Course

Syllabus

Suggested lab exercises:

1. EOQ Model Implementation – Develop a program to compute EOQ, reorder level, and total inventory cost; perform sensitivity analysis.
2. EOQ with Shortages – Implement deterministic inventory model with shortages and compare total cost with no-shortage case.
3. Probabilistic Inventory Model – Simulate uncertain demand (Poisson/Normal) and compute safety stock and reorder point.
4. Single-Period (Newsvendor) Model – Determine optimal order quantity under uncertain demand with and without setup cost.
5. M/M/1 Queue Model – Compute and simulate performance measures such as utilization, average waiting time, and queue length.
6. M/M/c Queue Model – Analyze multi-server systems and study the effect of varying number of servers.
7. M/G/1 Queue Model – Apply Pollaczek–Khintchine formula and compare results with M/M/1 model.

Unit 1

Deterministic Inventory Model

Types of inventories – Reason for carrying Inventory – Inventory Decisions – Costs Associated with Inventories – Factor Affecting Inventory Control – An Inventory Control Problem – The Concept of EOQ – Deterministic Inventory Model without shortages – Deterministic Inventory Model with shortages – Multi item deterministic problem

Unit 2

Probabilistic Inventory Model

Probabilitized EOQ Model – Probabilistic EOQ Model – Inventory Problem with Uncertainty Demand – Systems of Inventory Control – One Period Problem – One Period Problem without Set-up Cost – One Period Problem with set-up Cost, The Stochastic Process Associated with the Inventory System – Selection of an Operation Doctrine – Quantity discount “All Units Discount”

Unit 3

Nature of the Inventory System

Heuristic Approximate Treatment for the Backorders Case – Heuristic Approximate Treatment for the Lost Sale Case – Computation of Time Average. Exact Formulae for the Backorders Case with Poisson Demand and Constant Procurement Lead Time – An Important Special Case – The Normal Approximation – An example involving the use of the exact form of Total Cost – The lost sales case for constant lead times – Stochastic lead times – Models with Q=1

Unit 4

Queuing Systems

Elements of a Queuing Model, Role of Exponential Distribution, Pure Birth and Death Models (Relationship Between the Exponential and Poisson Distributions), Pure Birth Model, Pure Death Model, General Poisson Queuing Model, Specialized Poisson Queues, Steady-State Measures of Performance, Single-Server Models, Multiple-Server Models, Machine Servicing Model – (M/M/R): (GD/K/K), R<K

Unit 5

Other Queuing Models

(M/G/1) :(GD/infinity/infinity) – Pollaczek – Khintchine (P-K) Formula, , Queuing Decision Models, Cost Models, Aspiration Level Model

Text Books / References

Text Books

1. Hamdy A. Taha, “Operations Research an Introduction”, 8th Edition, Prentice – Hall is an imprint of Pearson, 2008.
2. G.Hadley and T.M.Whitin, “Analysis of Inventory Systems” Prentice – Hall, Inc., Englewood Cliff.N.J. 1963.
3. Kleinrock, L. (1975). Queuing systems, volume 1: Theory.

This course introduces the fundamental concepts and mathematical models of queueing systems and inventory management used in operations research and industrial engineering. It focuses on the analysis of stochastic models to optimize service systems and inventory policies under uncertainty.

Course Outcomes: After successful completion of the course, students will be able to

• CO1: Apply EOQ and other deterministic inventory models (with and without shortages) to minimize total inventory cost in multi-item systems.
• CO2: Analyze inventory systems under uncertain demand using probabilistic EOQ and single-period models, including quantity discount policies.
• CO3: Evaluate inventory models with backorders, lost sales, stochastic demand, and lead times using heuristic and exact approaches.
• CO4: Analyze single and multi-server queueing systems using birth–death processes and compute steady-state performance measures.
• CO5: Apply M/G/1 models and cost-based queueing decision techniques to determine optimal service policies under uncertainty.

CO-PO Mapping: