This document provides formulas and definitions for operations management concepts related to inventory management, forecasting, aggregate production planning, material requirements planning, scheduling, quality management, statistical process control, and service levels. Key formulas include economic order quantity, economic production quantity, safety stock calculation, various forecasting methods, inventory balance equation for aggregate production planning, net requirements calculation for MRP, job flow time and makespan for scheduling, quality indices, control charts, and service level determination based on z-values.

1. MOS 3330: Operations Management Formula Sheet
Inventory Management
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EOQ Q* = (2DCO/CH) TC = CO(D/Q) + CH(Q/2) R=dL Order cycle time = (#days/yr)/(#orders)
EOQ quantity discount TC = CO(D/Q) + CH(Q/2) + P·D
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EPQ Q* = [2DCO/CH(1 – d/p)] Length of production run = Q/p
TC = CO(D/Q) + CH(Q/2)(1 – d/p) Max. inventory level = Q(1 – d/p)
Safety stock Q system: R = d L + zσd(L½) P system: Q = d (P + L) + zσd(P + L)½ – I
Forecasting
Naïve Ft+1 = Dt Simple MA Ft+1 = (Dt + Dt–1 + L + Dt–(N–1)) / N
Weighted MA Ft+1 = WtDt + Wt–1Dt–1 + L + Wt–(N–1)Dt–(N–1) Exp. smoothing Ft+1 = αDt + (1 – α)Ft
Adj. exp. smooth. AFt+1 = Ft+1 + Tt+1 = [αDt + (1 – α)Ft] + [β(Ft+1 – Ft) + (1 – β)Tt]
Seasonality Ft+1,i = forecast for season i in t+1 = SiFt+1 Si = seasonal factor for season i = Di/ΣDi
Ft+1 = forecast for total demand in t+1 Di = actual total past demand for season i
Mean Absolute Deviation = Σ⏐Dt – Ft⏐/ N Mean Squared Error = Σ (Dt – Ft)2 / N
Mean Absolute Percentage Deviation = Σ⏐Dt – Ft⏐/ ΣDt Cumulative Error = Σ(Dt – Ft)
Aggregate Production Planning
Inventoryt = Inventoryt–1 + Productiont – Demandt Avg. demand = (total demand – open. Inv) / (# of periods)
Cumulative avg. demand = (total cumulative demand – open. Inv) / (# of cumulative periods)
MRP
Netting (Net requirements) = (Gross reqts) – (On-hand inventory) – (Quantity on order)
Scheduling
Job flow time = (waiting time) + (processing time) Makespan = finish time for the last job
Job lateness = Σall jobs (finish time − due time) Job tardiness = Σonly late jobs (finish time − due time)
Avg. # of jobs in the system = (Σall jobs job flow time)/(makespan)
Quality Management
Yield = (# of units to be produced)×(%good units) + (# of units to be produced)×(1 − %good units)×(%reworked)
Labour index = (quality cost) / (direct labour hours) Production index = (quality cost) / (product yield)
Sales index = (quality cost) / (sales) Quality-productivity index = (product yield) / (production cost)
Cost index = (quality cost) / (production cost)
Statistical Process Control
p-chart
UCL = p +z[ p (1 – p )/n]1/2 LCL = p –z[ p (1 – p )/n]1/2
c-chart 1/2 1/2
UCL = c + z (c) LCL = c – z (c)
R-chart
UCL = D4 R LCL = D3 R
x-bar-chart
UCL = x + A2 R LCL = x – A2 R
Pattern test conditions: • 14 points alternating up or down
• 8 consecutive points on one side of the center line • 2 out of 3 consecutive points in zone A
• 8 consecutive points up (or down) • 4 out of 5 consecutive points in zone A or B
Service level 90% 95% 96% 97% 98% 99%
z 1.28 1.65 1.75 1.88 2.05 2.33
n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31 0.29 0.27 0.25 0.24 0.22 0.21 0.20 0.19 0.19 0.18
D3 0 0 0 0 0 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 0.35 0.36 0.38 0.39 0.40 0.41
D4 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 1.64 1.62 1.61 1.60 1.59