Filter Systems produces air filters for domestic and foreign cars. One filter, part number JJ39877, is supplied on an exclusive contract basis to Oil Changers at a constant 200 units monthly. Filter Systems can produce this filter at a rate of 50 per hour. Setup time to change the settings on the equipment is 1.5 hours. Worker time (including overhead) is charged at the rate of $55 per hour, and plant idle time during setups is estimated to cost the firm $100 per hour in lost profit. Filter Systems has established a 22 percent annual interest charge for determining holding cost. Each filter costs the company $2.50 to produce; they are sold for $5.50 each to Oil Changers. Assume 6-hour days, 20 working days per month, and 12 months per year for your calculations.

Required:
a. How many JJ39877 filters should Filter Systems produce in each production run of this particular part to minimize annual holding and setup costs?
b. Assuming that it produces the optimal number of filters in each run, what is the maximum level of on-hand inventory of these filters that the firm has at any point in time?
c. What percentage of the working time does the company produce these particular filters, assuming that the policy in part (a) is used?

a. EOQ = 1449 units are the optimal number of units of Filters to be produced.

b. I = 1400.7 units is the maximum level of on hand inventory any time.

c. Portion of Uptime = 3.3%

Explanation:

Solution:

a.

First of we need to find out the total demand of the filters per year.

D = Demand

D = 200 x 12

Total Demand per year D = 2400 units per year.

Secondly, we need to calculate the production capacity by using the following formula:

PC = Rate of the Production x months in a year x working hours x working days.

PC = 50 x 12 x 6 x 20

PC = 7200 units is the production capacity for a year.

Thirdly, we need to calculate the holding cost by using the following formula:

Holding Cost = Annual interest rate x Production cost per unit.

HC = 0.22 x 2.50

HC = 0.55 is the holding cost

Now, we need to find the modified holding cost as well by using the following formula:

HC' = HC(1- )  

Where,

D = Total Demand

PC = Production Capacity per year.  

Just Plugging in the values, we get:

HC' = 0.55 x (1 - )

HC' = 0.5317 USD per unit.

Finally, for part a, we need to find the Economic Order Quantity, by using the formula:

EOQ =

Where,

OC = Ordering Cost.

Just plugging in the values:

EOQ =

Hence,

EOQ = 1449 units are the optimal number of units of Filters to be produced.

b.

For this part, firstly, we need to find the inventory at any time:

I = EOQ x (1 - )

We already know all the values, so just plug in the value into the above equation to calculate inventory at any time:

I = 1449 x ( 1 - )

I = 1400.7 units is the maximum level of on hand inventory any time.

c.

For this final part, first we need to find the cycle time as below:

CT =

CT = 1449/2400

Hence, the cycle time is:

CT = 0.60375 per year.

Now, we need to find the uptime:

UT =

We already know the values, just plug them in:

UT = 1449/72000

UT = 0.0201 per year

Finally, with all the data collected, we can now calculate the portion of cycle time according to uptime in the production process as follows:

Portion of uptime =

Portion of Uptime = 0.0201/0.60375

Hence,

Portion of Uptime = 3.3%

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