onsider a sequence of operations fi= 1,2,3, ⋯ , m. Use the Potential method. First, define the amortized cost ai and the actual cost ti for each operation fi. Hint: you need to first define the potential function and find the relationship between amortized cost, true cost, and the change in potential. Then, show that the amortized cost of the entire sequence of operations is at least the total actual cost. Full marks are given for complete mathematical formulation.

onsider a sequence of operations fi= 1,2,3, ⋯ , m. Use the Potential method. First, define the amortized cost ai and the actual cost ti for each operation fi. Hint: you need to first define the potential function and find the relationship between amortized cost, true cost, and the change in potential. Then, show that the amortized cost of the entire sequence of operations is at least the total actual cost. Full marks are given for complete mathematical formulation.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter8: Network Models

Section8.4: Cpm And Pert

Problem 3P

See similar textbooks

Similar questions

Assume that ABC Company has invested a budget of 36 million riyals for XY project and planned to complete in 12 months. In addition, assume that the company planned to spend the budget equally in each month. However, when the first two months has passed, the project manager has found out that the total of two million riyals spent. Based on the above scenario, answer the following: Suppose Rate of performance =0.25 a) What is the cost variance, schedule variance, cost performance index (CPI), and schedule performance index (SPI) for the project? b) How much will it actually cost the company to complete this project, and how long will it really take to complete it based on the performance to date? c) What do you think of the project performance? over/under the budget? behind /ahead the schedule? Justify your answer.
Clyde Clerk is reviewing his firm’s expense reimbursement policies with the new salesperson, Trav Farr. “Our reimbursement policies depend on the situation. You see, first we determine if it is a local trip. If it is, we only pay mileage of 45 cents a mile. If the trip was a one-day trip, we pay mileage and then check the times of departure and return. To be reimbursed for breakfast, you must leave by 7:00 A.M., lunch by 11:00 A.M., and have dinner by 5:00 P.M. To receive reimbursement for breakfast, you must return later than 10:00 A.M., lunch later than 2:00 P.M., and have dinner by 7:00 P.M. On a trip lasting more than one day, we allow hotel, taxi, and airfare, as well as meal allowances. The same times apply for meal expenses.” Draw a decision tree depicting the reimbursement policy in this Problem using LucidChart or Word document
A small engineering consulting firm is establishing a plan for next year. The director and thethree partners need to prioritize the eight projects. The expected profit for each project is givenin the following table together with the number of person-days required to prepare each project.Another measure included is the computing resource measured as the computer processingunit (CPU) time (in hours). You have been tasked to evaluate which projects they ought topursue based on efficiency. Given the sample data below, you plan to construct a dataenvelopment analysis (DEA) model:a. Which measures would you regard as inputs and outputs, respectively? Pleaseprovide your justification.b. Conduct data envelopment analysis, explain what type of DEA model is selectedand describe the project you regard as “efficient” and “inefficient”, respectively.c. Which project would you recommend and why?d. In what ways can you improve on your recommendation? You are free to openlysource for other datasets…
A small engineering consulting firm is establishing a plan for next year. The director and thethree partners need to prioritize the eight projects. The expected profit for each project is givenin the following table together with the number of person-days required to prepare each project.Another measure included is the computing resource measured as the computer processingunit (CPU) time (in hours). You have been tasked to evaluate which projects they ought topursue based on efficiency. Given the sample data below, you plan to construct a dataenvelopment analysis (DEA) model:a. Which measures would you regard as inputs and outputs, respectively? Pleaseprovide your justification.b. Conduct data envelopment analysis, explain what type of DEA model is selectedand describe the project you regard as “efficient” and “inefficient”, respectively.c. Which project would you recommend and why?d. In what ways can you improve on your recommendation? You are free to openlysource for other datasets…
