FORUMULATE a LINDO Script Electronic Hall produces Televisio

FORUMULATE a LINDO Script

Electronic Hall produces Televisions and DVD Players. During the coming year quarterly demand for these products is as shown in the following table:

Product

Q1

Q2

Q3

Q4

Televisions

1500

1000

2000

1200

DVD Players

1000

2000

1500

2500

The proprietor wants a production schedule that meets the demand requirements in each quarter. Leadership has also decided that the inventory level for each product must be at least 150 units at the end of each Quarter. There is no inventory on hand at the start of the first quarter.

During any quarter 12000 hours of production time are available. A Television requires 2 hours and a DVD Player requires 3 hours of production time. Televisions cannot be manufactured in the fourth quarter because the company plans to modify tooling for a new product line.

Assume that each Television left in inventory at the end of a quarter incurs a holding cost of $5 and that each DVD Player left in inventory at the end of a quarter incurs a cost of $7. The proprietor wants to plan its production schedule over the year in such a way that it meets the quarterly demands and minimizes the total inventory cost.

1. Formulate a LINDO script, constraints and variables

2. Solve this production planning problem.

2. Assume the solution need not be integer.

3. Without resolving state what an extra hour of production time in Q3 is worth.

Product	Q1	Q2	Q3	Q4
Televisions	1500	1000	2000	1200
DVD Players	1000	2000	1500	2500

Solution

MIN = 5*Television + 7*DVD;

Televisions<4,500:

DVD Players<7,000:

5/14,400*Televisions + 7/28,800 *DVD Players

SETS

  Televisions/Q1..Q4/:Capacity

  DVD players/Q1..Q4/:Capacity

ENDSETS

SETS:

Product/ X/Y;

Inventory Reduction cost L M/;

Give(product inventory reduction cost)/X L, X M, Y M/;

ENDSETS

         @FOR(Television(T): Reduction Cost (T) = 2,250

         @FOR(DVD Players(D): Reduction Cost(D)=  3,150

TOTAL_COST=@SUM(Television (T):(DVD Players(D): Reduction Cost(J));

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Product         Q1           Q2          Q3          Q4

Televisions    1,500         1,150      2,150       150

Inventory Cost= NIL          $750       $750      $750

Product         Q1           Q2          Q3          Q4

DVD Players    1,000       2,150       1,650       2,650

Inventory cost  NIL       $1,050       $1,050      $1,050

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Only 2 hours can be given extra hour of production time in Q3 is worth, for the television, because 4th quarter does not manufacture televisions so that time can be used for quarter 3.

DVD players not available any extra hour for Q3.

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