MOS 3330: Operations Management Formula Sheet

Inventory ManagementEOQ Q* = (2DCO/CH)½ TC = CO(D/Q) + CH(Q/2) R = d L Order cycle time = (#days/yr)/(#orders)

EOQ quantity discount TC = CO(D/Q) + CH(Q/2) + P·D

EPQ Q* = [2DCO/CH(1 – d/p)]½ TC = CO(D/Q) + CH(Q/2)(1 – d/p)

Length of production run = Q/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 Ft+1 = forecast for total demand in t+1

Si = seasonal factor for season i = Di/ΣDi 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 UCL = c + z ( c )1/2 LCL = c – z ( c )1/2

R-chart UCL = D4 R LCL = D3 R

x-bar-chart UCL = x + A2 R LCL = x – A2 R

Pattern test conditions: • 8 consecutive points on one side of the center line • 8 consecutive points up (or down)

• 14 points alternating up or down • 2 out of 3 consecutive points in zone A • 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