This website uses cookies to ensure you have the best experience. Learn more

Linear Programming Essay

993 words - 4 pages

METHODS/ APPROACH

This scheduling problem can be solved most expeditiously using linear programming. Let F denote the number of full-time employ- ees. Some number, F1, of them will work one hour of overtime between 5 PM and 6 PM each day and some number, F2, of the full- time employees will work overtime between 6 PM and 7 PM. There will be seven sets of part-time employees who begin their work day at hour j=j␣1,2,...,7,withP1beingthenumberofworkers beginning at 9 AM, P2 at 10 AM, . . . , P7 at 3 PM. Note that because part-time employees must work a minimum of four hours, none can start after 3 PM because the entire operation ends at 7 PM. Similarly, some number of part-time employees, ...view middle of the document...

4

Which is 40% of the day’s total requirement of 321 person hours. This also leads to the objective function. The total daily labor cost, which must be minimized, is:

Z 8(10.11)F 8.08(F1 F2) 7.82(10P1 9P2 8P3 7P4 6P5 5P6 4P7 −6Q4 −5Q5 −4Q6 −3Q7 −2Q8 −Q9)

Total overtime for a full-time employee is restricted to five hours or less, an average of one hour or less per day per employee. Thus, the number of overtime hours worked per day cannot exceed the number of full-time employees:

F1 F2 <= F
Because part-time employees must work at least four hours per day,

Q4 <= P1

for those leaving at the end of the fourth hour. At the end of the fifth hour, those leaving must be drawn from the P1 −Q4 remain- ing plus the P2 that arrived at the start of the second hour:
Q5 P1 P2 −Q4

Similarly, for the remainder of the day:

Q6 P1 P2 P3 −Q4 −Q5 Q7 P1 P2 P3 P4 −Q4 −Q5 −Q6 Q8 P1 P2 P3 P4 P5 −Q4 −Q5 −Q6 −Q7 Q9 P1 P2 P3 P4 P5 P6 −Q4 −Q5 −Q6 −Q7 −Q8

To ensure that all part-timers who began at 9 AM do not work more than seven hours:

Q4 Q5 Q6 Q7 P1 Q4 Q5 Q6 Q7 Q8 P1 P2
Q4 Q5 Q6 Q7 Q8 Q9 P1 P2 P3

Finally, to ensure that all part-time employees leave at some time:
P1 P2 P3 P4 P5 P6 P7 Q4 Q5 Q6 Q7 Q8 Q9


FINDINGS AND CONCLUSIONS

The resulting problem has 16 variables and 22 constraints. If integer programming software with sufficient capacity is not avail- able, the linear...

Other assignments on Linear Programming

Shuzworld Essay

6791 words - 28 pages had to use Prt Sc). C. EVALUATE THE TRADE-OFFS OF ALLOCATING PRODUCTION LINE WORKERS TO MINIMAZE PRODUCTION COST. In this case, linear programming is used to determine trade-offs. Usually companies have to be able to allocate their resources in order to meet their goals. One way that linear programming can be used is to minimize their production costs by developing a staffing plan that meets production line goals while minimizing staffing. A

Simulation Essay

1260 words - 6 pages , it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains. The first optimization technique, which is known as steepest descent, goes back to Gauss. Historically, the first term to be introduced was linear programming, which was invented by George Dantzig in the 1940s. Gradient descent is a first-order optimization

Om White Psper

1312 words - 6 pages determined information like number of workers, attended and unattended machines is required. Line balancing at its core tries to equally divide work to be done among workstations. The objective is to minimize No. of workers or workstations required on a production line to provide the required amount of capacity. Analysis Methods Various methods like Linear Programming, Dynamic Programming and other mathematical models possible but not useful for

Thesis

4522 words - 19 pages machine utilization of 63% is quite low. Most manufacturers strive for at least an 85% machine utilization. If we could determine the cause(s) of this poor utilization, we might find a key to a dramatic increase in capacity. 6. Chase Manhattan Bank, Ch. 8, page 339 This very advanced and challenging scheduling problem can be solved most expeditiously using linear programming, preferably integer programming. Let F denote the number of full-time

