Key Formulas & Equations
Throughput Rate: TH = 1/T0
Cycle Time: CT = 1/R
Utilization: ρ = λ/(cμ)
Reorder Point: ROP = d × L + SS
Safety Stock: SS = z × σL
Total Inventory Cost: TC = (D/Q)S + (Q/2)H
Balance Efficiency: Eb = Σti/(n × Tmax) × 100%
Number of Stations: n = Σti/Tc
Throughput: TH = WIP/CT
Normal Time: NT = OT × Rating Factor
Production Rate: Rp = 60/Tc × E
Slack: Si = LSi - ESi = LFi - EFi
PERT Expected Time: te = (a + 4m + b)/6
PERT Variance: σ² = ((b-a)/6)²
Core Concepts
Operations Research
The application of analytical methods to make better decisions. Includes linear programming, queuing theory, simulation, and optimization techniques.
Supply Chain Management
The management of the flow of goods and services from raw materials to final customers. Includes procurement, logistics, inventory, and distribution.
Quality Control
Techniques for ensuring products meet specifications. Includes statistical process control, Six Sigma, acceptance sampling, and quality management systems.
Facilities Planning
The design and layout of physical facilities. Includes plant location, material handling, storage, and workplace design for efficiency and safety.
Human Factors Engineering
The study of human capabilities and limitations in the workplace. Includes ergonomics, cognitive engineering, and human-machine interface design.
Production Planning
The coordination of manufacturing activities to meet demand. Includes master production scheduling, material requirements planning, and capacity planning.
Lean Manufacturing
A systematic approach to eliminating waste while maintaining productivity. Includes just-in-time, kaizen, 5S, and value stream mapping.
Project Management
The planning, organizing, and managing of resources to achieve project goals. Includes scheduling, budgeting, risk management, and team coordination.
Worked Examples
Example 1: EOQ Calculation
Problem: Annual demand = 10,000 units, ordering cost = $50, holding cost = $2/unit/year. Calculate EOQ.
Solution:
EOQ = √(2DS/H) = √(2 × 10000 × 50/2) = √500,000 = 707 units
Example 2: Little's Law
Problem: A system has average WIP of 50 units and throughput of 10 units/hr. Calculate cycle time.
Solution:
L = λW → W = L/λ = 50/10 = 5 hours
Example 3: PERT Analysis
Problem: Activity has optimistic = 4 days, most likely = 7 days, pessimistic = 16 days. Calculate expected time and variance.
Solution:
te = (4 + 4×7 + 16)/6 = 48/6 = 8 days
σ² = ((16-4)/6)² = 4 days²
Practice Problems
Problem 1
Calculate reorder point if daily demand = 100 units, lead time = 5 days, safety stock = 200 units.
Answer: ROP = 100 × 5 + 200 = 700 units
Problem 2
A line has 5 stations with times: 2, 3, 4, 2, 3 minutes. Calculate balance efficiency (cycle time = 4 min).
Answer: Eb = 14/(5 × 4) × 100% = 70%
Problem 3
Calculate standard time if normal time = 10 min and allowance = 15%.
Answer: ST = 10 × 1.15 = 11.5 minutes
Problem 4
Calculate utilization if arrival rate = 10/hr, service rate = 15/hr, servers = 1.
Answer: ρ = 10/15 = 0.667 = 66.7%
Problem 5
Calculate total inventory cost for D = 5000, Q = 500, S = $25, H = $5.
Answer: TC = (5000/500) × 25 + (500/2) × 5 = 250 + 1250 = $1500
Problem 6
Calculate throughput if WIP = 30 units and cycle time = 6 hours.
Answer: TH = 30/6 = 5 units/hour
Problem 7
Calculate PERT expected time for a = 2, m = 5, b = 8.
Answer: te = (2 + 4×5 + 8)/6 = 30/6 = 5 days