Case study of Supply Chain and Operation Management Email:
[email protected] This article discusses solution of Inventory and Aggregate Planning based on case in the book of supply chain by S. Chopra and Operation Management by J Heizer
Case 1 Motorola obtains cell phones phon es from its contract manufacturer located in Chin a to supply the U.S. market, which is served from a warehouse located in Memphis, Tennessee. Daily demand at the Memphis warehouse is normally distributed, with a mean of 5,000 and a standard deviation of 4,000. The warehouse aims for f or a Type I CSL of 99 percent. The company is debating whether to use sea or air transportation from China. Sea transportation results in a lead time of 36 days and costs $0.50 per phone. Air transpo rtation results in a lead time of 4 days and costs $1.50 per pe r phone. Each phone costs $100, and Motorola Motor ola uses a holding cost of 20 percent. Assume that Motorola takes ownership of the inventory on delivery. Assume that Motorola follows a periodic review policy. poli cy. Given lot sizes by sea and air, Motorola would have to place order every 20 days using sea transport but could order daily using air transport a. Assume that Motorola follows a periodic review policy. What Order up to level (OUL) and safety inventory should the warehouse aim ai m for when using sea or air transportation? How many days of safety inventory will Motorola carry under each policy? b. How many days of cycle inventory inventor y does Motorola carry carr y under each policy? c. Under a periodic review policy, do you recommend sea or air transportation? Answer: Given
Average Daily Demand (D) Minimum Lot Size Q Standard deviation Holding Cost 20% CSL=99%=Z=Norm.inv
Order frequency Unit cost (C) Order cost (S) Lead time (L)
Sea Transport
Air Transport
100.000
5.000
5.000 4000 0.2 2.33 every 20 days
every day
$ 0.5 per phone 36 days
$1.5 per phone 4 days
$100
Safety Stock= Z.
.√
ROP= Average daily demand x Lead time ti me + Z.
. √
Sea Transport Safety Stock =2.33 x 4000 x = 55.920 unit
√ 3636
ROP = 5.000 x 36 + Safety stock = 180.000 + 55.920 = 235.920 unit
. =
Air Transport Safety Stock =2.33 x 4000 x = 18.640 unit
√ 4
ROP = 5.000 x 4 + Safety stock = 20.000 + 18.640 = 38.640 unit
= . = 2.500
Cycle Inventory = =
Cycle Inventory =
50.000 unit/ 20 days = 2.500 unit /day
unit/day
Total Inventory = 55.920 + 2.500 = 58.420 Total cost = 58.420 x $ 0.5= $ 29.210
Total Inventory = 18.640 + 2.500 = 21.140 Total cost = 21.140 x $ 1.5= $ 31.710
Motorola should use Sea transport because it will give less cost compare to Air transport
Case 2 TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee, and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus delivering to each customer separately costs $1050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons a year, demand at the medium customer is 24 tons per year, and demand at small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton, and it uses a holding cost of 25 percent. Truck capacity is 12 tons. a. What is the annual transportation and holding cost if TopOil ships a full truckload each time customer is running out of stock? How many days of inventory is carried at each customer under this policy? b. What is the optimal delivery policy to each customer if TopOil aggregates shipments to each of the three customers on every truck that goes to Nashville? What is the annual transportation and holding cost? How many days of inventory are carried at each customer under this policy? c.what is the optimal delivery price to each customer if TopOil aggregates each shipments to each of the three customers on every truck that goes to nashville? what is the total annual transportatioin and hlding cost? how h ow many days of inventory are carried at each customer under this policy? Answer: given
Demand (D) Order cost (S) $800+$250 Holding cost as a friction (h) Cost per unit (C) Truck Capacity: 12 tons
Answer point B
Small Customer 8 tons/year $1 050 $1050 0.25 $10.000/ton
Small Customer
Medium Customer 24 tons/year $1050 0.25 $10.000/ton
Medium Customer
Large Customer 60 ton/year $1050 0.25 $10.000/ton
Large Customer
.().() =4.4 = .().() =7 =2.5 = ... = ..().(.() ) .(.) .(.) 2. 5 4. 4 7 Cycle Inventory = = 1. 2 5 = 2. 2 = 3.5 2 2 2 8 / = 3 24 / = 5 60 / = 8 2.5 7 4.4 1.25 (0.25).($10.000) 3.5 (0.25).($10.000) 2.2 (0.25).($10.000) = $8.750 = $5.500 (ℎ).() = $3125 2 EOQ (Q)=
Order frequency (n)
Annual holding cost
Annual order cost
3.($1050) = $3150
5.($1050) = $5250
8.($1050) = $8400
Average flow time
. =0.15/year .()
. =0.09/year .()
=0.05/year .()
() 2
Annual Cost= Cyc.inv.(h)(C) + order freq.(order cost)
=4/week
=8/week
1.25(0.25)($10.000)+ 3($1050) = $6275
=2/week
$17250
$10850
TC= $34375 Answer point C S=$800, S1=S2=S3= S1=S2=S3=$250 $250
∗=S+S1+S2+S3 =∗=$1550 (.)( )(. .) )+ +((.)( )(. .) )+ +((.)( )(. .) ) = . times/year Ʃ ()() = ∗ ∗
n=
Annual order cost = 8.6 x $1550 = $13330
Cycle inv= Q=
Avergflowtime
2
Annual hold cost
ℎ() 2
Cycl.iv x hold cost
TC=$26455
Small Customer
Medium Customer
Large Customer
= 0.9 ton/order .
= 2.7 ton/order .
= 6.9 ton/order .
