Question

There is no solution for question 7.3 in the textbook Matching Supply with Demand. Third edition

Bruno Fruscalzo decided to set up a small production facility in Sudney to sell at local restaurants that want gelato on their desser 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/hr) 10 15 5

set up time (hours) 3/4 1/2 1/6

Bruno first produces a batch of fragola, then a batch of chocolato, then a batch of bacio and tehn he repeats the 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 one flavor at a time)

a. suppose runo wants to minimize the amount of each flavor produced at one time while still satisfying teh demand for each of teh 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 flacor, how many kilograms should he produce each batch?

b. Given the answer in part (a), how many kilograms of fragola should he make with each batch?

c. Given your answer in part (a), what is the maximum inventory of chocolato? ( Assume production and demand occur at constant rates)

Answer 1

Fragola	Chocolate	Set-up	Bacau	Set-up	Fragile
		10 min		45 min

Total Set-up Time: 3/4 + 1/2 + 1/6 = 17/12 hours

Capacity demanded: 10 + 15 + 5 = 30 kg/hour

Rate: 50 kg/hour = 1/50 hours/kg

                               

Batch Size = (Capacity * S) / ((1-Capacity)*PT)

                  = (30 * 17/12) / ((1-30) * 1/50)

                  = 106 kg (Part A)

Fragile: 106 * (10/35) = 35.42 kg (Part B)