Operations Management Formula Calculators

Chapter 6: Managing Quality

Process Capability Ratio (`Cp`)

Cp = (USL - LSL) / (6σ)

Upper Specification Limit (USL): Lower Specification Limit (LSL): Standard Deviation (σ):

Example: USL = 10, LSL = 2, σ = 1.2 → Cp = (10 - 2) / (6 * 1.2) = 1.11

Process Capability Index (`Cpk`)

Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)]

USL: LSL: Mean (μ): Standard Deviation (σ):

Example: USL = 10, LSL = 2, μ = 6, σ = 1.2 → Cpk = min[(10 - 6)/(3*1.2), (6 - 2)/(3*1.2)] = 1.11

Chapter 7: Process Strategy

Total Cost (TC)

TC = F + V * Q

Fixed Cost (F): Variable Cost per Unit (V): Quantity (Q):

Example: F = 10000, V = 5, Q = 1000 → TC = 10000 + (5 * 1000) = 15000

Crossover Point

Q = (F₂ - F₁) / (V₁ - V₂)

Fixed Cost 1 (F₁): Variable Cost 1 (V₁): Fixed Cost 2 (F₂): Variable Cost 2 (V₂):

Example: F₁ = 10000, V₁ = 5, F₂ = 8000, V₂ = 6 → Q = (8000 - 10000)/(5 - 6) = 2000

Chapter 8: Location Strategies

Center of Gravity Method

x = Σ(xᵢ * wᵢ) / Σwᵢ, y = Σ(yᵢ * wᵢ) / Σwᵢ

X Coordinates (comma-separated): Y Coordinates (comma-separated): Weights (comma-separated):

Example: x = (2*10 + 4*20 + 6*30)/60 = 4.67, y = (3*10 + 5*20 + 7*30)/60 = 5.67

Factor Rating Method

Total Score = Σ(weight × score)

Weights (comma-separated): Scores (comma-separated):

Example: Score = (0.4×8 + 0.3×7 + 0.3×9) = 8.0

Chapter 9: Layout Strategies

Total Work Distance

Total Distance = Σ(dᵢⱼ × fᵢⱼ)

Distances (comma-separated): Flows (comma-separated):

Example: Total Distance = 5×4 + 10×3 + 8×2 = 54

Takt Time

Takt Time = Available Production Time / Customer Demand

Available Time (minutes): Customer Demand (units):

Example: Takt Time = 480 / 120 = 4 minutes/unit