= 3 weeks
= 3 weeks
0.9 = 0.45 2 . = 0.05 = 3 weeks ()
2.7 = 1.35 2 . = 0.05 ()
6.9 = 3.45 2 . = 0.05 ()
0.45.(0.25)($10000)=
$1125
$3375
$8625
Quantity order = Qsmall+Qmed+Qlarge =0.9+2.7+6.9=10.5 tons/order Quantity order
8 = 9 0.9
Medium Customer
24 = 9 2.7
Large Customer
60 = 9 6.9
Case 3 Prefab, a furniture manufacturer, uses 20,000 square feet of plywood per month. It's trucking company charges Prefab $400 per shipment, independent of the quantity purchased. The manufacturer offers an all unit quantity discount with a price of $1 per square foot for orders under 20,000 square feet, $0.98 per square feet, and $0.96 per square foot for orders larger than 40,000 square feet. Prefab incurs a holding cost of 20%. What is the optimal lot size for Prefab? Answer = given Order quantity < 20000 20000-40000 >40000
= 0000 000000 = 20000 = 40000
Price $ 1 0.98 0.96
= $1 = $0.98 = $0.96
Demand= 20000x12=240000/year h= 0.2 S= $400
Step 1 Define EOQ in the lowest cost
()= 31622 )= ... = .(). ..(.) Check= 31622<40001 (not feasible) Define T ! ()+ . (ℎ). () . () = ($400) . (0.2). ($0.96) 240000. ($0.96) EOQ (
= $236.640
()= 31298 )= ... = .(). ..(.) Check= 20000<31298<40000 (feasible) Define T ! ()+ . (ℎ). () . ($400 . (0.2). ($0.98) ( ) ) .( = $400) 8) 240000. 240000.(($0.98)8) EOQ (
= $241.334
T
< T so optimal lot size, when order larger than 40000 square feet
Aggregate case Missouri's Soda Pop Inc. has a new fruit drink for which it has high hopes. Steve Allen, the production planner, has h as assembled the following data d ata and demand forecast. He has to create c reate an aggregate plan. His three options are: A) Chase Strategy that hires and fires personnel as necessary to meet the forecast B) level strategy C) a level strategy that produces 1200 cases per quarter and meets the forecast demand with inventory and subcontracting
1)Which strategy provides the lowest cost? 2)If you are Steve's boss, which plan do you implement and why?
Quarter
Forecast
1
1800
2
1100
3
1600
4
900
Costs Pervious quarters inventory: 1300 cases Beginning Inventory: 0 cases Stockout Costs: $150 per case Inventory Holding Costs: $40 per case at end of quarter Hiring Employees: $40 per case Firing Employees: $80 per case Subcontracting Cost: $60 per case
Unit Cost on Regular Time: $30 per case Overtime Cost: $15 extra per case Capacity on Regular Time: 1800 cases per quarter Answer= Q
Forecast Inventory A
Production
B
Hiring
Layoff
Prod Cost ($30)
Hiring cost ($40) 20000
C
0
-
1300
1300
50 0 500
-
-
1
1800
-
1800
-
700
54000
2
1100
-
1100
500
-
33000
3
1600
-
1600
-
700
48000
4
900
-
900
-
-
27000
Total cost = $314000 (plan A)
56000 20000 56000
162000 40000
Q Forecast Production Inventory Hiring overtime Prod Cost A B C=B-A ($30)
Hiring Inv cost cost ($40) ($40)
0
20000
1300
1
1800
1350
2
1100
1350
3
1600
1350
4
900
1350
50 450 250
112000
40500 40500
OverT Cost ($15)
6750 10000
40500 450
5400 Level strategy=
Layoff cost ($80)
Ʃ = = Ʃ
40500
18000
162000 20000
28000
6750
Total Cost= 198750 (plan B)
Q Forecast A
Production Inventory B
0
subcont
C=B-A
1300
1
1800
1200
2
1100
1200
3
1600
1200
4
900
1200
layoff
Prod Cost ($30)
Inv cost ($40)
Subcont layoff cost Cost ($60) ($80)
100 600 100
8000 3600 3600
400 300
4000
3600 3600
Total Cost = $ 228000
36000
24000 12000
144000 16000 60000
8000
Plan B has the lowest cost at $198750. If I were the boss I would take plan B (level strategy)
Case Transport method Lon Min has developed a specialized airtight vacuum bag to extend the freshness of seafood shipped to restaurants. He has put to gether the following demand cost data: Q
Forecast (unit)
Regular time
Over time
Sub contract
1
500
400
80
100
2
750
400
80
100
3
900
800
160 160
100
4
450
400
80
100
Initial inventory = 250 units Regular time cost = $1.00/unit Overtime cost = $1.50/unit Subcon tracting cost = $2.00/unit Carrying cost = $0.50/unit/quarter Back -order cost = $0.50/unit/quarter Min decides that the initial inventory of 250 units will incur the 20c/unit cost from each prior quarter (unlike the situation in most companies, where a 0 unit cost is assigned). a) Find the optimal plan using the transportation method. b) What is the cost of the plan? plan ? c) Does any regular time capacity go unused? If so, how much in which periods?
Answer 1 Q 1
2
250 Reguler
250
overtime
3 1.5
1 1
150 80
4
dummy 2
1.5
400
2
80
subcontract 2
3
100
Reguler
400
overtime subcontract
400
80
1.5
80
40
2
60
Reguler
800
overtime
100
1.5
400
overtime
50
subcontract 500
750
100 800
Reguler
forecast
100
1
subcontract 4
capacity
900
450
60
160
100
100 400
1 1.5
30
80
100
100
450
3050
b) Total cost
250(0)+250(1)+150(1.5)+80(2)+400(1)+80(1.5)+40(2)+800(1)+100(1.5)+400(1)+50(1.5) = $2660 c) all regular time were used, so the answer No it does not
