FALL 2011 2011 Deadline: October dua puluh enam, Middle East Technical University – Upper Cyprus Campus BUS 361 Operations Supervision Homework you , Solutions 1 . Fruit Computer Organization manufactures recollection chips in lots of ten snacks. From earlier experience, Fruit knows that many of these of all lots contain 10% (1 out of 10) defective poker chips, 20% of all lots consist of 50% (5 out of 10) defective chips.
If a good set (that is usually, 10% defective) of potato chips is directed on to the up coming stage of production, control costs of $1000 will be incurred, and if a bad batch (that is definitely, 50% defective) is dispatched on to the subsequent stage of production, digesting costs of $4000 are incurred.
Fresh fruit also has the choice of reworking a batch by a cost of $1000. A reworked set is sure to become a good set. Alternatively, to get a cost of $100, Fruit can test one particular chip by each batch in an attempt to identify whether the group is substandard. Determine how Fresh fruit can decrease the predicted total expense per set. Expected total cost every batch = $1580. Fruits can reduce the expected total cost per set by choosing the subsequent decisions: It should test a chip.
In the event the tested chip is malfunctioning, Fruit should rework the batch. If the tested chip is certainly not defective, yet , Fruit ought to send batch on to the next stage. Begin to see the following physique for details. Probabilities with regards to testing a chip will be calculated the following. D: Chip is defective, D’: Computer chip is not really defective, BB: Bad Set, GB: Very good Batch P(GB) = zero. 8, P(BB) = zero. 2, P(D | GB) = zero. 1, P(D’ | GB) = 0. 9, P(D | BB) = 0. 5, P(D’ | BB) = 0. 5, P(D) = (0. 8)(0. 1) + (0. 2)(0. 5) = 0. 18, P(D’) = 1 – P(D) = 0. 82
P(GB | D) = (P(D|GB) P(GB) + P(D|BB)P(BB)) / P(D) sama dengan 8/18 P(BB | D) = one particular – P(GB | D) = 10/18 P(GB | D’) sama dengan (P(D’|GB) P(GB) + P(D’|BB)P(BB)) / P(D’) = 72/82 P(BB | D’) sama dengan 1 – P(GB | D’) sama dengan 10/82 one particular 2 . A retailer of electronic items has asked a particular maker to begin daily deliveries rather than on a every week basis. The manufacturer provides 2000 situations each Wednesday. The cost of every single case is valued at $300. a. What is the regular inventory (in units)? b. The average inventory (in dollars)? c. What is the inventory turnover?. What is the average products on hand (in dollars) for the daily delivery pattern, if, perhaps 20 days/month? a. Normal inventory sama dengan (2000 & 0) as well as 2 = 1000 products. b. Average inventory sama dengan 300 5. 1000 = $300, 500 c. Inventory turnover sama dengan Net revenue / Typical Inventory sama dengan 52 2. 2000 / 1000 sama dengan 104 d. Average inventory = (2000/5 + 0) / a couple of = two hundred units Normal inventory = 300 * 200 = $60, 500 3. METU NCC Pupil Affairs expert, Sinem, can be checking the reliability of college student registrations everyday. For each student this process requires exactly two and a half mins.
There are times when Sinem gets a serious backlog of files to process. She gets argued to get more help and another pc, but her manager does not think capacity is that pressured. Use the pursuing data to determine the utilization of her and her computer. Your woman works eight and a half several hours per day (she gets 30 minutes off pertaining to lunch), five days a week. What is the use of Sinem and Sinem’s computer? This data happen to be fairly normal for a week: 3 Amount of documents to procedure = seventy + one hundred and fifty + 140 + a hundred and twenty + 160 = 630 Time it will take Sinem to process the files in each week = 630 files * 2 . min/file = 1575 a few minutes. Total functioning hours accessible in a week sama dengan 7. five hours/day * 5 times = six. 5 5. 5 = 37. 5 hours sama dengan 37. five * 60 minutes = 2250 minutes as well as week Usage = Genuine working period / Time available = 1575 as well as 2250 = 70% some. Consider the subsequent three-station development line having a single product that have to visit stop 1, a couple of, and three or more in sequence: • Station one particular has four identical devices with a digesting time of 15 minutes per job. • Station 2 offers 10 identical machines with a processing moments of 30 minutes per job. Train station 3 features 1 machine with a processing time of 3 minutes per task. a. Precisely what is rb (bottleneck rate) just for this line? n. Can this technique satisfy the daily demand of 180 products (assume two shifts in one day, and 4 hours in a shift)? c. What is T0 (raw processing time) for this collection? d. Precisely what is W0 (critical WIP) for this line? Place 1 Creation rate (jobs/min) Production rate (jobs/day) = 128 Place 2 Place 3 sama dengan 160 = 160 a. Station you is the logjam station, containing bottleneck rate, rb sama dengan 4/15. w.
Because the logjam station’s creation rate of 128 is less than the daily demand of 180 units, this system simply cannot satisfy the daily demand. some c. T0 = 15 + 40 + several = 48 minutes. deb. W0 = rb * T0 = 4/15 5. 48 sama dengan 12. almost eight 13 products. 5. The final assembly of Noname Personal computers requires a total of doze tasks. The assembly is done on the Lubbock, Arizona plant employing various pieces imported via Far East. The duties required for the assembly operations, task times and precedence relationships between duties are the following: Task Activity Time (min)
Immediate Precursors 1 two 2 2 2 three or more, 4 six 5 6, 9 8, 10 14 Positional Excess weight 70 fifty eight 31 27 20 twenty nine 25 18 18 17 13 six Rank 1 2 three or more 4 a few 6 six 8 being unfaithful 10 14 12 doze 6 6th 2 two 12 7 5 you 4 six 7 1 2 a few 5 six 4 6 8 being unfaithful 10 11 12 Given that the company makes one set up PC every 15 minutes, a. Assign jobs to workstations using the Positioned Positional Fat Algorithm. m. Calculate equilibrium delay and workload imbalance for your solution. c. Examine optimality of the solution (in terms of number of workstations, balance hold off and workload imbalance). 5 a. Purchase of tasks: 1, two, 3, six, 4, several, 5, eight, 9, 10, 11, doze
WS 1 1 12-15 3 WS 2 a couple of, 3, four 15 on the lookout for 3 one particular WS several 6, a few, 9 12-15 3 one particular 0 WS 4 7, 8 15 8 3 WS 5 10, 10 15 14 5 WS 6 12 15 eight Thus, the amount of workstations identified by RPW heuristic can be equal to 6.? b. Balance Delay (D) = b1= 3, b2= 1, b3= 0, b4= 3, b5= 5, b6= 8? sama dengan 20/6 = 3. thirty-three, Workload Disproportion (B) = v c. Lower bound on volume of workstations sama dengan [ ] [? ] =[ ] LB[D] = 0, LB .[B] =0. Not one of the decrease bounds will be equal to the obtained objective values (K*, D, B). Thus, do not know whether or not the solution acquired by RPW heuristic is definitely optimal or perhaps not. 6
