Course Document

OT_CD

Following Course Learning Outcome will be evaluated: Analyse and appreciate variety of performance measures for various optimization problems

Model Formulation Sums For Practice

Formulation Sums

Lesson Planning

Sr.No.	Topics	Hours
1.	Introduction to Operations Research , Methods for solving ORØ  O.R.- Quantitative approach to Decision MakingØ  The history of Operation Research Ø  Nature and significance of OR Ø  Features of OR Ø  Advantages of OR	[1]
2.	Linear Programming Model FormulationØ  IntroductionØ  Structure and Linear Programming Ø  Advantages and Limitations of Linear Programming Ø  Application area of LP Ø  General mathematical model of LP Ø  Guidelines on LP	[3]
3.	Transportation problemØ  IntroductionØ  Mathematical model of transportation problem Ø  The transportation method Ø  Methods for finding initial solution Ø  Test for optimality Ø  Variation in transportation problem Ø  Maximization transportation problem	[6]
4.	Graphical solution method Ø  IntroductionØ  Graphical solution Ø  Special Cases	[3]
5.	Simplex MethodØ  IntroductionØ  Maximization – Simplex Algorithm, Ø  Minimization – Simplex Algorithm using Big-M method, Ø  Minimization – Simplex Algorithm Two phase method Ø  Dual Simplex Method	[9]
6.	Assignment ProblemØ  Introduction to assignment problems.Ø  Solution methods of assignment problems. Ø  Variations to assignment problems.	[5]
7.	Integer ProgrammingØ  Types of integer linear programming problems.Ø  Cutting Plane method Ø  Branch & Bound Method Ø  Zero – one Integer programming	[5]
	Sessional
8.	SequencingØ  IntroductionØ  Notations, terminology and assumptions Ø  Processing N jobs through  two Machines Ø  Processing N jobs through three Machines Ø  Processing N jobs through m Machines	[6]
9.	Activity Network AnalysisØ  Network diagramØ  Critical path analysis Ø  Probability in PERT analysis Ø  Project time  Cost Trade off Ø  Resource allocation	[8]
10.	Inventory ModelØ  IntroductionØ  The meaning of inventory control Ø  Functional role of inventory Ø  Reasons for carrying inventory Ø  Factors involved in inventory problem analysis Ø  Inventory model building Ø  Inventory control models Ø  Inventory control models with shortages Ø  Multi item inventory models with constraints Ø  EOQ models with quantity discounts	[6]
11.	Queuing TheoryØ  Introduction,   Operating CharacteristicsØ  Probability distribution in queuing System Ø  Classification of Queuing Model	[3]
12.	SimulationØ  IntroductionØ  Steps of Simulation Method Ø  Stochastic Simulation & Random Number Ø  Simulation of different problem (inventory, queuing, investment etc)	[5]
	Total Hours	60hrs

Queuing Theory Video

Queuing Theory Formulas

Queuing Theory Notes_Rushabh

Deterministic Inventory Control Models Formulas and Sums

Deterministic Inventory Control Model_Formulas_Rushabh

Deterministic Inventory Control Models

13. Deterministic Inventory Control Models

Introduction:

Inventory, in wider sense, defined as any idle resource of an enterprise. The word inventory refers to any kind of resource having economic value and is maintained to fulfil the present and future needs of an organization. Such resources may be classified into three categories: (i) Physical resources such as raw materials, semi-finished goods, finished goods, etc. (ii) human resource such as unused labour and (iii) financial resource such as working capital, etc.

Types of Inventories:

