ASSIGNMENT-4 (week 12 to 14) QUANTITATIVE METHODS (STAT-201) Student Full Name: Student ID: CRN No.: Note: 1. All questions are compulsory. 2. Due date: December 28, 2016 11:59 PM. 3. Points: Section-I 16=6 Section-II 16=6 Section-III 63=18 Total 30 Section-I State whether the following statements are True or False. (16 = 6) 1- PERT is deterministic, whereas CPM is probabilistic. 2- PERT and CPM are quantitative analysis tools designed to schedule and control large project. 3- In a quantity discount model, the purchase cost or material cost must be included in the total cost calculation. 4- A Simulation model is designed to arrive at a single specific numerical answer to a given problem. 5- Reducing a project's completion time is called crashing. 6- PERT often assumes time estimates follow a beta probability distribution. Section-II Circle/tick the right answer from the answers given below. (16 = 6) 1- The critical path is the: (a) Shortest path in a network. (b) Longest path in a network. (c) Path with the smallest variance. (d) None of the above. 2- In a PERT network , the earliest (activity) start time is the: (a) Earliest time that an activity can be finished without delay in the entire project. (b) Latest time that an activity can be started without delay the entire project. 2 (c) Earliest time that an activity can start without violation of precedence requirements (d) Latest time that an activity can be finished without delay the entire project. 3- Slack time in a network is the: (a) Amount of time that an activity would take assuming very unfavorable condition. (b) Shortest amount of time that could be required to complete the activity. (c) Difference between the expected completion time of the project using pessimistic times and the expected completion time of the project using optimistic time. (d) Amount of time that an activity can be delayed without delaying the entire project. 4. When simulating the Monte Carlo experiment, the average simulated demand over the long run should approximate the; (a) Real demand. (b) Expected demand. (c ) Sample demand. (d) Daily demand. 5. The logic in a simulation model is presented graphically through which of the following: (a) Flow chart (b) Scatter plot (c) Blue prints (d) Decision tree 6. The \"point at which to reorder\" depends directly on which of the following? (a) EOQ (b) Ordering Cost (c) Lead time (d) Storage Costs Section-III Answer the following Essay Type Questions (63=18) 1. A small software development project has five major activities. The times are estimated and provided in the table below. Activity A B C Immediate Predecessor ----A a m b 2 10 4 5 10 7 8 10 10 3 D B 2 5 14 E C 3 3 3 Draw the PERT network associated with the activity and calculate expected time. 2. Development of a new deluxe version of a particular software product is being considered. This deluxe version has seven major activities. The times are estimated and provided in the table below: Activity Immediate Optimistic Most likely Pessimistic Predecessor a m b A B C D E F G ----A B B D, C E 3 6 6 0.5 2 4 1 4 7 9 1 3 5 3 5 14 12 1.5 10 12 11 (a) Construct a network for this problem (b) Determine the expected time and variance for each activity. 3. Jean Walker has laid out the major steps and eight activities to complete the wing assembly for an experimental air craft. These activities have been labeled A to H in the following table, which also shows their estimated completion time (in weeks) and immediate predecessors. Activity Immediate Predecessors a m b A --------1 2 3 B -------2 3 4 C A 1 2 3 D B 2 4 6 E C 1 4 7 F C 1 2 9 G D, E 3 4 11 H F,G 1 2 3 (a) Determine the earliest start, latest start and finish time and slack time for each activities. (b) Determine variance of the critical path and expected project completion length. 4. The number of cars arriving at a self-service gasoline station during the last 50 hours of operation are as follows: Number of cars arriving 6 7 8 Frequency 10 14 18 4 9 8 (a) Set up a probability and cumulative probability distribution for the variable of car arrivals. (b) Estimate random number intervals for the variables. (c) The following random numbers have been generated: 99, 98, 26, 09, 49, 52, 33, 89, 21, and 37. Simulate 10 hours of arrivals at this gas station. What is the average number of arrivals during this period? 5. Higgins plumbing and Heating maintains a stock of 30-gallon hot water heaters that it sells to home owners and installs for them. Owner Jerry Higgins like the idea of having a large supply on hand to meet customer demand, but he also recognizes that it is expensive to do so. He examines hot water heater sales over the past 50 weeks and note the following: Hot Water Heater Sales Per Week Number of Weeks this number was sold 4 6 5 5 6 9 7 12 8 8 9 7 10 3 Total 50 (a) If Higgins maintains a constant supply of 8 hot water heaters in any given week, how many times will he be out of stock during a 20 week simulation? (b) What is the average number of sales per week (including stock out) over the 20- weeks periods? 6. Habsum Appliances Center sells and services several brand s of major appliances. Past sales for a particular model of refrigerator have resulted in the following probability distribution for demand: Demand per week 0 1 2 3 4 Probability 0.20 0.40 0.20 0.15 0.05 The lead time, in weeks, is distributed by the following distribution: Lead time (Weeks) 1 2 3 Probability 0.15 0.35 0.50 Based on the cost considerations as well as storage space, the company has decided to order 10 of these each time an order is placed. The holding cost is $1 per week for each unit that is left in inventory at the end of the week. The stock out cost has been set at $40 per stock. The company has decided to place an order whenever there are only two refrigerators left at the end of the week. Simulate 10 weeks of operation for Habsum Appliances assuming there are currently 5 units in inventory. Determine what the weekly stock out cost and weekly holding cost would be for the problem. (Use the following random numbers 52, 37, 82, 69, 98, 96,33, 50,88, 90 when simulating demand and 06, 63, 57, 02, 94, 52, 69, 33, 32, 30 when simulating lead time