4) (40 points) ice cream: vanilla, chocolate, strawberry and peanut fudge. Each

Question

4) (40 points) ice cream: vanilla, chocolate, strawberry and peanut fudge. Each b produced in the same la your grandma. Currently you produce four flavors of atch of ice cream is rge vat, thus you can produce only one batch at a time. Currently you have the following orders of ice cream: Flavor Vanilla Order size (gallons 385 450 190 170 Due Date Chocolate Strawberry Peanut fudge It takes one day to make ice cream and a maximum of 100 gallons can be produced orn one day Also, the production of one flavor has to be completed before the next flavor can be produced, and you cannot switch flavors in mid-day. Treat each ice cream flavor as a different job. a) Find the sequence that minimize the mean flow time for all the flavors. b) Find the sequence that minimizes the number of flavors that are late. c) Now management (you) decided that you always have to produce vanila and strawberry before the other flavors! Find the optimal sequence of the flavors to minimize the maximum lateness using Lawler's algorithm. Part lI) Dillons Bakery has received a rush order for five specialty cakes: a wedding cake, a birthday cake, a graduation cake, a retirement cake and an anniversary cake. Baking these cakes involve two processes: baking and decorating (in that order). The time required for each job differs followi the processed so that the rush order will be completed as soon as possible. Find that completion time (i.e. find that makespan) ing processing times (in hours) determine the order in which the cakes should be Cake Birthday Wedding Anniversary Retirement Graduation

Explanation / Answer

A maximum of 100 gallons of icecream can be produced per day. So processing time required for each ice cream is as follows:

Vanilla = 385/100 = 3.85 ~ 4 days (roundedup, because you cannot switch flavors mid-day, so although production of Vanilla will finish in 3.85 days, but the next flavor could be produced starting next day only, i.e. 5th day)

Chocolate = 450/100 = 4.5 ~ 5 days

Strawberry = 190/100 = 1.9 ~ 2 days

Peanut Fudge = 170/100 = 1.7 ~ 2 days

a) The sequence that minimizes mean flowtime is obtained by Shortest Processing Time (SPT) rule. JOb with the shortest processing time is scheduled first.

Flowtime is obtained by formula: Flowtime of this job = Flowtime of previous job + procesing time of this job.

Mean flowtime = (2+4+8+13)/4 = 6.75

b) Due date of Vanilla is 3, which is less than its process time (4 days). Therefore, to minimize the number of late jobs, there is no use to schedule Vanilla earlier, and hence it should be scheduled at last.

Rest of the three jobs should be scheduled as per Earliest Due Date rule. So, Strawberry should be scheduled first, followed by Chocolate and Peanut Fudge. Resultiing sequence is as follows

Lateness is measured as: Flowtime - Due Date

Number of jobs that are lates = 1 (Vanilla)

c) According to Lawler's algorithm, look for jobs with no predecessors or successors. It is given that Vanilla and Strawberry have to be produced first. So, these tasks do not have predecessors.So we schedule them first and the other two flavors at last. The first two and last two jobs are scheduled as per EDD rule to minimize the lateness

Maximum Lateness = 3

SPT sequence Flavor(Job) Order size Processing time Due Date Flowtime Peanut Fudge 170 2 11 2 Strawberry 190 2 6 4 Vanilla 385 4 3 8 Chocolate 450 5 8 13

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