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), bacio (chocolate with hazelnut). After a short time he determined his demand and setup times, as shown in the table below. Demand (kg/hours) 5 45 Fragola Chocolato Bacio 10 20 15 Setup time (minutes) 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 180 kgs (30 kg of fragola, 60 kgs of chocolato kgs per hour and 90 kgs of bacio). What is the capacity of the gelato making process (in kgs per hr)? (Round your answer to 2 decimal places.) Suppose they operate with a production cycle of 180 kgs (30 kg of fragola, 60 kgs of chocolato and 90 kgs of bacio). What is the utilization of the gelato making process? b. (Round your answer to 2 decimal places.) Suppose they operate with a production cycle of 180 kgs (30 kg of fragola, 60 kgs of chocolato and 90 kgs of bacio). What is the average inventory of chocolato? kgs C. (Round your answer to 2 decimal places.) Suppose Bruno wants to minimize the amount of each flavor produced at one time while still d. satisfying the demand for each of the favors. (He can choose a different quantity for each flavor.) kgs 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? kgs

Explanation / Answer

a. With production cycle of 180 kgs, total production time = Sum of Setup times and processing times = 45+20+15+(180/48)*60 = 305 minutes

Capacity of the process = 180 kg / (305 minutes / 60 minutes per hour) = 35.40 kgs per hour

b. Production cycle time = 180/(5+10+15) = 6 hours

Total production time = 305 minutes = 5.083 hours

Utilization = 5.083/6 = 84.72 %

c. Average inventory of Chocolato = (Q/2)*(1-d/p) = (60/2)*(1-10/48) = 23.75 kgs

d. Let x be the total quantity produced in a single run.

For minimum amount of inventory, total production time must be equal to the production cycle time

(45+20+15)/60 + x/48 = x/30 (x/30 is the production cycle time, where 30 is total hourly demand of 3 flavors combined)

Solving for x, we get,

x = 106.67 kgs

e. Kgs of Fragola to make with each batch = 106.67*5/30 = 17.78 kgs

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