24. Example: Transportation vs. Inventory Cost Tradeoff
The Carry-All Luggage Company produces a line of luggage goods. The typical
distribution plan is to produce a finished goods inventory located at the plant site. Goods
are then shipped to company-owned field warehouses by way of common carriers. Rail
is currently used to ship between the East Coast plant to a West Coast warehouse. The
average transit time for rail shipment is T=21 days. At each stocking point, there is an
average of 100,000 units of luggage having an average value of C=$30 per unit.
Inventory carrying costs are I=30 percent per year.
The company wishes to select the mode of transportation that will minimize
total costs. It is estimated that for every day that transit time can be reduced from the
current 21 days, average inventory levels can be reduced by 1 percent, which represents
a reduction in a safety stock. There are D=700,000 units sold per year out of the West
Coast warehouse. The company can use the following transportation services:
Transportation
Service
Rate ($/unit) Door-to-door Transit
Time (days)
No. of shipments per
year
Rail 0.10 21 10
Piggyback 0.15 14 20
Truck 0.20 5 20
Air 1.40 2 40
25. Example (continued)
A diagram of the companyâs current distribution is shown below. By selecting
alternate modes of transportation, the length of time that inventory is in transit will be
affected. Annual demand (D) will be in transit by the fraction of the year represented by
T/365 days, where T is average transit time. The annual cost of carrying this in-transit
inventory is ICDT/365.
The average inventory at both ends of the distribution channel can be
approximated as Q/2, where Q is the shipment size. The holding cost per unit is IïŽC, but
the item value C must reflect where the inventory is in the channel. For example. The
value of C at he plant is the price, but at the warehouse it is the price plus the
transportation rate.
21days
East Coast Plant West Coast Warehouse
Inventory = 100,000 units Inventory = 100,000 units
26. Modal Choices
Cost Type Method of
Computat-
iona
Rail Piggyback Truck Air
Transportation RïŽD (0.10)(700,000) =
70,000
(0.15)(700,000) =
105,000
(0.2)(700,000) =
140,000
(1.4)(700,000) =
980,000
In-transit
Inventory
ICDT/365 [(0.30)(30)
(700,000)(21)]/
365 = 363,465
[(0.30)(30)
(700,000)(14)]/
365 = 241,644
[(0.30)(30)
(700,000)(5)]/
365 = 86,301
[(0.30)(30)
(700,000)(2)]/
365 =34,521
Plant Inventory ICQ/2 [(0.30)(30)
(100,000)b] =
900,000
[(0.30)(30)
(50,000)(0.93)c] =
418,500
[(0.30)(30)
(50,000)(0.84)c] =
378,000
[(0.30)(30)
(25,000)(0.81)c] =
182,500
Field Inventory ICâDQ/2 [(0.30)(30.1)
(100,000)] =
900,300
[(0.30)(30.15)
(50,000)(0.93)c] =
420,593
[(0.30)(30.2)
(50,000)(0.84)c] =
380,250
[(0.30)(31.4)
(25,000)(0.81)c] =
190,755
Total $2,235,465 $1,185737 $984,821 $1,387,526
aR = transport rate; D = annual demand; I = carry cost (%/yr); C = product value at plant; Câ=product value
at warehouse (C+R); T = time in transit; and Q = shipment size.
b100,000 is more than the shipping quantity/2 to account for safety stock..
cAccounts for improved transport service and number of shipments per year.
27. Tradeoffs in Transportation Design
ï”Transportation, facility, and inventory cost tradeoff
â Choice of transportation mode
â Inventory aggregation
ï”Transportation cost and responsiveness tradeoff
ï”Similarly, lead-time and lead-time variability has an
impact on inventory and hence overall costs
34. 34
Supply Chain Contracts
ïź A contract specifies the terms of the orders and deliveries
between the buyer and the supplier
ïź Quantity, Price, Delivery lead time, Quality
ïź Over/under-stocking risks?
ïź Fixed quantity, long lead time ï buyer bears risk
ïź Short lead time ï supplier bears risk
(buyer can wait until demand known)
ïź Each link in the supply chain optimises based on its own
profit/cost margins (without considering other links in the
supply chain)
ïź May reduce profits of the entire supply chain
Manufacturer Retailer
36. 36
Double Marginalisation Example
ïź With retailer doing own optimisation, 1000 units
produced, and total supply chain profit is $76,063
+ $90,000 = $166,063
ïź In fact, for the supply chain (as a whole):
ïź Cu =200-10, Co=10
ïź CSL* = 190/200=0.95
ïź Optimal production level = 1493
ïź Total supply chain profit = $183,812
ïź Considering Manufacturer and retailer
TOGETHER, the supply chain profit is higher!
37. 37
Double Marginalisation
If each party makes decisions considering
only a part of the supply chain, the
decisions may not maximize profits for the
whole supply chain!
ïź Could contracts be designed to encourage retailer
to purchase more to increase product availability
ïź Supplier must share in the retailerâs demand
uncertainty
47. 47
Quantity Flexibility contracts
Manufacturer allows retailer to adjust
quantity ordered after observing demand
ïź Retail orders O
ïź Manufacturer commits to deliver Q=(1+a)O,
0< a < 1
ïź Retailer commits to buying at least q=(1-b)O,
0< b < 1
Manufacturers share risk with retailers
No returns required