1. Lot-size (or cycle) Inventories: Lot-size (or cycle) Inventories exist whenever one produces (or buys) in larger quantities than are needed to satisfy the immediate requirements.
2. Pipeline (or transit) Inventories: These arise due to the fact that transportation time is involved in transferring substantial amount of resources. For example, when coal is transported from the coalfields to an industrial town by train, then the coal, while in the transit, cannot provide any service to the customers for power generation or for burning in furnaces.
3. Buffer Inventories: These are maintained to meet uncertainties of demand and supply. Such “buffer” inventories which are in excess of those necessary to just meet the average demand during the lead time (the time elapsing between placing the order and having the goods in stock ready for use), held for protecting against the fluctuation in demand and lead time are also termed as safety stocks
4. Seasonal (or Anticipating) Inventories: Anticipation inventories are held for the reason that a future demand for the product is anticipated. Production of specialized items like crackers well before Diwali, umbrellas and raincoats before rains set in, fans while summers are approaching, are all examples of anticipating inventories. Thus seasonal inventories are built up in advance or procured during the period of low demand to be used in peak demand period.
5. Decoupling Inventories: If various production stages operate successively then in the event of breakdown of one or any disturbance at some stage can affect the entire system. This kind of inter-dependence is not only costly but also disruptive for the entire system. The inventories used to reduce the interdependence of various stages of production system are known as decoupling inventories.

Inventories Decision:

In any inventories controls situation there are three basic questions to be answered. They are:

1. How much to order? That is to say, what is the optimal quantity of an item that should be ordered whenever an order is placed?
2. When should the order be placed?
3. How much safety stock should be kept? Thus, what quantity of an item in excess of the expected requirements should be held as buffer stock in anticipation of the variations in demand and/or the time involved in acquiring fresh supplies?

 

Inventories Costs

            Various costs associated with inventory control are often classified as follows:

1. Set-up cost: This is the cost associated with the setting up of machinery before starting production. Set-up cost is generally assumed to be independent of quantity ordered for or produced.
2. Ordering cost: This is a cost associated with ordering or raw material for production purposes. Advertisements, consumption of stationery and postage, telephone charges, rent for space used by purchasing department, traveling expenditures incurred, etc. constitute the ordering cost.
3. Purchase (or production) cost: The cost of purchasing (or producing) a unit of an item is known as purchasing (or producing) cost. The purchase price will become important when quantity discounts are allowed for purchases above a certain quantity or when economics of scale suggest that the per unit production cost can be reduced by a larger production run.
4. Carrying (or holding) cost: The carrying cost is associated with carrying inventories. This cost generally includes the costs such as rent for space used for storage, interest on the money locked-up, insurance of stored equipment, production, taxes, depreciation of equipment and furniture used, etc.
5. Shortage (or stock out) cost: The penalty cost for running out of stock (i. e. when an item cannot be supplied on the customer’s demand) is known as shortage cost. This cost includes the loss of potential profit through sales of items and loss of goodwill, in terms of permanent losses of customers and its associated lost profit in future sales.

Other factors involved in inventories analysis:

Besides the costs that determine the profitability, other factor play an important role in the study of inventory problems are the following:

1. Order Cycle

An ordering cycle is the time period between two successive placement of orders. The ordering cycle may be determined in one of the two ways:

(1)               Continuous review: In this case the level of inventory is updated continuously as current level is reached at which point is reached (also called reorder point) a new order is placed.

(2)               Period review: In this case the orders are placed at equal interval of time, but the size of the order may vary with the variations in demand.

1. Lead time or delivery tag When an order is placed, it may require some time before delivery is reached. The time between the placement of an order and its receipt is called delivery lag or lead time.
2. Stock Replenishment When the stock is purchased from outside sources, instantaneous replenishment occurs; while uniform replenishment may occur when the product is manufactured locally within the firm.
3. Planning Horizon (or period) The time period over which the inventory level will be controlled is called the period horizon. This horizon may be finite or infinite depending upon the nature of the demand for the commodity.

ECONOMIC ORDER QUANTITY

            The inventory problems in which demand is assumed to be fixed and completely pre-determined are usually referred to as the Economic Order Quantity (EOQ) or Lot-size problems. By the order quantity we mean the quantity produced or procured during one production cycle. This is also termed as re-order quantity. When the size of order increases, the ordering costs (cost of purchasing, inspection, etc.) will decrease whereas the inventory carrying costs (cost of storage, insurance, etc.) will increase. Thus in the production process there are two opposite costs, one encourages the increase in the order seize and the other discourages. Economic Order Quantity (EOQ) is that size of order which minimizes total annual costs of carrying inventory and cost of ordering.

 

 

 

 

Simplex Algorithm

Simplex Algorithm Video