Four workers are available to perform jobs 1–4.Unfortunately, three workers can do only certain jobs:worker 1, only job 1; worker 2, only jobs 1 and 2; worker3, only job 2; worker 4, any job. Draw the network for themaximum-flow problem that can be used to determinewhether all jobs can be assigned to a suitable worker.
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Four workers are available to perform jobs 1–4.
Unfortunately, three workers can do only certain jobs:
worker 1, only job 1; worker 2, only jobs 1 and 2; worker
3, only job 2; worker 4, any job. Draw the network for the
maximum-flow problem that can be used to determine
whether all jobs can be assigned to a suitable worker.
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- Consider the following tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task. There exists unlimited demand unless stated otherwise. Time to Complete Task (seconds): Task 1: 30 Task 2: 25 Task 3: 15 Task 4: 20 Task 5: 15 Task 6: 20 Task 7: 50 Task 8: 15 Task 9: 20 Task 10: 25 Task 11: 15 Task 12: 20 The current conveyor-paced assembly-line configuration assigns the workers in the following way: • Worker 1: Tasks 1, 2, 3 • Worker 2: Tasks 4, 5, 6 • Worker 3: Tasks 7, 8, 9 • Worker 4: Tasks 10, 11, 12 What is the direct labor content (in seconds per unit)?One possible solution method for the machine-tojob assignment problem is the following heuristic procedure. Assign the machine to job 1 that completes job 1 quickest. Then assign the machine to job 2 that, among all machines that still have some capacity, completes job 2 quickest. Keep going until a machine has been assigned to all jobs. Does this heuristic-procedure yield the optimal solution for this problem? If it does, see whether you can change the job times so that the heuristic does not yield the optimal-solution.William 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?
- JOHNSON’S RULE Five specialty jobs at a La Crosse, Wisconsin, tool and die shop must be processed through two workcenters (drill press and lathe). The time for processing each job follows:Work (processing) Time for Jobs (hours)JOBWORK CENTER 1(DRILL PRESS) WORK CENTER 2(LATHE)A5 2B3 6C8 4D 10 7E 7 12Diablo 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?One possible solution method for the machine-to job assignment problem is the following heuristic procedure. Assign the machine to job 1 that completes job 1 quickest. Then assign the machine to job 2 that, among all machines that still have some capacity, completes job 2 quickest. Keep going until a machine has been assigned to all jobs. Does this heuristic procedure yield the optimal solution for this problem? If it does, see whether you can change the job times so that the heuristic does not yield the optimal solution.
- 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. CThe single machine-scheduling problem consists of: Select one: None is correct n jobs with the same single operation on each of the jobs. n jobs with m operations on each of the jobs. n jobs with different operations on each of the jobs.J.C. Howard's medical testing company in Kansas wishes to assign a set of jobs to a set of machines. The following table provides the production data of each machine when performing the specific job: Job 1 234 a) The optimal assignment of jobs to machine that will maximize total production is: b) The total production of the assignment= units (enter your response as a whole number). A 11 9 12 7 Machine A Machine B Machine C Machine D ↑ ↑ ↑ ↑ B 5 11 8 9 Machine с 9 5 13 8 D 8 99 6 10
- b. The Healthy Food Restaurant, a 24-hour restaurant, faces changing requirements from hour tohour. More workers are needed for peak hours, and fewer are needed in between. The followingTable 6 (below) shows the worker requirement for the first 12 hours in the restaurant:Table 6. Staff Requirement at the Healthy Food RestaurantTime Period 10AM11AM12PM1PM2PM3PM4PM5PM6PM7PM8PM9PMRequirement 8 10 12 12 9 7 6 7 9 10 12 8AssignedOn DutyOverstaffed8(i) You are required to apply the first-hour principle to staff each hour with the required number ofcafeteria staff, showing how many staff are on duty each given hour, the number of staffyou have assigned to work each hour and any overstaffing for each hour. i. Schedule the staff to work in 8-hour shifts.of There are three work centers (A, B, and C) in a factory that can each fit into three spaces (1, 2, and 3) off the corridor behind the processing equipment. The distance from 1-2 is 10 feet, 2-3 is 30 feet, and 1-3 is 40 feet. The matrix of work (trips per day) at the three centers are shown in the following table. Assume that each trip must be a round-trip (from 1 to 2 and back, for example). Find the optimal assignment that minimizes distance traveled. any B. A. 20 50 B. 30 OA-1, B-2, C-3 A-2, B-3, C-1 A-3, B-2, C-1 O A-1, B-3, C-2 A-2, B-1, C-3Consider a manufacturing process depicted by the following flowchart. A1 B: 4 minutes A2 A3 B Either of C1 and C2: 2 minutes. C1 Station A has 3 parallel operators, A1, A2, and A3. Station C has 2 parallel operators, C1 and C2. Each unit only needs to be processed by one of the operators A1, A2 and A3. After being processed at Station B, a unit then needs to be processed by either C1 or C2. The process time of the individual operators are given as follows. Each of A1, A2, and A3: 20 minutes C2 What is the capacity (in units/hour) of the whole process? Round your final answer to 2 decimal places if it is not a whole number.