A personnel director wishes to compare the effectiveness of two methods of train- ing industrial employees to perform a certain assembly operation. Employees are to be divided into two equal groups: the first receiving training method 1 and the sec- ond training method 2. Each will perform the assembly operation, and the length of assembly time will be recorded. It is expected that the assembly times for both groups will have a range of approximately 8 minutes. For the estimate of the difference in mean times to assemble to be correct to within minute with a probability equal to .95, how many workers must be included in each training group? 16c3d JPG Fi DO
A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units H and software programs S is given by TC=aH+bS - CHS where a, b, and c are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale? For the product-specific case for hardware, the firm experiences neither economies nor diseconomies of scale. For the product-specific case for software, the firm experiences of scale.
Correct answer will be upvoted else downvoted. Computer science. Utilizing these cost transforms you are approached to work out the swelling coefficients for every month as the proportion of current cost increment pi to the cost toward the beginning of this current month (p0+p1+⋯+pi−1). Your supervisor said you unmistakably that the expansion coefficients should not surpass k %, so you chose to expand a few qualities pi in such a manner, that all pi remain integers and the swelling coefficients for every month don't surpass k %. You know, that the greater changes — the more clear cheating. That is the reason you want to limit the all out amount of changes. What's the base complete amount of changes you want to make all expansion coefficients not more than k %? Input The primary line contains a solitary integer t (1≤t≤1000) — the number of experiments. The primary line of each experiment contains two integers n and k (2≤n≤100; 1≤k≤100) — the length of exhibit p and…
It has been observed by management that some faculty members at theuniversity demonstrate a lackadaisical attitude toward teaching. They seldom go to class yet at the end of each month they receive full salary. Management has decided that GHs 200, 300, 400, and 500 will be deducted from a faculty’s salary if he/she offends once, twice, third time and forth time respectively in a month. This means that if a faculty member offends once in a month GHs200 will be deducted, if a faculty member offends twice in a month, GHs 500 (i.e. 200+300) will be deducted, if a faculty member offends three times in a month GHs 900 (i.e. 200+300+400), will be deducted and if a faculty member offends four times in a month GHs 1,400 (i.e. 200+300+400+500). Assuming all faculty members are on a flat salary rate of GHs 2000.a. Write a program to request for the names of four faculty members and number times he/she has absented him/herself from class in a month.One of them should have absented him/herself…
SIMULATION AND MODELING 1. XYZ has a policy of ordering stock when level falls to 15 units the quantity ordered from the supply is always 20 units. The stock at beginning of 1st week is 20 units. The stock holding costs are sh. 10 per week / unit. The cost of placing one order = 25. The stocks out cost are Sh100 per unit. The usage (demand) and lead time (time taken by supply to deliver stock) is uncertain as shown below. NB: Ordering is done the following week upon discovery of the shortages. Demand Probability Lead time Probability 0 0.02 1 0.23 1 0.08 2 0.45 2 0.22 3 0.17 3 0.34 4 0.09 4 0.18 5 0.06 5 0.09 6 1.00 6 0.07 7 1.00 Required; Use the following random numbers 68 52 50 90 59 08 72 44 95 85 81 93 28 89 15 60 03 Use 14 trial numbers to find the cost 2. Customers arrive at a milk booth for the required…
For the following problem, what would be the objective function that aims at maximizing the total revenue considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? Manufacturing time (hr) per unit Machine Cost per hr ($) Product 1 Product 2 Product 3 Product 4 Capacity (hr) 1 10 3 4 2 500 3 2 1 2 380 3 2 1 450 70 55 2 5 3 4 Unit selling price (S) O a. 12X1+8X2+7X3+5X4 O b. None of the answers OC. 20X1+30X2+40X3+20X4 d. 75X1+70X2+55X3+45X4 7 75 45
Consider an example where five jobs (J1, J2, J3, J4 and J5) need to be executed by five workers (W1, W2, W3, W4 and W5), one job per worker. The matrix below shows the cost of assigning a certain worker to a certain job. The objective is to minimize the total cost of the assignment. Do assignment using Hungarian method, one job per worker mentioning minimum cost. J1 J2 J3 J4 J5 W1 10 4 8 3 W2 2 11 7 7 W3 5 10 11 8 W4 5 3 2 5 W5 11 7 10 11 7 6. 4.
3. Consider the following graph for question a and b. 8 E (a) What is the highest-cost path for finding the goal G? (b) What is the lowest-cost path for finding the goal G?