Dr. Abedini
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Inventory analysis
Space and money prevent companies from
producing goods
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Total Cost= Pc+Cc+Oc
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Where
• Pc= Purchasing Cost per year
• Cc=Carrying or Holding Cost per year
• Oc= Ordering Cost per year
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C= $Cost/unit
D= Annual demand
H=$Holding cost/unit/year
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(Based on Annual Demand)
Q= Order Quantity
P= $Ordering cost/order/year
R= Reorder Point (quantities)
Total Cost= (C)(D)+H(Q/2)+P(D/Q)
dTC/dQ = (0)+H/2 – PD/Q
Therefore Q*= √(2DP/H)
Q*= Economic Order Quantity
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R=Lead time
Q*= Economic ordering quantity
• (How many to order)
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T= Time
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C= $10/unit
D= 365,000
H= $5/unit/year (based on demand)
P= $500
Q*=√[2(365,000)(500)/5] = 8544
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(# of units per order)
365,000/8544 = 42.7
(times in year you order)
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Total cost of carrying inventory=
10(365,000)+5(8544/2)+500(365,000/8544)
3650000+21360+21360
$3,692,720.02
Under these conditions we assume that the
demand is constant and the lead time is
constant
This is known as Simple E.O.Q.
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% of quantity ordered that can be
supplied from the available stock
Ex.)
You want 100 parts but the company
has only 90
Service Level = 90%
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Service level when demand is
distributed discretely 0<n<20
• More than 20 data points becomes
continuous
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S.L. =
D
P
1
.01
2
.04
3
.10
4
.20
5
.30 Reorder
5
.20
6
.10
7
.04
8
.01
9
6
7
8
9
SS
0
SL
.30
.35 .2(1)+.1
1
2
3
.20
.10
.04
.15
.05
.01
4
.01
0
88.8%
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Probability that you run out of stock
before you receive your new order
With uncertain demand
(Continuous distribution)
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Now you don’t know when you will run out
σ
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Z = X- µ/ σ
µ= 1000/day
σ = 100/ day
σ
Remember
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If you an 84 % service level then you
would just add 1 standard deviation
If you want a 97 % service level then
you add 2 standard deviations
84% = 1000+100 = 1100
97% = 1000+2(100) = 1200
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Annual Demand = 365,000
Daily Demand = 1000 units/day
P = $50 / order
H = $1.25 / unit / year
L = 9 days
C = $12.50 / unit
SL = 95 %
σ = 1000 units / day
Z = 1.64
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SS = Zσ√(L)
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R = DL + SS
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= (1000)9 + 492
= 9492 Units
This is when you reorder
Q* = Q*= √(2DP/H)
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= 1.64(100) √(9)
= 492 Units
= √[2(365,000)(50)]/ 1.25
= 5,404 Units
This is the number of units you
should order during reorder time
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Priority rules
1.) First come first serve
2.) Shortest processing time (SPT)
3.) Earliest due dates (EDD)
• Prioritize as what is due next
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i = task
di = due date for task i
ti = processing time for i
Li = lateness for I = (Fi - di)
• Negative values represent early times
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Fi = flow time for i
Ti = tardiness for i (never negative)
SLi = slack time for I = (di - ti)
Ci = make span for i (time to complete all
tasks)
Wi = weight for i
Scheduling n tasks to 1 processor
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Rule 1: minimize the average flow time by
sequencing in the order of (SPT)
Task i
ti
di
Li
Fi
Li
1
10
15
.1
31 16
100 40
25
15
0
2
5
15
.2
5
-10 25 12
-3
5
-10
3
18
20
.3
78 58
10
33
13
4
7
30
.05 12 -18 23 7
-23 49
19
5
17
50
.05 60 10
340 78
28
98
48
6
20
40
.05 98 58
400 98
58
69
29
7
9
29
.05 21 -8
180 49
20
42
13
8
12
42
.05 43 1
240 61
19
81
39
16.75
49
18.88
µ
wi Fi
100 %
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43.5
Li
13.4
Ti/wi
Fi
90 30
46.9
Rule 1 : t2, t4, t7, t1, t8, t5, t3, t6
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List Activities
Set Precedence
Compute each crash time
Design network
Compute early start times
Compute late finish times
Design critical path
Compute project cost
Crash one activity
Iterate
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Critical path –
Occurs when early start times equal
late finishes
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Project evaluation and review
technique
Use expected values rather than
estimated values