4064 words - 17 pages

DECISION MODELING

DECISION

WITH

WITH

MICROSOFT EXCEL

MICROSOFT

Linear Optimization

Linear Optimization

A constrained optimization model takes the form of a

constrained

performance measure to be optimized over a range of

feasible values of the decision variables.

The feasible values of the decision variables are

determined by a set of inequality constraints.

constraints

Values of the decision variables must be chosen such

that the inequality constraints are all satisfied while

either maximizing or minimizing the desired

performance variable.

These models can contain tens, hundreds, or thousands

of decision variables and constraints.

Linear Optimization

Very ...view middle of the document...

The use of a certain type of crude oil in producing

gasoline is restricted by the characteristics of the

gasoline (e.g., octane rating, etc.)

Formulating LP Models

A constrained optimization model represents the

constrained

problem of allocating scarce resources in such a way as

to optimize an objective of interest.

To illustrate this, we will return to the Oak Products

model. However, we will start with a simplified model.

Oak Products, Inc.

Oak

Based on economic forecasts for the next week, it has

been determined that it will be possible to sell as many

Captains or Mates chairs as the firm can produce.

So, the question becomes: How many Captains and

Mates chairs should be produced given our constraints

in order to maximize next week’s profit contribution?

Formulating LP Models

Consider the following major factors:

1. The unit contribution margin (price minus unit

variable cost) is $56 for each Captain sold and

$40 for each Mate.

2. Long dowels, short dowels, legs and one of two

types of seats are needed to assemble the chairs.

3. We have a limited inventory of 1280 long dowels

and 1600 short dowels for next week’s

production.

Each Captain uses 8 long and 4 short dowels.

Each Mate uses 4 long and 12 short dowels.

Formulating LP Models

4. The inventory of legs is 760 units and each chair

produced of either type uses 4 legs.

5. The inventory of heavy and light seats is 140 and

120, respectively. Each Captain produced uses a

heavy seat and each Mate uses a light seat.

6. In order for management to honor an agreement

with the union, the total number of chairs

produced of both types cannot fall below 100.

Let’s summarize the information given so far in a table:

Given these considerations, now decide how many

Captains and Mates to produce next week.

This is called an optimal product mix problem or an

optimal

optimal production plan.

optimal

The first step in solving this is to identify the constraints

constraints

and objective function.

objective

For notation purposes, let C = number of Captains

chairs and M = number of Mates chairs to be produced.

Start with the number of long dowels:

Both types of chairs require long dowels.

So, we can mathematically describe this as:

8(# Captains produced) + 4(# Mates produced) = 1280

or

8C + 4M = 1280

Once again, here is the equation for the long dowels:

8C + 4M = 1280

However, since only 1280 long dowels are available and

we can use at most, only that amount, we must make

at

this equation an inequality in order to satisfy this

restriction. In this case:

8C + 4M < 1280

We use the < (less than or equal to) inequality because,

we can use all 1280 long dowels, we can use less than

that amount, but we will never be able to use more than

1280.

This is called an inequality constraint.

inequality

Left hand side (LHS) is called a constraint function.

constraint

Right hand side (RHS) specifies the limitation.

Now let’s...

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