Practice problems set 2 - Kassem Mahfouz PDF

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Practice Problems Set 2

By: Kassem Mahfouz

Professor: Krzystzof Fleszar MBA – DCSN 310

Practice Problems Set 1

Project Management Consider the dependency matrix and the activity durations provided below. Information providing activity A1

A2

A3

A4

A5

A6

A7

A8

X

X

A9

Information receiving activity

A1 A2

X

A3

X

A4

X

A5

X

A6

X

A7

X

A8

X

A9 A10

X

X

A10

Activity

A1

A2

A3

A4

A5

A6

A7

A8

A9

A10

Time

5

4

8

5

1

12

4

7

6

2

1. Build a project graph, visually depicting the evolution of this project.

2. Find the critical path. What is the earliest time that the project can be completed? The critical path: Path 1: A1  A2  A4  A10: 5+4+5+2 = 16 days Path 2: A1  A2  A5  A7  A9  A10: 5+ 4+ 1+ 4+ 6+ 2= 22 days Path 3: A1  A3  A6  A8  A9  A10: 5+ 8+ 12+ 7+ 6+ 2= 40 days The critical path is path 3: it is the earliest time that the project can be completed which is in 40 days.

3. For each activity, compute the latest start time, the latest completion time, and the slack time. *They are computed in the figure above (question 1)

Project Management with Uncertainty A small project consists of activities: A, B, C, D, and E. In order to start activity E, all other activities (A, B, C, and D) need to be completed. The duration of activity A will be 1 day with probability 50% or 9 days with probability 50%. Activities B, C, and D have the same random duration distribution as activity A. Assume durations of activities A, B, C, and D are independent from each other. Activity E takes 1 day. What is the expected completion time of the project?

Scenario A: Late B: Late C: Late D: Late

Probability 0.0625

Start of E 9 since A, B, C, D would take 9 days

Completion 10

A: Early B: Late C: Late D: Late A: Late B: Early C: Late D: Late A: Late B: Late C: Early D: Late A: Late B: Late C: Late D: Early A: Early B: Early C: Late D: Late

0.0625

A: Early B: Late C: Early D: Late

0.0625

A: Early B: Late C: Late D: Early

0.0625

A: Late B: Early C: Early D: Late

0.0625

A: Late B: Early C: Late D: Early

0.0625

A: Late B: Late C: Early D: Early

0.0625

A: Early

0.0625

0.0625

0.0625

0.0625

0.0625

9, since A would take 1 day but B, C, D would take 9 days 9, since B would take 1 day but A, C, D would take 9 days 9, since C would take 1 day but A, B, D would take 9 days 9, since D would take 1 day but A, B, C would take 9 days 9, since A & B would take 1 day each but C & D would take 9 days each 9, since A & C would take 1 day each but B & D would take 9 days each 9, since A & D would take 1 day each but C & B would take 9 days each 9, since B & C would take 1 day each but A & D would take 9 days each 9, since B & D would take 1 day each but A & C would take 9 days each 9, since C & D would take 1 day each but A & B would take 9 days each 9, since A,B & C

10

10

10

10

10

10

10

10

10

10

10

B: Early C: Early D: Late A: Early B: Early C: Late D: Early A: Early B: Late C: Early D: Early A: Late B: Early C: Early D: Early A: Early B: Early C: Early D: Early

would take 1 day each but D would take 9 days 9, since A,B & D would take 1 day each but C would take 9 days 9, since A,C & D would take 1 day each but B would take 9 days 9, since B,C & D would take 1 day each but A would take 9 days 1, since A,B,C,& D would all take 1 day

0.0625

0.0625

0.0625

0.0625

10

10

10

2

Completion time= 0.0625 (probability)  15 (scenarios in which project finishes in 10 days)  10 + 0.0625  1 (1 scenario in which project finishes in 2 days)  2= 9.5 days

Gelato (Capacity Analysis with Batching and Setup Times) 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

Demand (kg/hour) Setup time (hours)

Fragola

Chocolato

10 3/4

15 1/2

Baci o 5 1/6

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 one flavor at a time).

1. 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 of all flavors produced in a single cycle, how many kilograms should he produce in each batch? Setup time= ¾ + ½ + 1/6 = 17/12 hours = 85 minutes Demand per hour= 10+15+5 = 30 kg/hr = 0.5 kg/min Time per each unit: 1.2 min/kg Capacity: Batch size/((setup time) + Batch Size x time per unit) Batch size = capacity * ((setup time) + Batch Size x time per unit) Batch Size = 0.5 x (85 + Batch size x 1.2) Batch Size = 42.5 + 0.6 batch size Batch Size = 106.25 kg

2. Given your answer in part 1, how many kilograms of fragola should he make with each batch? Fragola Quantity: 106.25 x 10/30 = 35.41 KG with each batch 3. Given your answer in part 1, what is the maximum inventory of chocolato? (Assume production and demand occur continuously at constant rates.) Inventory of chocolate: Batch Size x (1 – demand rate/production rate) Inventory of chocolate= 106.25 x (1-15/50) = 74.375 Kg Kinga Doll Company (Batching and Setup Times) Kinga Doll Company manufactures dolls in three steps: molding, painting, and dressing. The table below lists the required processing and setup times at each step. The same batch size is used in all steps. A setup can begin on a machine only after the previous batch is finished and a complete batch is transferred from the preceding machine. For what batch sizes will painting be a bottleneck?

Setup Time Activity Time

Molding Machine 45 min 0.15 min/unit

Painting Machine 20 min 0.20 min/unit

Batch Size: BS Time required for molding: 45 min + 0.15 * BS Time required for painting: 20 min + 0.2 * BS

Dressing Machine No setup 0.25 min/unit

Time required for dressing: 0.25 * BS First option: 20 + 0.2 BS >= 0.25 BS 0.25 BS – 0.2 BS = 25 B >= 500 Thus we can conclude that if a batch is more than 500, the painting will be the bottleneck....