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 Chocolate BacioDemand (kg/hours) 5 10 15setup time (minutes) 45 20 15Bruno 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.)a. Suppose they operate with a production cycle of 150 kgs (25 kg of fragola, 50 kgs of chocolato and 75 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.)b. Suppose they operate with a production cycle of 150 kgs (25 kg of fragola, 50 kgs of chocolato and 75 kgs of bacio). What is the utilization of the gelato making process?_________%(Round your answer to 2 decimal places.)c. Suppose they operate with a production cycle of 150 kgs (25 kg of fragola, 50 kgs of chocolato and 75 kgs of bacio). What is the average inventory of chocolato?_______kgs(Round your answer to 2 decimal places.)d. 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?_______kgs(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

Answer 1

Answer:

a. Capacity = 33.64 kg/hour

b. Utilization = 70.09%  

c. Average inventory = 19.79 kg

d. The desired Batch size = 106 kg

e. 17.77 kg of Fragola must be produced.

Explanation:

For part a:

We have the formula of Batch size:

Batch size = (Capacity x Setup time)/(1 - Capacity x Processing time)

Here, we have:

Setup time = 3/4 hours + 1/3 hours + 1/4 hours = 4/3 hours

Batch size = 150 kg

Processing time = 1/48 hr/kg

Solve for Capacity now,

Capacity = 33.64 kg/hour

For Part B:

We have the formula of Utilization as:

Utilization = Actual capacity / Designed capacity

Utilization = 33.64/48 x 100 = 70.09%

Utilization = 70.09%

For part C:

We know that, The Flow Rate of chocolato is 10 kgs/hr

And The processing time of chocolato is 1/48 hr / kg

And Chocolato is 1/3 of total demand, so the batch  size for chocolato is 1/3 x 150 = 50 kgs.

Formula for Average inventory is:

Average inventory = (1/2) x Batch size x (1- Flow rate x Processing

time)

Average inventory = 0.5 x 50 x (1 – 10 x 1/48 )

Average inventory = 19.79 kg

For part d:

We already know the formula for Batch size. So,

Batch size = (Capacity x  Setup time)/(1- Capacity x Processing time)

Each batch consists of three flavors, so:

We know the following data as well:

Setup time = 3/4 hours + 1/3 hours + 1/4 hours = 4/3 hours

Desired Capacity = 5 kg + 10 kg + 15 kg = 30 kg

Processing time = 1/48 hr/kg

Hence,

The desired batch size =  (30 x 4/3)/(1 - (30 x 1/48)) = 106 kg

The desired Batch size = 106 kg

For Part e:

Fragola is 5/30 of the total demand, so produce:

(5 kg/30 kg)/(106 kg) = 17.77 kg

17.77 kg of Fragola must be produced.