Decision Making

The maximum units that can be assembled in one month are: 3000 chairs, 1000 tables and 580 bookshelves.

Total time required to assemble all the units = (3000*20)+(1000*40)+(580*15) min = 108,700 min

Total labor minutes available when all employees are available (assuming 4 weeks a month) = 150*8*5*4*60 min = 1,440,000 min

Month | No. of employees available | Total Labor minutes |

May | 130 | 1,248,000 |

June | 125 | 1,200,000 |

July | 105 | 1,008,000 |

Since the labor hours available clearly outnumber the time required in assembling maximum capacity production, leave can be granted without any issues.

ASSUMPTIONS:

* All the pending leaves for the months of May, June, July have been granted

* Ending inventory of July is zero

VARIABLES:

Variable | Description |

x1 | No. of chairs assembled in May |

x2 | No. of chairs assembled in June |

x3 | No. of chairs assembled in July |

y1 | No. of tables assembled in May |

y2 | No. of tables assembled in June |

y3 | No. of tables assembled in July |

z1 | No. of book-shelves assembled in May |

z2 | No. of book-shelves assembled in June |

z3 | No. of book-shelves assembled in July |

CONSTRAINTS:

The no. of products to be assembled, are constrained by production capacity of plant.

* x1, x2, x3 <= 3000

* y1, y2, y3 <= 1000

* z1, z2, z3 <= 580

Another constraint is in the form of availability of labor hours (it may not be a binding constraint)

* 20x1+40y1+15z1 <= 1,248,000

* 20x2+40y2+15z2 <= 1,200,000

* 20x3+40y3+15z3 <= 1,008,000

There are also some demand constraints so as to meet the sales forecast and maintain minimum inventory to minimize storage cost. Assuming that ending inventory in July is zero

* x1+30 >= 2800

* x1+30+x2 >= 2800+2300

* x1+30+x2+x3 = 2800+2300+3350

* y1+100 >= 500

* y1+100+y2 >= 500+800

* y1+100+y2+y3 = 500+800+1400

* z1+50 >= 320

* z1+50+z2 >= 320+300

*...