Question

A local firm manufactures children's toys. The projected demand over the next four months for one particular model of toy robot is as follows:

MONTH---------------WORKDAYS------------FORECAST DEMAND (IN AGGREGATE UNITS)

July 23 3825

August   16 7245

September 20 2770

October 22 4440

Assume that the normal workday is 8 hours. Hiring costs are $350 per worker and firing costs (including severance pay) are $850 per worker. Holding costs are $4 per aggregate unit held per month. Assume that it requires an average of 1 hour 40 min for one worker to assemble one toy. Shortages are not allowed. Assume that the ending inventory for June was 600 of these toys and the manager wishes to have at least 800 units on hand at the end of October. Assume that the current workforce level is 35 workers.

a. Find the minimum constant workforce plan for the four month and the total hiring, firing, and holding cost of that plan.

b. determine the plan that changes the workforce level each month to most closely match the demand and the cost of that plan.

solve it using manual tables and calculations. NOT EXCEL OR LINEAR PROGRAMMING

Answer 1

Given data-

Normal Workday time-8 hrs.

Hiring cost per worker-$ 350

Firing Cost per Worker( Including severance pay)-$ 850

Holding Cost per Aggregate unit per month-$ 4

Time taken assembling one toy by one worker-1 hr 40 min

Ending Inventory for june-600 units

Current workforce-35 workers

In hand inventory Required in October end-800 units

Month	Workdays	Forcast Demand ( in Aggregate units)
July	23	3825
August	16	7245
September	20	2770
October	22	4440

(a) Min constant workforce plan for four months-

let us have min constant 35 workers for four months.

for July-

Toys inventory in hand-600 toys.

toy produced by one worker in one day=8 hrs/1hr 40 min

=480 minutes/100 minutes=4.8 toys

Toy produced by 35 workers in 1 day=35*4.8=168 toys

toy produced in 23 days=168*23=3864 toys

Now total toys available=3864+600=4464 toys

toy Dispatched in month of july=3825 toys

Closing toys inventory in July=639 toys

For August-

Toys Inventory in hand-639 toys.

Toys demand-7245 Toys.

Toys can be Produced with 35 workers in 16 days=35*4.8*16=2688 toys

Toys required after adjusting previous inventory=3918 toys

more workers required to complete this order in 16 days=3918/4.8*16=51 workers

With these workers we will produce toys in 16 days=51*4.8*16=3916 toys

Now total toys in august-3916+3918=7834 toys

Closing toy inventory in august=7834-7245=589 toys.

Hiring cost of workers=51*350=$ 17850

firing cost after august=51*850=$ 43350

For September-

Opening inventory-589 toys

Toy will produce in 20 days by 35 workers=35*20*4.8=3360 toys

Closing inventory after dispatching 2770 toys=3360-2770=590 toys

For October-

Opening inventory=590 toys

Toy will produce by 35 workers in 22 days=35*22*4.8=3696 toys.

we require 9 more workers to fulfil the condition of 800 units at the oct end.

hiring cost of 9 workers=9*350=$ 3150

firing cost of 9 workers=9*850=$7650

(b)

for july-

we require only 30 workers for this month order

opening inventory=600 toys.

30 workers will produce in 23 days=30*4.8*23=3312 toys.

closing inventory after dispatching this order=3912-3825=87 toys

firing cost of 5 employees=5* 850=$ 4250

For august-

here we need 63 more employees to complete the order

hiring cost of 63 employees=63*350=$ 22050

Firing cost of 63 employees=63*850=$ 53550

For Sep-

30 workers will produce in 20 days=30*20*4.8=2880 toys