A manufacturer of roofing supplies has developed a monthly forecast for their products. Data for the first 6 months of the year is presented in the table below. The company would like to begin development of an aggregate plan

mounth. forecast production days

January 8000. 21

February. 8000. 20

march. 15000. 23

April. 10000. 18

may 14000. 21

jun. 7000. 21

sum. 62000. 124

last year the company produced exactly 125000 unit. the year consisted of 250 working days, and the company had on average 1000 employees working every day.

a) calculate the K-factor i,e how much one worker in average will produce I one day.

the cost of hiring one worker is approximately $400, and the cost of firing a worker is approximately $800. the cost of storing one unit of inventory in one month is estimated to $40. other cost are not considered in this example.

the company has 1000 workers employed at the end of December and has a stock of 2000 units of inventory. they would also plan with a stock of at least 2000 units at end of the planing period.

b) develop a production plan for the company using the Chase ( Zero - inventory ) strategy and find the cost of this solution.

c) develop another production plan by using the constant workforce strategy and find the cost of this solution.

d) by using more advanced optimization software, a third potential solution is found. this solution suggest that the number of workers for each of the six month should be 726, 726, 1228, 1230, 1231, 1231, respectively. calculate the cost of this production.

e) Analyse the three difference solutions. compare the cost, and describe eventual structural difference between them.