JL.51 Carl\'s Custom Cans produces small containers which are purchased by candy

Question

JL.51 Carl's Custom Cans produces small containers which are purchased by candy and snack food producers. The production facility operates 300 days per year and has annual demand of 12,000 units for one of its custom cans. They can produce up to 100 of these cans each day. It costs $50 to set up one of their production lines to run this can. (Carl pays $12 per hour for setup labor.) The cost of each can is $1 and annual holding costs are $0.50 per can.

1. What is the optimal size of the production run for this can? (Round your answer to the nearest whole number.)

2. How many production runs will be required each year? (Round your answer up to the nearest whole number.)

3. Suppose the customer for this custom can wants to purchase in quantities of 1,000 units. What is the required setup cost to make this order quantity an optimal production run quantity for Carl's Custom Cans? $ (Round your answer to two decimal places.)

4. Based on your answer to the previous question (reduced setup cost), how long (in minutes) should it take to set up this production line? minutes (Round your answer to two decimal places.)

Explanation / Answer

1). Demand rate = 12000/300 = 40 per day

Optimal Production run size as per EPQ model = (2*annual demand*setup cost / holding cost / (1 - demand rate/production rate)^0.5 = (2*12000*50/0.5/(1-40/100))^0.5 = 2000 units

2). Number of production runs required per year = 12000/2000 = 6 runs per year

3). Required setup cost = 1000^2*0.5*(1-40/100)/2/12000 = $ 12.5 per setup

4). Time required to setup = Total setup cost / labor cost per hour*60 = 12.5/12*60 = 62.50 minutes

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