A machine shop has four machines of different types and must produce five different part styles during its 40 hours per week operation. The part-mix ratios, batch quantities, part routings, machines, servers, and production setup times and cycle times (in hours) are given in the table below for the part styles produced in the shop. Operation sequence for each part style is in the order of station number. Part styles are identified by letter and stations are identified by number. Determine the maximum production rate (determined by the bottleneck station) (pieces/hour, 3 decimal points). Part style (i) Part mix (pj) Batch quantity (Qb) Station Servers (i) (si) 1 2 3 4 3 3 2 2 A 0.23 TSUA 29 TCA 3.3 0.38 B 0.1 1.5 0.49 22 1.8 0.15 3 0.17 1.7 0.47 0.22 C 2.3 3.4 30 D 0.2 TsuB TcB Tsuc TCC TsuD TcD TSUE TCE 2.8 0.1 21 2.8 0.5 0.34 2.2 0.39 0.14 E 0.28 19 1.8 0.5 2.3 0.52 1.6 0.57
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- Part A is processed on a MILLING machine; Part B is processed on a LATHE machine. Two parts (A and B) are then assembled on an ASSEMBLY machine. Standard times, scrap rates, efficiency, and availability of each machine and the assembly are given in the table below. Determine the number of milling (M), the lathe (L) and the assembly (A) machines needed to produce 100 good parts from this production system during and 8-hour (480 minutes) shift. (Note: Round up the number of parts processed on each station and then round up the number of machines needed).Show your step-by-step process using the SPECIAL PURPOSE LINEAR PROGRAMMING: ASSIGNMENT METHOD to solve this problem. Four Engineers are to work on 4 projects of Dora Company. The problem is to decide which engineer should be assigned to which project. Each engineer charges different fees on each project, due to distances of the projects and the complexity of the work. The cost of assigning particular engineers to particular projects are as stated below. The objective is to find the lease cost of assignment. Engineer 1 to Projects A, B, C, D = $11k, $8k, $10k, $7k respectively.Engineer 2 to Projects A, B, C, D = $6k, $5k, $3k, $8k respectively.Engineer 3 to Projects A, B, C, D = $4k, $8k, $10k, $9k respectively.Engineer 4 to Projects A, B, C, D = $11k, $10k, $5k, $7k respectively.A manufacturing system is used to produce a product.Each unit of product must be processed sequentially through workstations.V -----> W -----> X -----> Y The capacity of each workstation are as follows:Workstation V, 16 units per hour,Workstation W, 22 units per hour, Workstation X, 13 units per hour,Workstation Y, 18 units per hour. The raw material is always available in the front of workstation V. The manufacturing system has a cycle time of __________ minutes per unit. Use at least 4 decimals.You must show your calculation steps and brief explanation on your Excel spreadsheets.
- A manufacturing system is used to produce a product.Each unit of product must be processed sequentially through workstations.V -----> W -----> X -----> Y The capacity of each workstation are as follows:Workstation V, 24 units per hour,Workstation W, 16 units per hour, Workstation X, 32 units per hour,Workstation Y, 26 units per hour. The raw material is always available in the front of workstation V. The utilization rate of workstation X is ________ percent. Use at least 4 decimals.You must show your calculation steps and brief explanation on your Excel spreadsheets.A service process is described by the above flowchart. After going through workstation A, an order needs to be processed by one of the three lines, B1-C1-D1, B2-C2-D2, or B3-C3-D3 (in other words, they are substitutable). Finally, all orders need to go through workstation E. The capacities of the individual workstations are given as follows: Workstation A has a capacity of 2 orders/hour Workstation B1, B2, and B3 have the same capacity of 3 orders/hour Workstation C1, C2, and C3 have the same capacity of 3 orders/hour Workstation D1, D2, and D3 have the same capacity of 3 orders/hour Workstation E has a capacity of 4 orders/hour What is capacity of the service process in orders/hour? Note: Please do not include the unit of measure. For example, if your answer is 10 orders/hour, enter 10.Assign the 4 departments in Table X to locations A, B, C, and D, which are separated by the distances shown in Table y, in such a way that transportation cost is minimized. Use this heuristic: assign departments with the greatest interdepartmental workflow first. (See attached table) Illustrate the configuration of the 4 departments in each of the 4 locations. Show the distances between departments and total interdepartmental workflows of department pairs.
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- In an evaluation of labor assignment rules when workers are not perfectly interchangeable, Paul. M. Bobrowski and Paul Sungchil Park created a dynamic job shop with 9 work centers and 9 workers, both numbered 1–9. The efficiency of each worker is specified in the following labor efficiency matrix, which represents the degree of worker cross-training.† Work Centers 1.00 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 0.85 1.00 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 0.85 1.00 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 0.85 1.00 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 0.85 1.00 0.95 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 1.00 0.95 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 1.00 0.95 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 1.00 0.95 0.95 0.95 0.95 0.95 0.85 0.85 0.85 0.85 1.00 W o r k e r s (a) For what work center(s) is worker 2 least efficient? (Enter your answers as a comma-separated list.) (b) For what…Posh Nails Katie Posh runs an upscale nail salon. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parentheses): Activity 1: Welcome a guest. (1 minute)Activity 2: Clip and file nails. (3 minutes)Activity 3: Paint. (5 minutes)Activity 4: Dry. (10 minutes)Activity 5: Check out the customer. (4 minutes)Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment of tasks to servers is the following: S1 does Activity 1. S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair (equipped with fans for drying). The time to do this is negligible. There exists only one drying chair in the salon. Assume a wage rate of $12 per hour. What are the direct labor costs for one customer (in dollars)?Posh Nails Katie Posh runs an upscale nail salon. The service process includes five activities that are conducted in the sequence described below. (The time required for each activity is shown in parentheses): Activity 1: Welcome a guest. (1 minute)Activity 2: Clip and file nails. (3 minutes)Activity 3: Paint. (5 minutes)Activity 4: Dry. (10 minutes)Activity 5: Check out the customer. (4 minutes)Three servers (S1, S2, and S3) offer the services in a worker-paced line. The assignment of tasks to servers is the following: S1 does Activity 1. S2 does Activities 2 and 3. S3 does Activities 4 and 5. The drying process does not require server 3’s constant attention; she/he needs to only escort the customer to the salon’s drying chair (equipped with fans for drying). The time to do this is negligible. There exists only one drying chair in the salon. What is the average labor utilization of the servers (in decimal form)? Assume that there is unlimited demand and that the process only admits…