ORI 390Q Models and Analysis of Manufacturing Systems First Exam, fall 1994

Transcription

1 ORI 90Q Models and Analysis of Manufacturing Systems First Exam, fall 1994 (time, defect rate) (12,0.05) 5 6 V A (16,0.07) (15,0.07) (5,0) M M1 M2 O A (10,0.1) 7 8 V B (8,0.2) M4 2 4 M5 The figure shows the processes for two products. The operation times and defect rates are shown on the figure. s are in minutes. Inspections are perfect. Machine assignments are shown adjacent to the operations. Note that machines M1 and M2 are used for both products. Product A is made from a single raw material 1. Product B is made from two raw materials, 1 and 2. The table below gives the maximum sales and revenues for the products, and the unit costs for the raw materials. Assume 0 hours per week and 60 minutes per hour. The information on this page is used for several problems in the exam. You may use the results of one problem to aid in the analyses of the others. Finished Goods Max. Sales per week Revenue per unit of finished good Raw materials A 100/week $58 1 $0 B 100/week $95 2 $20 Cost per unit of raw material 1

2 Process A Name Index Next Oper. Defect Rate Defects Out Remove d A Start Op5 Op % M % 0.0% In6 In % Insp % 5.0% A End % % 0.0% 1 0 Ratio Unit Process B Name Index Next B Start Oper. Defect Rate Defects Out Remove d Op4 Op % M % 0.0% Op7 Op % M % 0.0% Op8 In % Insp % 28.0% B End % % 0.0% 1 0 Ratio Unit Process C Name Index Next Oper. Defect Rate Defects Out Remove d C Start Op1 Op % M % 0.0% Op2 Op % M % 0.0% In In % Insp % 1.5% C End % % 0.0% 1 0 Ratio Unit 2

3 1. (20 Points) The number of machines available for each type is shown in the table below. M1 M2 M M4 M5 Number Unlimited We identify three modules in the problem: Module A: operations 5 and 6, Module B: operations 4, 7, and 8, Module C: operations 1, 2 and. Write the linear programming model that will determine the optimum product mix. Include variables for the three modules and the raw material amounts. Total Name: A B C 1 2 Values: Linear Obj. Coef.: Lower Bounds: Upper Bounds: E+07 1E+07 Constraints Name Constraint Coefficients M M M M M = = 0 Con = 0 Max 58A + 95B + 9C subject to: M1: 18.5C 5400 M2: 17.C 600 M: 12.62A 1800 M4: 1.889B 1800 M5: A : C -1 = 0 2: 1.889B -2 = 0 Conservation: A B - C = 0 0 A 100, 0 B 100, C 0, 1 0, 2 0

4 (10 Points) For the situation in the figure, what is the throughput dollars per unit for each product? The throughput dollars per unit is the revenue raw material cost. For A: 58 u 1 *u 5 *0 (we must multiply the two flow ratios together to find the amount of 1 per unit of A. TP$ A = 58* - (1.24)*(1.056)*0 = 50 0*1.299 = For B: 95 u 1 *u 7 *0 u 4 *20 TP$ B = : 95 (1. 24)(1.89) * *20 = (10 Points) After the linear programming model is solved, we discover the following information from the sensitivity analysis. The reduced cost for product B is 9.22, and all the other reduced costs are zero. The dual variable for the constraint for machine M2 is 1.1. What do these two numbers tell you? The value of 9.22 indicates the value of increasing the market for product B by 1 unit. The value of 1.1 is the increase in the objective by increasing the availability of machine 2 by 1-minute. 4

5 . (20 Points) It turns out that the market demand for product B is a bottleneck and the time available on machine M2 is a bottleneck. We would like to get more profit from the business. Evaluate the following changes as to whether or not the throughput will increase after the change. Explain your reasoning briefly. Action Invest in a marketing strategy that will increase the maximum sales of product A. Improve the Throughput? Why or Why not? This will not help. Product B is not a bottleneck. You might have a greater demand, but you won t sell any more. The throughput will stay the same. Outsource some of the production of module C. The cost per unit of the product from the outside supplier is $40. This material has no defects. This might help because it will take some load off the M2 machine and allow more production of product B. The raw material cost for module C per unit out of C is 0*u 1 = 0*1.246.= 7.0. Although the outsourceing cost is greater, the TP will be increased. Add an inspection station after operation 4. This change will reduce the flow ratio for operation 7 and thus the amount of time per unit of B on the bottleneck machine. Thus change will allow more production of B. It also will reduce the cost of 1 for product B. Add an inspection operation after operation 1. This change will have the effect of reducing the flow ratio for operation 2. Thus more product will be able to be manufactured on machine 2. The throughput will increase. 5

6 4. (20 Points) You decide to manufacture the products on two separate lines. The processes now appear as in the figure below. (time, defect rate) (16,0.07) (15,0.07) (5,0) (12,0.05) V A M1 M2 M (16,0.07) (15,0.07) (5,0) (10,0.1) A 7 8 V B M1 M2 (8,0.2) M4 2 4 M5 The allocation of machines to the two lines is indicated in the table below. Machines now produce only one product. How does this change the product mix? Is separating the lines a good idea? Machine Assignment for Process A M1 M2 M M4 M5 Number Unlimited Machine Assignment for Process B M1 M2 M M4 M5 Number Unlimited With this information each product has its own bottleneck. Based on the unit times, the bottleneck for product A is machine 1. The maximum production is 1800/2.7 = 92 units The bottleneck for product B is M2 with the maximum production allowed of 74 units. This is not a good idea, since the throughput of both products is reduced. 6

7 6. (10 Points) Now consider only the system for product B. We decide to manufacture 150 units per week of product B. We will provide as many machines of each type as necessary. (16,0.07) (15,0.07) (5,0) (10,0.1) A 7 8 V B M1 M2 (8,0.2) M4 2 4 M5 In addition to the information in the figure, we discover an unexplained delay of 0 minutes in front of each inspection operation. a. What is the value of WIP for this production rate? We must compute the WIP for three separate parts since the flow the parts is different and the Raw material contents is different. For operations 1, 2 and, the flow is *150 = 241. The residence time is = 66 min or weeks The WIP is 241* = 8.82 units The value of the WIP is 8.82*0 = For operation 4, the flow is 1.889*150 = 208. The residence time is 8 min or weeks The WIP is 208* = units The value of the WIP is *20 = $18.51 For operations 7 and 8, the flow is 1.889*150 = 208. The residence time is = 47 min or weeks The WIP is 208* = 5.44 units The value of the WIP is 5.44 *50 = $ Total WIP is Total Value of WIP is $555 b. What is the throughput time for a unit of product? The throughput time is the time for the longest path (1. 2., 7, 8). Add 1 hour for the inspection delays. The time is = 11 minutes. c. How much raw material of 1 must be supplied for this production rate? The amount of 1 is 150 u 1 = 150* =

8 7. (6 Points) In the book The Goal, the heat-treat process is discovered as a bottleneck. Give three specific examples of steps taken to exploit the heat-treat process. I'm particularly interested in exploiting rather than elevating or subordinating. Exploiting the heat-treat is getting as much out of the current capacity as possible. Some steps taken in the book are: Station a worker at the heat-treat machine so that it is never idle after it finishes the job. Try to make larger batches by adding parts with similar processing times. Improve the setup process so that the heat-treat machine is not delayed because of setup. 8 (4 Points) Give one example of steps taken to elevate, rather than exploit the heattreat process. An example of elevating was to outsource the heat-treat process. Another is to re-engineer the products so as not to require heat-treat. 8