r linear optimization
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- What is Machine Scheduling in Integer linear optimization and put example.Using the FCFS rule for scheduling, the sequence is Sunny Park Tailors has been asked to make three different types of wedding suits for separate customers. The table below highlights the time taken in hours for cutting and sewing (process 1) and delivery (process 2) of each of the suits Times Taken for Different Activities (hours) Cut and Sew Suit 1 2 3 7 4 5 Deliver 2 3 6 Assume that orders for suits have been listed in the above table in the order in which they were received. CWilliam Beebe owns a small shoe store. He has 10 pairs of shoes that requireresoling and polishing. He has a machine that can resole one pair of shoes at atime, and the time required for the operation varies with the type and condition of theshoe and the type of sole that is used. Shoes are polished on a machine dedi-cated tothis purpose as well, and polishing is always done after resoling. His assistant generally does the polishing while Mr. Beebe does the resoling. The resoling and polishingtimes (in minutes) are Shoes Resoling Time Polishing Time1 14 32 28 13 12 24 6 55 10 106 14 67 4 128 25 89 15 510 10 5In what order should the shoes be repaired in order to minimize the total makespanfor these 10 jobs?
- Why are m × n machine-scheduling algorithms notwidely used in practice?Currently a company that designs Web sites has five customers in its backlog. The time since the order arrived, processing time, and promised due dates are given in the following table. The customers are ready to be scheduled today, which is the start of day 190. Customer Time Since Order Arrived (days ago) Processing Time (days) Due Date (days from now) Upper AA 6 18 66 Upper BB 3 24 58 Upper CC 2 32 100 Upper DD 10 22 26 Upper EE 8 12 50 a. Develop separate schedules by using the FCFS and EDD rules. Compare the schedules on the basis of average flow time and average days past due. Part 2 Using the FCFS (first come, first served) decision rule for sequencing the customers, the order is: Sequence 1 2 3 4 5 Customer D E A B C Part 3 Using…Jane Reed bakes breads and cakes in her home for parties and other affairs on a contract basis. Jane has only one oven for baking. One particular Monday morning she finds that she has agreed to complete five jobs for that day. Her husband John will make the deliveries, which require about 15 minutes each. Suppose that she begins baking at 8:00 A.M. (given) Determine the sequence in which she should perform the jobs in order tominimizea. Mean flow time.b. Number of tardy jobs.c. Maximum lateness.
- A1 Credit provides credit information to its customersthroughout the country, 24 hours per day. Credit representativesanswer customer calls and provide information. Based on demandpatterns, the estimated number of representatives needed duringfour-hour time periods of each day are shown in the table. Employees work shift s of eight consecutive hours, and shift scan start at the beginning of any of the six periods shown inthe table. Assume this schedule will be repeated day aft er day,so that someone starting at 8 pm will contribute to the need forrepresentatives in the midnight–4 am time period. Th e supervisorhas been instructed to schedule employees so that all demandscan be met with a minimum possible number of employees.(a) Formulate an LP to minimize the number of representativesneeded.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution.b. What is the minimum cycle time that can be considered? Determine the balancethat results from the ranked positional weight technique for this cycle time.Diablo Electronics manufactures four unique products (A, B, C, and D) that are fabricated and assembledin five different workstations (V, W, X, Y, and Z) using a small batch process. Each workstation is staffedby a worker who is dedicated to work a single shift per day at an assigned workstation. Batch setuptimes have been reduced to such an extent that they can be considered negligible. A flowchart denotesthe path each product follows through the manufacturing process as shown in Figure 5.2, where eachproduct’s price, demand per week, and processing times per unit are indicated as well. Inverted trianglesrepresent purchased parts and raw materials consumed per unit at different workstations. Diablo canmake and sell up to the limit of its demand per week, and no penalties are incurred for not being able tomeet all the demand.Which of the five workstations (V, W, X, Y, or Z) has the highest utilization, and thus serves as the bottle-neck for Diablo Electronics?
- Now you are being hired as a scheduler in the manufacturing unit of surgical instruments. Your job is to schedule four jobs on the two machines. The job processing time in minutes for the four jobs is given below: A с D Machine 1 Machine 2 3.43 0.11 B 1.58 0.46 3.62 2.29 4.05 4.52 The optimal schedule using Johnson method and makespan for the jobs is: (A)BCBA, 12.79 minutes (B) ABCD, 5.41 minutes (C) DCBA, 12.79 minutes (D) CDBA, 5.41 minutesCurrently a company that designs Web sites has five customers in its backlog. The day when the order arrived, processing time, and promised due dates are given in the following table. The customers are listed in the order of when they arrived. They are ready to be scheduled today, which is the start of day 190. Customer Time SinceOrder Arrived(days ago) ProcessingTime (days) Due Date(days fromnow) A B C D E 10 8 6 3 2 20 12 28 24 32 26 50 66 58 100 a. Develop separate schedules by using the FCFS and EDD rules. Compare the schedules on the basis of average flow time and average days past due.b. Comment on the performance of the two rules relative to these measures. Which one gives the best schedule? Why?A nursing home must schedule nurses in a manner that balances providing adequate patient care while keeping costs down. From historical records, administrators can project the minimum number of nurses to have on hand during each day/time slot. This data is shown below. Shift Time Slot Minimum number of nurses needed 1 12 am-4 10 2 4 am-8 6 3 8 am-12 8 4 12 pm-4 12 5 4 pm-8 10 6 8 pm-12 14 Nurses must start work at the beginning of one of the four-hour shifts (starting as early as 12 am midnight or as late as 8pm evening) and work for eight hours. Nurses who begin working at 8 pm will work until 4 am the next morning. Formulate and solve the nurse-scheduling problem so as to minimize excess stagging while satisfying minimum staffing requrements. What is the value of total excess staffing?