Cost Optimization: Linear Programming Model for Business Development

This assignment presents a linear programming model designed to minimize costs for a business. The student developed a model incorporating various factors, including hiring and firing costs, production quantities, overtime hours, and demand. The objective function aims to reduce total expenses, while constraints address integer values for workers, production capacity, and demand fulfillment. The analysis includes input variables such as initial inventory, worker count, wages, and costs related to labor and materials. The model calculates and analyzes key metrics like total production hours, shoe production, stock levels, and monetary outputs across four months. Finally, the assignment provides recommendations to the CEO, suggesting optimal staffing levels to balance demand and minimize costs, ultimately enabling the business unit to achieve its objectives.

Linear Programming

TABLE OF CONTENTS
REQUIREMENTS......................................................................................................................................................................................3
1. Developing a LP model for the problem given...................................................................................................................................3
2...............................................................................................................................................................................................................3
3. Giving recommendations to the CEO of company..............................................................................................................................6

REQUIREMENTS
1. Developing a LP model for the problem given
Linear programming model:
B18 + C18 + D18 + E18
B19+ C19 + D19 + E19
B24 + C24+ D24 + E24
Decision variables:
 Number of workers hired and fired (monthly value)
 Number of shoes produced
 Overtime hours used
Objective: Reduction of total cost
Min = $F$50
Constraints:
$B$18:$E$18 = integer
$B$18:$E$18 = integer
$B$24:$E$24 <= 3520
$B$32:$E$32 <= 10560

$B$36:$E$36 >= 11000
Z1 + Z2 + Z3 + Z4 >= 11000
 Overtime labor hours used must be less than and equal to maximum allowance
 Production must be < or = to capacity
 Stock in hand after production must be > or = to the demand level

2.
Production function and labor policy
Input variables:
Input Data
Initial Inventory 500
Initial workers 20
Standard working hours 160
Max overtime hours 20
Hiring cost
$
1,600.00
Firing cost
$
2,000.00
Regular wages
$
1,500.00
Overtime wage rate
$
13.00
labour hours
$
4.00
Raw material cost
$
15.00
Holding cost
$
3.00
Shortage cost
$
20.00
Total forecasted demand 11000
Stock after production 52200
Availability of maximum labor 3520

hours
Overtime labor hours 14080
capacity related to production 10560
shoes manufactured 28160
Total cost
192504
0
workers fired by CEO 47
Workers hired by CEO 86
Worker plan Month 1 Month 2 Month 3 Month 4
Workers from previous month 20 66 20 31
Workers hired 47 0 11 28
workers fired 1 46 0 0
Workers available after hiring and
firing 66 20 31 59
Regular time available (in hours) 10560 3200 4960 9440
Overtime labor hours used 3520 3520 3520 3520
Maximum overtime labor hours
available 1320 400 620 1180
Total production hours 14080 6720 8480 12960
Production plan Month 1 Month 2 Month 3 Month 4
Shoe produced 10560 3200 4960 9440

Production capacity
$
3,520.00
$1,680.0
0
$
2,120.00
$
3,240.00
Stock after production 11060 11260 11220 18660
Forecasted demand 3000 5000 2000 1000
Closing stock 8060 6260 9220 17660
Monetary outputs Month 1 Month 2 Month 3 Month 4
Hiring cost 75200 0 17600 44800 137600
Firing cost 2000 92000 0 0 94000
Regular time wages 99000 30000 46500 88500 264000
Overtime wages 45760 45760 45760 45760 183040
Raw material cost 158400 48000 74400 141600 422400
Holding cost 161200 125200 184400 353200 824000
Total 541560 340960 368660 673860 1925040
Objective
is to
minimize
total cost
3. Giving recommendations to the CEO of company
From assessment, it has found that CEO of the business unit should hire 47 personnel and fire 1 employee for meeting demand
as well as reducing the cost level. Thus, by taking into account above LP model business unit would become able to accomplish its
goals and objectives.