vk Z k ; for all K
∑X
j=1
ijk

∑Y
l=1
L
ikl
; for all I and K
X ijk ≥ 0; for all I, J, K Yikl ≥ 0; for all I, K, L Z k = {0,1} , for all K
∑ ∑X
j=1 K k=1 L
J
K
≥ Dil ; for all I and L ≤ Pij ; for all I and J
ijkl
∑ ∑X
k=1 I l=1 J i=1 j=1
Where: X ijkl = Total annual volume of product i produced at plant j and shipped through DC k on to customer zone l Zk = {0,1};1 if the DC at k is selected, else 0 Dil = annual demand for product i at customer zone l Pij = maximum annual capacity for product i at plant j Vk = maximum annual throughput volume at DC at k Fk = The fixed annual operating cost of a DC at k Cijkl = The variable cost to produce one unit of product i at plant j and ship it through DC k to customer zone l so that Cijkl =C[mnfg]ij +TLijk +DCTHPTik +LTLikl
Treat shipment flows as links or arcs
V
V P
V P
V P W C C
V
V P W C
V P W C C C
V
W C C
W C C C
W C
W
C
C
C
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Std Dev of Demand
Average Supplier Lead Time
∑Y
k=1 K
K
ikl
≥ Dil ; for all I and L ≤ Pij ; for all I and J
ijk
Where: X ijk = Total annual volume of product i produced at plant j and shipped through DC k Yikl = Total annual volume of product i shipped from DC k to customer zone l Z k = {0,1};1 if the DC k is selected, else 0 A ijk = The variable cost to produce one unit of product i at plant j and ship it to the DC at k Bikl = The variable cost to move one unit of product i through the DC at k and ship it to the customer zone at l Dil = annual demand for product i at customer zone l Pij = maximum annual capacity for product i at plant j Vk = maximum annual throughput volume at DC at k Fk = The fixed annual operating cost of a DC at k
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Issues & Concerns
Data Issues
Demand Point Aggregation Demand over Time Periods Profiling freight cost data Fixed Costs: Periodic versus One-Time Cost Estimating Functions Freight Rate Availability Transfer Prices and Taxes Exchange Rates Duty and Duty Drawback What about Inventory? What about Customer Service? Supply Chain Extensions
A “Better” MILP Formulation
Minimize: Subject to:
∑∑∑ A
i=1 j=1 k=1
I
J
K
ijk
X ijk + ∑∑∑ Bikl Yikl + ∑ Fk Z k
i=1 k=1 l=1 k=1
I
K
L
K
How big is this formulation? 20 Plants, 30 Products/ Product Groups, 50 Potential DCs, and 400 Customers Regions, there are: 50,000 (30k IB & 20k OB) possible flows
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