Exercise $8\mathrm{.}1$ Exercise $8\mathrm{.}1$

Skycell, a major European cell phone manufacturer, is making production plans for the coming year.

Skycell has worked with its customers $($the service providers$)$ to come up with forecasts of monthly

requirements $($in thousands of phones$)$ as shown in the table below. Manufacturing is primarily an

assembly operation, and capacity is governed by the number of people on the hours each day. One

person can assemble a phone every $10$ minutes. Workers are paid $20$ euros per hour and a $50$ per$-$cent

premium for overtime. The plant currently employs $1,250$ workers. Component costs for each cell

phone total $20$ euros. Given the rapid decline in component and finished$-$product prices, carrying

inventory from one month to the next incurs a cost of $3$ euros per phone per month. Skycell currently

has a no$-$layoff policy in place. Overtime is limited to a maximum of $20$ hours per month per employee.

Assume that Skycell has a starting inventory of $50,000$ units and wants to end the year with the same

level of inventory.

a$.$ Assuming no backlogs, no subcontracting, and no new hires, what is the optimum production

schedule?

b$.$ What is the annual cost of this schedule?

c$.$ Is there any value for management to negotiate an increase of allowed overtime per employee

per month from $20$ hours to $40?$

d$.$ Reconsider parts $($a$)$ and $($b$)$ if Skycell starts with only $1,200$ employees. Reconsider parts $($a$)$ and

$($b$)$ if Skycell starts with $1,300$ employees. What happens to the value of additional overtime as

the workforce size decreases?

e$.$ Consider part $($a$)$ for the case in which Skycell aims for a level production schedule such that the

quantity produced each month does not exceed the average demand over the next $12$ months

$(1,241,667)$ by $50,000$ units. Thus, monthly production, including overtime, should be no more

than $1,291,667.$ What would be the cost of this level production schedule?

Monthly Demand for Cell Phones, in Thousands

Skycell, a major European cell phone manufacturer, is making production plans for the coming year.

Skycell has worked with its customers $($the service providers$)$ to come up with forecasts of monthly

requirements $($in thousands of phones$)$ as shown in the table below. Manufacturing is primarily an

assembly operation, and capacity is governed by the number of people on the hours each day. One

person can assemble a phone every $10$ minutes. Workers are paid $20$ euros per hour and a $50$ per$-$cent

premium for overtime. The plant currently employs $1,250$ workers. Component costs for each cell

phone total $20$ euros. Given the rapid decline in component and finished$-$product prices, carrying

inventory from one month to the next incurs a cost of $3$ euros per phone per month. Skycell currently

has a no$-$layoff policy in place. Overtime is limited to a maximum of $20$ hours per month per employee.

Assume that Skycell has a starting inventory of $50,000$ units and wants to end the year with the same

level of inventory.

a$.$ Assuming no backlogs, no subcontracting, and no new hires, what is the optimum production

schedule?

b$.$ What is the annual cost of this schedule?

c$.$ Is there any value for management to negotiate an increase of allowed overtime per employee

per month from $20$ hours to $40?$

d$.$ Reconsider parts $($a$)$ and $($b$)$ if Skycell starts with only $1,200$ employees. Reconsider parts $($a$)$ and

$($b$)$ if Skycell starts with $1,300$ employees. What happens to the value of additional overtime as

the workforce size decreases?

e$.$ Consider part $($a$)$ for the case in which Skycell aims for a level production schedule such that the

quantity produced each month does not exceed the average demand over the next $12$ months

$(1,241,667)$ by $50,000$ units. Thus, monthly production, including overtime, should be no more

than $1,291,667.$ What would be the cost of this level production schedule?

Monthly Demand for Cell Phones, in Thousands

Month Demand

January $1,000$

February $1,100$

March $1,000$

April $1,200$

May $1,500$

June $1,600$

July $1,600$

August $900$

September $1,100$

October $800$

November $1,400$

December $1,700$

$\backslash$table$[[,,,,],[$Input Data $($Demand$),,$Input Data $($Costs etc.$),,],[,,,$Cost,$],[$Month$,$Demand,,Item,$],[$January$,,$Materials cost$/$unit$,,],[$February$,,$Inventory holding cost$/$unit$/$month$,,],[$March$,,$Marginal cost of stockout$/$unit$/$month$,,],[$April$,,$Hiring and training cost$/$worker$,,],[$May$,,$Layoff cost$/$worker$,,],[$June$,,$Labor hours required$/$unit$,,],[$July$,,$Regular time cost$/$hour$,,],[$August$,,,$Over time cost$/$hour$,],[$September$,,,$Marginal subcontracting cost$/$unit$,],[$October$,,,,],[$November$,,,,],[$December$,,,$Initial Workforce size,$],[,,,$Maximum overtime per worker per month,$],[,,,,]]$