# Operations Management Formula Sheet

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• Published : March 26, 2012

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1. EVPI = Expected value with perfect information – Maximum EMV
= EVwPI – Maximum EMV

2. Moving Average

[pic]

3. Weighted Moving Average

[pic]

4. Exponential Smoothing

[pic]

5. Linear Regression

[pic]

[pic]

7. EOQ
[pic]
Q*=Optimal number of units per order (EOQ)
Q = Number of units per order
D = Annual Demand, Units
H = Holding (or Carrying) Cost, \$ / unit /year
S = Ordering (or Setup) Cost, \$ / order or setup
P = Price per unit

Total Cost = [pic]

8. EOQ (Production order quantity model):

[pic]
Total Cost = [pic]
Imax = [pic]
p = Daily production rate
d = Daily demand rate, or usage rate

9. REORDER POINT: (Fixed Order Quantity Model)

I. Demand varies, Lead time constant

ROP = (Average daily demand * Lead time in days) + Z[pic]

II. Lead time varies, Demand constant

ROP = (Daily demand * Average lead time in days) + Z(Daily demand) * [pic]

III. Both Demand and Lead time vary

ROP = (Average daily demand * Average lead time) + Z[pic]

Where [pic]= Standard deviation of demand per day
[pic]
[pic]= Standard Deviation of lead time in days
Z = Number of standard deviations

10. ORDER QUANTITY: (Fixed Time Period Model)

[pic]

11. Single period inventory model

Service level = [pic]
where
[pic]= Cost of Shortage = Sale price/unit – Cost/unit
[pic]= Cost of Overage = Cost/unit – Salvage value/unit

12. Process Control Using Attribute Measurements

[pic]

where
[pic]=mean fraction defective in the samples
z = number of standard deviations
[pic]= standard deviation of the sampling distribution

13. Process Control by Variables

[pic]
Where
[pic]=mean of the sample means
[pic]=average range of the samples
[pic] = values from the chart below

Factors for Computing Control Chart Limits (3 Sigma)

|Sample |Mean |Upper |Lower |
|Size |Factor |Range |Range |
|(n) |(A2) |(D4) |( D3) |
|2 |1.880 |3.268 |0 |
|3 |1.023 |2.574 |0 |
|4 |0.729 |2.282 |0 |
|5 |0.577 |2.115 |0 |
|6 |0.483 |2.004 |0 |
|7 |0.419 |1.924 |0.076 |
|8 |0.373 |1.864 |0.136 |
|9 |0.337 |1.816 |0.184 |
|10 |0.308 |1.777 |0.223 |
|12 |0.266 |1.716 |0.284 |

14. Process Capability Ratio
[pic]

15. Center of Gravity Method

where
[pic]= x-coordinate of location i
[pic]= y-coordinate of location i
[pic]= Quantity of goods moved to or from location i

16. Assembly Line Balancing

Cycle time
= Production time available per day / Units required per day

Minimum number of workstations
= Sum of each task times / Cycle time

Efficiency
= Sum of each task times . (actual number of workstations * cycle time)

17. Waiting Line Model (One channel)

The average number of units waiting in queue:
[pic]

The average number of units in the system:
[pic]

The average time a unit spends waiting in the queue:
[pic]

The average time a unit spends in the system, (waiting time plus service time)
[pic]

Utilization factor for the system:
[pic]

Probability of zero units in the system:
[pic]

Probability of n units in the system:
[pic]

Probability of more than k units in the system
where n is the number of units in the system:
[pic]

18. Waiting Line Model (Multiple...