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 Demand (kg/hours) 15 Setup time minutes 10 35 25 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 35 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 50 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 240 kgs (120 kg of fragola, 80 kgs of chocolato and 40 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.) h Suppose they operate with a production cycle of 240 kgs (120 kg of fragola, 80 kgs of chocolato and 40 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 240 kgs (120 kg of fragola, 80 kgs of chocolato and 40 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 kas of fragola should he make with each batch?kas

Answer 1

a)

Capacity = Batch size / (Total setup time + Batch size * Processing time)

Total setup time = (35+25+15)/60 = 75 minutes = 1.25 hours

Processing time = 1/50 hours per kg

Capacity = 240 / (1.25 + 240*1/50) = 39.67 kgs per hour

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b)

Utilization = 39.67 / 50 = 79.34 %

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c)

Average inventory of Chocolato = Batch size * ( 1- Demand rate / Production rate) / 2

= 50 * ( 1 - 10 / 50) / 2

= 20 kgs

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d)

To minimize the inventory, we need to make the production cycle time equal to demand cycle time.

Let Q be the batch size in kg

Production cycle time = Setup time + Batch size * processing time = 1.25 + Q * 1/50   ---(1)

Total demand rate = 15+10+5 = 30 kg per hour

Demand cycle time = Q / 30 ---(2)

Equating (1) and (2), we get

1.25 + Q/50 = Q/30

Q/30 - Q/50 = 1.25

Q = 93.75 kg

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e)

Quantity of Fragola to make in each batch = 93.75*15/30 = 46.875 kg

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