PM 212 Bottleneck, flow, break-even & Kanban formulas

Cycle Time

CT = Processing Time at Bottleneck Station

Throughput Rate

TR = 1 / Cycle Time

Maximum Output per Day

= Available Production Time per Day / Cycle Time

Little’s Law

Average Inventory = Throughput Rate × Average Flow Time

Break-Even Point

• = Fixed Costs / (Selling Price per Unit − Variable Cost per Unit)

• = FC / (SP - VC)

NB: Round up

Multi-Product Break-Even Process

• CM₁ = P₁ − V₁ and CM₂ = P₂ − V₂

• use sales mix ratio to relate quantities (e.g. Q₁ = kQ₂)

• set F = CM₁Q₁ + CM₂Q₂

• substitute using mix

• solve for units

• Revenue = (Q₁ + Q₂) × P;

Number of Kanban Cards

• K = (Demand Rate × Lead Time × (1 + Safety Factor)) / Container Size

• = (D*L(1 + S)) / C

NB: Round up

Break-Even Revenue

Revenue = Break-Even Quantity (BEP) × Selling Price per Unit

Target Profit Quantity

• = (Fixed Costs + Target Profit) / (Selling Price − Variable Cost)

• = (FC + Target profit) / (SP - VC)

Weighted Contribution Margin

WCM = Sum of (Contribution Margin per Product × Sales Mix Proportion)