Transportation & Supply Chain Costs

1. Transportation & Supply Chain Costs John H. Vande Vate Spring, 2001 1

2. Moving (change of place) Handling loading unloading ... Transportation Holding (change of time) from production to consumption (goods) from investment to revenue ($) Two Primary Types 2

3. Rent (Fixed) Cost of the space Handling equipment Maintenance Waiting or Holding Costs (Variable) (Opportunity) Cost of capital tied up in goods Shrinkage, Spoilage Obsolescence Holding Cost 3

4. System Costs • Including those we don’t bear • These are the costs the ultimate customer sees • These costs influence our competitiveness • Supply Chain Management • Examples? 4

5. Uses of Inventory Cycle Stock consequence of batching or to avoid changeovers Anticipatory Inventory storing capacity for peak period advance purchasing to exploit discounts Safety Stock buffer against variability in lead-time demand Pipeline Inventory Goods in transit Holding Costs 5

6. Cycle Stock As influenced by transportation awaiting shipment shipment awaiting sales Anticipatory Inventory Safety Stock buffer against variability in lead-time demand Pipeline Inventory Goods in transit Our Focus 6

7. Cycle Stock As influenced by transportation awaiting shipment shipment awaiting sales Anticipatory Inventory Safety Stock buffer against variability in lead-time demand Pipeline Inventory Goods in transit Constant Demand 7

8. Constant Demand Cumulative Production Cumulative number of items kth item nth item Cumulative Demand In transit In transit In transit consumed shipped produced received Time Constant Demand 8

9. Constant Demand Cumulative Production Cumulative number of items Cumulative Demand In transit Time Item-hours waiting 9

10. Assumption: Ship all that’s produced Item-hours waiting = Area Area = (base * height)/2 Area = (headway*shipment size)/2 Avg. Waiting time per item = headway/2 Maximum Inventory = Production Rate*Maximum Headway Inventory at Origin Item-hours waiting 10

11. How does the average inventory at the origin compare with the common estimate: Average Shipment Size/2 or Production Rate * Average Headway/2? Do not turn anything in, just give a clear explanation if called on next class Assignment #1 (Group) 11

12. Apparent Contradiction Cumulative Production Cumulative number of items Cumulative Demand In transit Time “The maximum accumulation at the destination is the same as it is at the origin” Max. Inv. at Destination Max. Inv. at Origin 12

13. Explain this apparent contradiction. Is Daganzo just plain wrong? Can we calculate the maximum inventory at the destination? What about the average inventory? Assignment #2 13

14. Fixed vs Sunk costs Sunk Costs: Money already spent that cannot be influenced by the decisions in question Capital investments in real estate, buildings, equipment,… IGNORE Fixed Costs: If we are considering liquidating capital investments or making additional investments. DON’T COMPARE WITH OPERATING COST Rent or “Fixed” costs 14

15. Grow with the maximum inventory Probably economies of scale Only appropriate if Space is leased or Strategic planning for facility investments Rent or Fixed Costs 15

16. Cost per Unit ci = holding cost per item per year Typically the product of a “cost of funds” rate i the cost or value of an item Total Holding Cost ci *(Item-years in inventory) ci (Annual production rate*Time from production to consumption) Holding Costs 16

17. Inventory at the source ci (Average inventory at the source) Pipeline Inventory ci (Average inventory in transit) ci (Annual Demand)(Avg. transit time in yrs) Inventory at the destination ci (Average inventory at the destination) ci typically larger here -- we invested in handling and transportation Finer View 17

18. Our Example in Class reduced inventory value by $130 million How do we account for those savings? What are they worth? Basic Understanding 18

19. Before & After $150 mil. Expenses Revenues $130 mil $20 mil. Expenses Revenues Did we save the company $130 mil/yr? What did we save the company? Did we save the company $130 mil? 19

20. What would you pay to reduce the minimum balance you must hold in your checking account? Analogy 20

21. Parcel LTL - less than truckload Truckload Rail car Unit train ... Transportation Costs 21

22. Freight Class Weight range 0-500lbs 500-1000 lbs 1000-5000 lbs 5000-1000 lbs ... Origin ZIP (3 digit) Destination ZIP (3 digit) LTL Rates Base Rate } 22

23. Bundled rates Exchanges Combinatorial bidding …. What is the Rate? 23

24. fixed origin, destination and class Increasing in weight Increasing at a decreasing rate Concave 24

25. LTL Rates Total = fixed + variable*volume Variable Total Cost fixed 25 Volume Shipped

26. E(f(x))  f(E(x)) Avg. Cost of Shipment  Cost of Avg. Shipment Assignment 3: What relationship is there between Avg. Cost of Shipment Cost of Avg. Shipment? Assignment #3 26

27. Fix the range e.g. 1,000-5000 lbs Transportation Cost fixed + variable * volume Inventory ci $/item/year item in inventory for (roughly) volume/Annual demand Cost per item ci (volume/Annual demand) + fixed/ volume + variable Shipment Size 27

28. Cost per item ci (volume/Annual demand) + fixed/ volume + variable Shipment Size volume = (fixed*Annual Demand/ci) Assume you can handle from here…. EOQ 28

29. If EOQ falls in range... If EOQ exceeds range… If EOQ falls below range… etc. Handle from here 29

30. Pull strategies, e.g, (s, S) or continuous review policies When inventory (on hand and on order) drops to s, order S. s consists of expected lead time demand + safety stock protection against variability in lead time demand Variability 30

31. Demand modeled as a diffusion process rate D’(items per year) index of dispersion  (items) In a period of length t Demand is normally distributed mean is D’t variance is D’t Lead time taken as normally distributed mean tm variance 2 Common Model 31

32. Expected Lead time Demand D’tm Variance in Lead time Demand D’22 + D’tm Lead Time Demand 32

33. Set safety stock to 2 or 3 standard deviations in lead time demand This increases average inventory by 2 or 3 standard deviations in lead time demand Classical Approach 33

34. Expedite ce constant cost per unit expedited (e.g., next day air) Need to calculate f(s) Expected number of items expedited per regular order if we set the reorder point at s (treat this as fixed) Alternate Approach 34

35. Expediting vs Safety Stock 35

36. Transportation fixed + variable*volume + cef(s) Inventory ci(volume + Safety Stock)/Annual Demand EOQ formula for volume Expediting 36

37. Shipment Size vs Safety Stock 37

38. The major influence of expediting is to Change the shipment size? Change the reorder point? …. We want to trade off Costs of expediting vs ??? How important was this? 38

39. Previous method finds best shipment size for each re-order point s: S(s) The best cost at reorder point s: cost (s, S(s)) Search for the best value of s Why does shipment size matter? Does this raise an issue with f(s), the expected number expedited per regular shipment if the reorder point is s? How to go about this? 39

40. Cost vs Safety Stock 40