a.) Formulate a LP model of this problem An assembly line consisting of three consecutive stations produces two radio models: HiFi-1and HiFi-2. The following table provides the assembly times of the three workstations.Workstation112323Minutes per unitHiFi1654HiFi-2456The daily maintenance for stations 1,2, and 3 consumes 10%, 14%, and 12%, respectively, ofthe maximum 480 minutes available for each station each day. Determine the optimalproduct mix that will minimize the idle (unused) times in the three workstations.

Decision Variables: Suppose-X be the no. of radio medel HiFi-1 to be producedY be the no. of radio…

Answered: An assembly line consisting of three…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section10.6: The Effects Of Input Distributions On Results

Problem 28P

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At a manufacturing assembly line, 30 jobs arrive perhour. Each job must pass through two production stages:stage 1 and stage 2. Stage 1 takes an average of 1 minute tocomplete, and 1 worker is available to perform stage 1.After completing stage 1, the job immediately passes tostage 2. Stage 2 takes an average of 2 minutes to complete,and 2 workers are available to work on stage 2. Aftercompleting stage 2, each job is inspected. Inspection takesan average of 3 minutes, and 3 workers are available toperform inspection. After inspection, 10% of the jobs mustbe returned to stage 1, and they then repeat both stages 1and 2. After inspection, 20% of all jobs return to stage 2 andrepeat stage 2. Assume that interarrival times and servicetimes are exponential.a What is the average time a job spends in the systemfrom arrival to completion?b What percentage of the time is each worker busy?
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.
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PLease use excel Maintenance at a major theme park in central Florida is an ongoing process thatoccurs 24 hours a day. Because it is a long drive from most residential areas to thepark, employees do not like to work shifts of fewer than eight hours. These eighthour shifts start every four hours throughout the day. The number of maintenance workers needed at different times throughout the day varies. The following table summarizes the minimum number of employees needed in each four-hour time period. Time Period Needed Minimum Employees 12 a.m. – 4 a.m. 804 a.m. – 8 a.m. 2108 a.m. – 12 p.m. 24512 p.m. – 4 p.m. 1604 p.m. – 8 p.m. 2958 p.m. – 12 a.m. 120 The maintenance supervisor wants to determine the minimum number ofemployees to schedule that meets the minimum staffing requirements.1. Formulate the LP model for this problem.2. Create the spreadsheet model and use Solver to solve the…
Four doctors work in a hospital emergency room thathandles three types of patients. The time a doctor spends with each type of patient is exponentially distributed, witha mean of 15 minutes. Interarrival times for each customertype are exponential, with the average number of arrivalsper hour for each patient type being as follows: type 1, 3patients; type 2, 5 patients; type 3, 3 patients. Assume thattype 1 patients have the highest priority, and type 3 patientshave the lowest priority (no preemption is allowed). What isthe average length of time that each type of patient mustwait before seeing a doctor?
Consider a manufacturing process depicted by the following flowchart. flowchart 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. A1, A2, and A3: 12 minutes B: 14 minutes C1 and C2: 6 minutes. The process initiates the production of a new unit every 18 minutes. What is the utilization of Operator C2 in percentage? Note: Provide a number without the % mark. Round your final answer to 2 decimal places if it is not a whole number.
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A linear programming computer package is needed. Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 4,500 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Component Manufacturing Cost Purchase Cost Frame $39.00 $52.00 Support $12.50 $16.00 Strap $7.50 $8.50 Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows. Component Department Cutting Milling…
A linear programming computer package is needed. Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 5,500 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Component Manufacturing Cost Purchase Cost Frame $39.00 $52.00 Support $12.50 $16.00 Strap $7.50 $8.50 Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows. Component Department Cutting Milling…
A linear programming computer package is needed. Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 5,500 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Component Manufacturing Cost Purchase Cost Frame $39.00 $52.00 Support $12.50 $16.00 Strap $7.50 $8.50 Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows. Component Department Cutting Milling…

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