Bruno Fruscalzo decided to set up a small production facility in Sydney to sell to local restaurants that want to offer gelato on their dessert menu. To start simple, he would offer only three flavors of gelato: fragola (strawberry), Chocolato (chocolate), and bacio (chocolate with hazelnut). After a short time he found his demand and setup times to be

Fragola Chocolato Bacio

Demand (kg/hour) 10 15 5

Setup time (minutes) 45 30 10

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 set up the ice cream machine, but he needs only 10 minutes to switch from chocolato to bacio. When running, his ice cream machine produces at the rate of 50 kg per hour no matter which flavor it is producing ( and, of course, it can produce only on flavor at a time).

Round answers to 2 decimal places.

a. Suppose they operate with a production cycle of 120 kgs (40 kg of fragola, 60 kgs of chocolato and 20 kgs of bacio). What is the capacity of the gelato making process (in kgs per hr)?

b. Suppose they operate with a production cycle of 120 kgs (40 kg of fragola, 60 kgs of chocolato and 20 kgs of bacio). What is the utilizatin of the gelato making process?

c. Suppose they operate with a production cycle of 120 kgs (40 kg of fragola, 60 kgs of chocolato and 20 kgs of bacio). What is the average inventory of chocolato?

d. Suppose Bruno wants to minimize the amount of each flavor produced at one time while stil 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?

e. Given your answer to part (d) how many kgs of fragola should he make with each batch?

## Expert Answer

Here, the bottleneck process would be to produce bacio because it takes 1/5 hrs for eack kg. Therefore Each batch consists of the three flavors. The total set up time is 45+30+10= 85 mins. Here, the bacth size given is 120 kgs (40 kg of fragola, 60 kgs of chocolato and 20 kgs of bacio). The machine produces only one flavor at a time at the rate of 50kgs/hr.

a. In the 120 kgs, 60 kgs is of chocolate. The rate is 50kgs/hr but the set up time is 30 mins, therefore 60 kgs will take 30/60 + 60/50= 1.7 hrs

after that we will produce 20kgs of bacio, but the set up time is 10 mins between the two, therefore, the time it will take with the same rate of 50kgs/hr is = 10/60 + 20/50 = 0.566 hrs

after that we will produce 40kgs of fragola, the set up time is 45 mins and with the same rate the time that it will take is = 45/60 + 40/50 = 1.55 hrs.

so, 120 kgs is produced in 1.2+0.566+1.55 = 3.816 hrs.

Therefore the capacity of the process is 120/3.816 = 31.446 kgs/hr.

b. The demand rate per hr is 10+15+5= 30kgs

The process capacity is 31.446kgs/hr

therefore, utilization = demand rate/ actual production capacity = (30/31.446) *100 = 95.4 %

c. average inventory of the whole process is 120/2= 60 kgs and since chocolato was 50% of the batch earlier therefore with the same percentage, 50% of 60 gives 30gs as average inventory for chocolato.

d. Each batch consists of a single flavor. The setup time for each is 45, 30 , 10 (mins) for fragola, chocolato and bacio, respy. The desired capacity is 10kg for fragalo, 15 kg for chocolato and 5 kg for bacio .The activity time is 1/50 hrs / kg.The desired batch size for fragilo is 10 x 85/60 / (1- 10 x1/50) = 17.7 kgs. The desired batch for chocolato is 10*85/60/(1-10/50)=11.33 kgs, for bacio it is 5*85/60/ (1-5/50)=7.87 kgs.