QUESTION 1 Consider the aggregate planning problem of a golf cart manufacturing
ID: 337765 • Letter: Q
Question
QUESTION 1
Consider the aggregate planning problem of a golf cart manufacturing plant. The plant has a total of 20 working days in each month, and each employee works 8 hours per day on regular time. The labor hours required to produce one unit is 2 hours/unit. All stockouts are backlogged and supplied from the following months’ production. The following sales forecast is estimated for the next three months:
Period
Sales Forecast
(Units)
1- January
100
2- February
150
3- March
175
You will write a linear programming model to develop an optimal aggregate plan for the next three months using the following decision variables:
Hi= Employment level increase (hires) in Month i, i=1…3
Fi = Employment level decrease (fires) in Month i, i=1…3
Wi = Workforce level in Month i, i=1…3
Ii = Units of ending inventory in Month i, i=1…3
Si = Number of units backlogged at the end of Month i, i=1…3
Oi = Overtime hours worked in Month i, i=1…3
Xi = Number of units produced in Month i, i=1…3
Because of labor rules, no employee can work more than 8 hours of overtime per month. Which constraint below limits the total overtime hours for March ( i=3 ) to be no more than 8 hours for each worker?
X3 ? 8 O3
W3 ? 8 O3
O3 ? 8 X3
O3 ? 8 W3
QUESTION 2
For the previous question (Q1), which of the following gives the inventory balance constraint for the month of February ( i = 2), considering the inventory, backlog, production and demand.
I1 + X2 = 150 + S1 + I2 - S2
I1 + X2 = 150 + I2
I1 + X2 = 150 + I2 - S2
X2 = 150 + I2 - S2
QUESTION 3
For the previous question (Q1), which constraint limits the production for March (i=3) by the available capacity, assuming that the production capacity is determined primarily by the total labor hours worked?
X3 ? 80 W3
X3 ? 80 W3 + O3
X3 ? 80 W3 + O3 /2
X3 ? 160 W3
Period
Sales Forecast
(Units)
1- January
100
2- February
150
3- March
175
Explanation / Answer
QUESTION 1
Consider the aggregate planning problem of a golf cart manufacturing plant. The plant has a total of 20 working days in each month, and each employee works 8 hours per day on regular time. The labor hours required to produce one unit is 2 hours/unit. All stockouts are backlogged and supplied from the following months’ production. The following sales forecast is estimated for the next three months:
Period
Sales Forecast
(Units)
1- January
100
2- February
150
3- March
175
You will write a linear programming model to develop an optimal aggregate plan for the next three months using the following decision variables:
Hi= Employment level increase (hires) in Month i, i=1…3
Fi = Employment level decrease (fires) in Month i, i=1…3
Wi = Workforce level in Month i, i=1…3
Ii = Units of ending inventory in Month i, i=1…3
Si = Number of units backlogged at the end of Month i, i=1…3
Oi = Overtime hours worked in Month i, i=1…3
Xi = Number of units produced in Month i, i=1…3
Because of labor rules, no employee can work more than 8 hours of overtime per month. Which constraint below limits the total overtime hours for March ( i=3 ) to be no more than 8 hours for each worker?
X3 ? 8 O3
W3 ? 8 O3
O3 ? 8 X3
O3 ? 8 W3
QUESTION 2
For the previous question (Q1), which of the following gives the inventory balance constraint for the month of February ( i = 2), considering the inventory, backlog, production and demand.
I1 + X2 = 150 + S1 + I2 - S2
I1 + X2 = 150 + I2
I1 + X2 = 150 + I2 - S2
X2 = 150 + I2 - S2
QUESTION 3
For the previous question (Q1), which constraint limits the production for March (i=3) by the available capacity, assuming that the production capacity is determined primarily by the total labor hours worked?
X3 ? 80 W3
X3 ? 80 W3 + O3
X3 ? 80 W3 + O3 /2
X3 ? 160 W3
Period
Sales Forecast
(Units)
1- January
100
2- February
150
3- March
175
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