Optimization using LP modelsOptimization using LP modelsRepco Pharmaceuticals (Ex 4.6)Repco Pharmaceuticals (Ex 4.6)

Ravi Krishna RavulaRavi Krishna Ravula

Dsc 8240Dsc 8240

Situation and ObjectiveSituation and Objective

Repco is a Drug Mfg companyRepco is a Drug Mfg company It produces 3 drugs (A,B,C) and are It produces 3 drugs (A,B,C) and are

sold @ $8, $70 and $100 sold @ $8, $70 and $100 respectively.respectively.

2 units of A are required to produceB2 units of A are required to produceB 1 unit of B is required to produce C1 unit of B is required to produce C Objective: Maximize sales revenueObjective: Maximize sales revenue

Variables and MeasuresVariables and Measures

Input VariablesInput Variables::

Required labor hrs to produce a Required labor hrs to produce a unit unit

Unit of a product used to Unit of a product used to produce another productproduce another product

Unit selling price of each drug.Unit selling price of each drug.

Output variablesOutput variables::

Revenue from Sales.Revenue from Sales.

Amount of products soldAmount of products sold

ConstraintsConstraints::

Amount produced = Amount Amount produced = Amount used to produce other used to produce other products + Amount soldproducts + Amount sold

Total labor hours availableTotal labor hours available

Goods used in producing another Goods used in producing another product cannot be sold.product cannot be sold.

Decision VariablesDecision Variables::

Amount of goods produced Amount of goods produced (these are the trial values)(these are the trial values)

Mathematical formulationMathematical formulation

Labor hrs reqd to produce A = 1 hr. B = 2 + 2 = 4 hrs and C = Labor hrs reqd to produce A = 1 hr. B = 2 + 2 = 4 hrs and C = 3 + 4 = 7hrs3 + 4 = 7hrs

Unit of product used to produce another product.Unit of product used to produce another product.

A B CA B C

A 0 2 0A 0 2 0

B 0 0 1B 0 0 1

C 0 0 0C 0 0 0

Amount of products sold = Units produced – Units used as Amount of products sold = Units produced – Units used as inputs to produce other unitsinputs to produce other units

Revenue from Sales = Sum of each Product unit selling price * Revenue from Sales = Sum of each Product unit selling price * amt of product soldamt of product sold

Spreadsheet modelSpreadsheet model The inputs are in the green The inputs are in the green

box on the left side.box on the left side. The grey shaded area has The grey shaded area has

the rangesthe ranges The production plan is in The production plan is in

orange colored cells.orange colored cells. The production plan The production plan

includes the changing cells includes the changing cells (units produced) and (units produced) and output cells (units sold)output cells (units sold)

The yellow cells show the The yellow cells show the Balance constraintsBalance constraints

The red and blue cells The red and blue cells show the Revenue (Target show the Revenue (Target cell)cell)

Using SolverUsing Solver

After invoking the solver, After invoking the solver, and filling in the target and filling in the target cell (Revenue), cell (Revenue), changing cells (Units changing cells (Units produced, sold) and produced, sold) and the constraints, click the constraints, click on options and choose on options and choose Non-negativity and Non-negativity and linear model linear model assumption.assumption.

Optimum Solution from SolverOptimum Solution from Solver

Optimal Production A = 20 units, B Optimal Production A = 20 units, B =10 units.=10 units.

Optimal revenue is $700Optimal revenue is $700 All units of A are used to produce BAll units of A are used to produce B Only product B is being sold.Only product B is being sold. Though C has the highest selling Though C has the highest selling

price it is not being formed because price it is not being formed because it involves larger labor requirements.it involves larger labor requirements.

((View in excelView in excel))

Sensitivity AnalysisSensitivity Analysis

To see how the optimal solution To see how the optimal solution changes as we change one or more changes as we change one or more of the inputs of the inputs

Solver table is invoked to perform Solver table is invoked to perform sensitivity analysis.sensitivity analysis.

One way tableOne way table Sensitivity of revenue, Sensitivity of revenue,

units produced and units produced and units used as inputs to units used as inputs to product C selling product C selling price. price.

with the price of C at with the price of C at $130, there is a $130, there is a production of 5.714 production of 5.714 units of C, resulting in units of C, resulting in revenue of $743. revenue of $743.

Only product C is Only product C is being sold. being sold.

Using a 2-way tableUsing a 2-way table

Sensitivity of amount Sensitivity of amount of C produced to of C produced to selling price of C and selling price of C and labor hour availability labor hour availability

Though there is an Though there is an increase in labor hours increase in labor hours there is no production there is no production in C till the price in C till the price reaches $130reaches $130

100

120

140

160

180

200

40

1000

5

10

15

Number of C produced

Selling Price of C

Labout hour Availability

Sensitivity of C produced to Selling price of C and labor hour abailability

It was seen that though there is an It was seen that though there is an increase in labor hours there is no increase in labor hours there is no production in C till the price reaches $130 production in C till the price reaches $130 as it was in the previous analysis. as it was in the previous analysis.

B requires 4 labor hours and C needs 7 B requires 4 labor hours and C needs 7 hours. Revenue of B for one unit is $70. hours. Revenue of B for one unit is $70. when divided by Labor hours needed it when divided by Labor hours needed it shows that $17.50 is revenue per labor shows that $17.50 is revenue per labor hour. hour.

To earn more C should sell at a minimum To earn more C should sell at a minimum of 7 * 17.50 = $122.50.of 7 * 17.50 = $122.50.