Bruno Fruscalzo decided to setup a small production facility in Sydney to sell t

Question

Bruno Fruscalzo decided to setup a small production facility in Sydney to sell to the local restaurants who want to offer gelato on their dessert menu. To start simple, he would offer only 3 flavors of gelato: fragola (strawberry), chocolato (chocolate), and bacio (chocolate with hazelnut). After a short time he determined his demand and setup times, as shown in the table below Fragola Chocolato Bacio 10 20 Demand (kg/hours)5 15 Setup time (minutes) 45 15 Bruno first produces a batch of fragola, then a batch of chocolato, then a batch of bacio and then he repeats that sequence For example, after producing bacio and before producing fragola, he needs 45 minutes to setup the ice cream machine, but he needs 15 minutes to switch from chocolato to bacio. When running, his ice cream machine produces at the rate of 48 kgs per hour no matter which flavor it is producing (and of course it can produce only one flavor at a time) (Round your answer to 2 decimal places.) Suppose they operate with a production cycle of 120 kgs (20 kg of fragola, 40 kgs of chocolato and 60 kgs of bacio). What is the capacity of the gelato making process (in kgs per hr)? kgs per hour (Round your answer to 2 decimal places.) Suppose they operate with a production cycle of 120 kgs (20 kg of fragola, 40 kgs of chocolato and 60 kgs of bacio). What is the utilization of the gelato making process? (Round your answer to 2 decimal places.) Suppose they operate with a production cycle of 120 kgs (20 kg of fragola, 40 kgs of chocolato and 60 kgs of bacio). What is the average inventory of chocolato? (Round your answer to 2 decimal places.) Suppose Bruno wants to minimize the amount of each flavor produced at one time while still satisfying the demand for each of the flavors. (He can choose a different quantity for each flavor.) If we define a batch to be the quantity produced in a single run of each flavor, how many kgs should he produce in each batch? (Round your answer to 2 decimal places.) e. Given your answer to part (d) how many kgs of fragola should he make with each batch?

Explanation / Answer

a. Setup time = 45+20+15 = 80 min

Run time = (210/48)*60 = 262.5 minutes

Total Production time = 80+262.5 = 342.5 minutes = 5.7083 hours

Capacity = 210 kg / 5.7083 hours = 36.79 kgs per hour

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b.

Actual demand or output rate = 5+10+15 = 30 kgs per hour

Utilization = Actual output / Design capacity = 30/36.79 = 0.8155 or 81.55 %

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c.

Maximum inventory of Chocolato = 70*(1-10/48) = 55.41 kg

Minimum inventory = 0

Average inventory during the first production cycle = (55.41+0)/2 = 27.71 kgs

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d. In order to minimize the inventory, total production should be equal to total demand over the production cycle time and utilization should be 100%.

let x be the batch size, i.e. total quantity of 3 flavors produced

Cycle time = x/48 + 80/60 hours

Demand rate = 5+10+15 = 30 kgs per hour

Total demand during cycle time = (x/48+8/60)*30 = 0.625x + 40

We know that total output during cycle time = x

Equating the demand and output

x = 0.625x + 40

x = 40/(1-0.625) = 106.67 kgs

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e. Quantity of fragola he should make = 106.67*5/30 = 17.78 kgs

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