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Shivangi- Ch:13 &14-LINEAR OPTIMIZATION-Business Analytics (James…
Shivangi- Ch:13 &14-LINEAR OPTIMIZATION-Business Analytics (James Evans)
7. PRODUCTION / MARKETING
It is used to understand the optimal production in different product mix in order to achieve maximum profit.
It combines product-mix model with marketing budget allocation decisions based on demand elasticity.
OBJECTIVE FUNCTION
Maximize the profit on the basis of elasticity of demand and constraint of budget.
TYPICAL CONSTRAINTS
Budget limitation
Production limitations
Demand requirements
DECISION VARIABLES
Allocation of advertising expenditures within the product mix.
Production quantities.
1. PRODUCT MIX
These problems are usually used to understand the right proportion of Product to be sold in order to maximize profit.
OBJECTIVE FUNCTION
Aim of using these problems involve maximizing the profit.
TYPICAL CONSTRAINTS
The scarcity of resources include:
Production time
Labor
Material
Maximum sales requirements
Maximum sales potential
DECISION VARIABLES
It involves quantities of products to be produced and sold.
3. BLENDING
Blending problems involve mixing several raw materials that have different characteristics to make a product that meets certain specifications
Examples include: Dietary planning, gasoline and oil refining.
OBJECTIVE FUNCTION
It aims to minimize the cost of production by using the most optimal composition of ingredient in the product.
TYPICAL CONSTRAINTS
Specifications required in one unit of the output.
For eg; 20% carbohydrate, 55% proteins and 25% fiber.
DECISION VARIABLES
Quantities of ingredients to mix in order to produce one unit of output.
For eg: The amount of corn flour, sugar, added flavors required to produce one cookie.
2. PROCESS SELECTION
Process selection models generally involve choosing among different types of process while production.
Examples includes: Make or buy decisions
TYPICAL CONSTRAINTS
Demand requirements
Available hours in each process
Number of common process stages.
OBJECTIVE FUNCTION
Minimize the cost of production by optimally using the hours in each process.
DECISION VARIABLES
Quantities of product to make using alternative processes.
5. TRANSPORTATION
Transportation models determine the amount to ship from a set of sources of supply (factories, warehouses etc.) to a set of demand locations (warehouses, customers, etc.) at minimum cost.
OBJECTIVE FUNCTION
Minimize the total transportation cost by fulfilling the demand requirement of the destination and optimally utilizing the production by the source plant.
For eg: How many units of car should the company transport from each plant to different dealers such that the overall transportation cost for the company reduces.
TYPICAL CONSTRAINTS
Limited availability at sources (Cars produced by source or manufacturing plant).
Required demands met at destinations ( Demand at the dealers end for cars).
DECISION VARIABLES
Units to ship from the sources of supply to the destinations.
For eg: The units of car to be transported from the manufacturing unit as Manesar to the showroom in Delhi.
4. PORTFOLIO SELECTION
Financial investments models, involving blending decisions regarding stock mix.
OBJECTIVE FUNCTION
Aims to maximize future return or minimize risk exposure.
For eg: Get maximum return from the individual portfolio or to minimize the risk ascertaining to a particular capital structure.
TYPICAL CONSTRAINTS
Limit on available funds
Sector requirements or restrictions
Proportional relationships on investments mix
DECISION VARIABLES
Proportions to invest in different financial instruments.
For eg: Percentage of investment in equity, preference, bonds etc.
8. MULTI PERIOD PRODUCTION PLANNING
Decisions as to the amount to produce in each time period to meet anticipated demand over each period.
Producing more than the demand when the cost of production is lower than inventory holding cost, helps in cost optimization.
OBJECTIVE FUNCTION
Minimize total production and inventory costs.
DECISION VARIABLES
Quantities of product to produce in each of several time periods
Amount of inventory to hold between periods
TYPICAL CONSTRAINTS
Limited production rates
Material balance equations
6. MULTI PERIOD FINANCIAL MANAGEMENT
It occurs over an extended horizon which can be formulated as multi period optimization models.
It is used when there are multiple investment choices with different maturity period and the business has some minimum cash balance requirement
DECISION VARIABLES
Amount to invest in short-term instruments at different period.
OBJECTIVE FUNCTION
Maximize the cash balance at the end of the time period.
TYPICAL CONSTRAINTS
Cash balance equations
Required cash obligations
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DEFINITION OF LINEAR OPTIMIZATION
It is a process of selecting values of decision variables that minimizes or maximize some quantity of interest.
All constraints and variables must be linear function of the decision variables.
STEPS TO FORMULATE OPTIMIZATION
Formulate the Objective Function
The quantity we seek to minimize or maximize using the variable functions and given constraints.
Identify the Constraints
They are limitations, requirements, or other restrictions that are imposed on any solution, either from practical or technological considerations or by management policy.
Types of Constraints
Simple Bounds: Constrain the value of single variable. For eg: Xa>= 120
Limitations: They usually involve the allocation of scarce resources. For eg. Material used in production cannot exceed the amount available in inventory.
Requirements: Involve the specification of minimum levels of performance. For eg: Amount of cash reserve to be kept in a particular month.
Proportional relationships: Involve the the ratio of one variable to another. For eg: Used in blending mix problems like pharmaceuticals etc, where components are to be in a specific ratio
Balance constraints: Problems like input=output. For example Production in July and inventory in the beginning of July should match the demand in July and inventory at the end of the month.
Identify the Decision Variable
Unknown values that a model seeks to determine by maximizing or minimizing the objective function.
Conversion as mathematical Expression
The decision variables are represented by descriptive names, abbreviations or subscripted letters.
Constraints are expressed as algebraic inequalities or equations.
