Homework-Chapter 16
Problem 1
a) The lead time for a computer is 3+2 = 5 weeks
The answers for b,c and d are the last 3 rows of the following table.
Month
Demand
Invent.
Returns
Net.Requir.
3
Prod./Order
Mboard
140
4
175
Orders
DiskDrives
5
6
210
70
7
175
-
9
125
-
10
70
-
175
70
8
170
40
130
280
130
140
125
125
70
280
350
260
250
140
560
Note: we assume that returns occur at the beginning of each month.
Problem 2
a) lot-for-lot scheduling
Week
Demand
Orders
50
Set-up Cost
120
Inventory
1st Nov
50
83
120
0
2nd Nov
83
27
120
0
3rd Nov
27
55
120
0
4th Nov
55
0
Total cost =4*120= $480
b) Economic Order Quantity
First we find the demand for the month of November = 50+83+27+55=215
So annual demand = 12*215=2,580 units
Also annual holding cost =52*1 (since it’s $1 per week)
So, order size =[ ( 2*2,580*120) / (52) ]1/2= 109 units
Week
Demand
Scheduled Rec.
Sched. Order
109
End.of period Inv
Setup cost
120
Inv. Holding Cost
1st Nov
50
109
109
59(=109-50)
120
59
2nd Nov
83
109
0
85 (=59+109-83)
3rd Nov
27
0
0
58(=85-27)
4th Nov
55
0
0
3(=58-55)
85
58
3
11
300
20
280
Total cost = 2*120 + 59+85+58+3 = $ 445
c) Least Unit Cost heuristic
Cover week 1 : Order 50 units
setup cost= 120 and inv. cost= 0 => cost/unit = 120/50=2.4
Cover weeks 1&2 : Order 133 units
Setup cost= 120
Inventory cost = (133-50)* 1 = 83
so cost/unit= 203/133= 1. 526 < 2.4 so continue
Cover weeks 1&2&3 : Order 160 units
Setup cost= 120
Inventory cost = (160-50)* 1 + (110-83)*1 = 137
so cost/unit= 257/160= 1. 61 >1.526 so stop.
So we should only cover periods 1 and 2.
We start over from week 3.
Cover week 3 : Order 27 units
Setup cost= 120
Inventory cost = 0
so cost/unit= 120/27= 4.44
Cover weeks 3&4 : Order 82 units
Setup cost= 120
Inventory cost = 55
so cost/unit= 175/82= 2.134 < 4.44 so order this quantity.
So our total cost will be the cost of ordering at the beginning of week 1 and 3.
That is, (120 + 83) + (120 +55) = $378 which is the lowest among options a,b,
and c.