MGT 3110 Exam 3 Formulas
Chapter 13: ROP Models
Reorder point model with Normal distribution:
Reorder point (ROP) = Average demand during lead time + Safety stock
̅̅̅ + Z dLT
i.e. ROP = d̅ x ̅LT
dLT= Standard deviation of demand during lead time (as give in table below)
Lead time is constant
Lead time is variable
Demand is constant
𝜎dLT = 0
𝜎dLT = d𝜎𝐿𝑇
Demand is variable
𝜎dLT = d√𝐿𝑇
2
𝜎dLT = √𝐿𝑇𝜎𝑑2 + 𝑑 𝜎𝐿𝑇
2
where, d = Demand rate per period, d̅ = average demand rate
̅̅̅̅ = average lead time
LT = Lead time, LT
d = Standard deviation of demand per period
LT = Standard deviation of lead time in periods
Z = Normal table value for the given service level
Annual Service Level
E(n) = E(z)dLT
where E(n) = Expected number of units short per cycle
E(z) = Standardized number of units shorts (Table 13.3, page 583)
dLT= Standard deviation of demand during lead time
𝐷
E(N) = E(n)(𝑄 )
where E(N) = Expected number of units short per year
2DS
and Q = √
SLannual = 1 -
𝐸(N)
D
=1-
H
𝐸(𝑧)𝜎𝑑𝐿𝑇
𝑄
where SLannual = Annual service level
E(N) = (1 – SLannual)D
Fixed Order Interval Model
Q = 𝑑̅(OI + LT) + zd√OI + LT - A
where Q = Amount of order
OI = Order interval (length of time between orders)
A = Amount on hand at reorder time
Single-Period model
𝐶
SL = Service level = 𝐶 +𝑠𝐶 , where Cs = Cost of shortage, Ce = cost of excess
𝑠
𝑒
Cs = Lost profit = Revenue – Cost per unit
Ce = Original cost/unit – Salvage value/unit
Uniform distribution for demand:
S0 = a + SL (b – a)
where a = lower limit for demand, b = upper limit for demand, SL = Service level
Normal distribution
S0 =  + Z, where  = mean demand,  = standard deviation of demand
Chapter 16 Scheduling
Input Output Control Chart
Cumulative deviation of input = Previous cumulative deviation + actual input – planned input
Cumulative deviation of output = Previous cumulative deviation + actual output – planned output
Cumulative backlog = Previous backlog + Actual input – Actual output
Completion time (Flowtime) = Previous completion time + processing time
Average flow time =
Sum of flow time
Number of jobs
Average job tardiness =
Total tardiness
Number of jobs
Average number of jobs in the system =
Sum of flow time
Makespan
Makespan = Completion time of the last job
Critical Ratio =
Due date
Processing time
Slack per remaining operations (SRO) =
Due date−Processing time
Number of remaining operations
Chapter 17 Project scheduling
Activity Slack = LS – ES or = LF - EF
PERT
For each activity, te =
t o +4t m + t p
6
and 2 = (
tp− to 2
6
)
TE = Project completion time = = ∑ t e of the activities on the critical path
2path = ∑ 𝜎 2 of the activities on the path; 2P = ∑ 𝜎 2 of the activities on the critical path
Z=
T - TE
𝝈P
, where T = project due date
Project due date (T) for a given probability = TE + z P