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

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

3 3 Holding Cost 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

4 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?

5 5 Holding Costs 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

6 6 Our Focus –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

7 7 Constant Demand –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

8 8 Time Cumulative number of items Cumulative Production Cumulative Demand k th item produced consumed shipped received In transit n th item Constant Demand In transit

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

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

11 Assignment #1 (Group) 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

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

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

14 Rent or “Fixed” costs 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

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

16 Holding Costs Cost per Unit –c i = 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 –c i *(Item-years in inventory) –c i (Annual production rate*Time from production to consumption)

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

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

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

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

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

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

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

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

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

26 Assignment #3 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?

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

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

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

30 Variability 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

31 Common Model 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 t m –variance  2

32 Lead Time Demand Expected Lead time Demand –D’tm Variance in Lead time Demand –D’ 2  2 + D’  t m

33 Classical Approach 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

34 Alternate Approach Expedite –c e 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)

35 Expediting vs Safety Stock

36 Expediting Transportation –fixed + variable*volume + c e f(s) Inventory –c i (volume + Safety Stock)/Annual Demand EOQ formula for volume

37 Shipment Size vs Safety Stock

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

39 How to go about this? 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?

40 Cost vs Safety Stock