The Waterfall Model In Ict

1853 words - 8 pages online is usually safe but not all the time. If a site is not secure or does not encrypt personal credit card data, a hacker can access it putting your oersinal financial information in jeopardy. 2 (a) The ‘Waterfall’ model is considered the simplest software development life cycle. Its stages are arranged in a linear order. The models stages descend from top to bottom hence the name waterfall. The stages are listed

Ffff

4622 words - 19 pages . Accumulator Loops lxxxvii. Loops for File I/O XV. Top-Down Design . What is it? lxxxviii. Top-Down Design is a way of programming that helps increase the efficiency and organization of the programmer when writing code. lxxxix. It starts with looking at the problem as the big picture, and then simplifies it by breaking it down into smaller problems to solve one at a time. . How do you use it? xc

1fldj As

1699 words - 7 pages Linear programming Digital computer Simulation, waiting line theory, decision theory, PERT/CPM Operations Research MRP, EDI, EFT, CIM See your textbook page 8 Copyright 2011 John Wiley & Sons, Inc. Evolution of Operations and Supply Chain Management • Supply chain management – Management of the flow of information, products, and services across a network of customers, enterprises, and supply chain partners Copyright 2011 John Wiley

Termpaper

2137 words - 9 pages faculty from theCollege of Engineering and Arts and Sciences assisted him. The system that is web baseduses PHP programming language with data stored in MySQL is run through the intranet of SSU.A dry-run for this automated enrolment was done last summer and the first semester of this school year. Offices affected with the automation were the registrar, cashier, accounting, and the Colleges of Education, Engineering, Arts and Sciences,Industrial

My Paper

2521 words - 11 pages companies or retail via hardware partners) and enable the company to better leverage its powerful brand. We would suggest that they work with a major company to arrange co-branded TiVo Premiere DVR's (note: TiVo bills the Premiere as combining linear TV, DVR, VOD and Internet-delivered video into a unified experience delivered via an Adobe Flash-based user interface), as well as TiVo-developed non-DVR client set-top boxes. This will help TiVo

Unknown

5042 words - 21 pages : ca14h 11.5-7 Diff: 3 Terms: relevant revenues, relevant costs Objective: 5 76) B ID: ca14h 19.5-10 Diff: 3 Terms: throughput contribution Objective: 5 77) C ID: ca14h 11.7-7 Diff: 3 Terms: linear programming (LP), constraint Objective: 7 78) C ID: ca14h 7.5-7 Diff: 2 Terms: flexible-budget variance Objective: 5 79) C ID: ca14h 7.5-8 Diff: 2 Terms: price variance Objective: 5 80) A ID: ca14h 7.5-9 Diff: 2 Terms: price variance Objective: 5 19

Dss In Supply Chain Management And Design

2843 words - 12 pages response time which contributes to the overall response cycle time of the supply chain. With the increase of complexity across supply chain that comes together with manufacturing processes and product customization complexity, there is a need to have a solver based tool to support supply chain analysis. As such, Intel made use of technologies such as mathematical programming, statistical calculations, and computer simulations. Intel implemented Linear

Similar Documents

Week 6 Essay

406 words - 2 pages A look at linear programming, using the simplex method Earlier in the class we were introduced to linear programming and now we are going to introduce a different method using a more geometric version called the simplex method. First, I am going to have to explain theory of the simplex method and then we’ll explain the real world uses of this algebraic math Ok, so earlier in the class we were introduced into liner equations and inequalities

Managing Pricing Decisions Essay

443 words - 2 pages ? Answer: LINEAR PROGRAMMING A firm wants to determine how many units of each of two products (products X and Y) they should produce in order to gain profit. The profit from making a unit of product X is RM100 and the profit from making a unit of product Y is RM80. The firm can sell any amount of either product; it is limited by its total labor hours and total machine hours available. The total labor hours per week are 800 hours. Product X

Mat540 Quiz3 Essay

1175 words - 5 pages : False Question 2 2 out of 2 points Correct A linear programming problem may have more than one set of solutions. Answer Selected Answer: True Correct Answer: True Question 3 2 out of 2 points Correct A linear programming model consists of only decision variables and constraints. Answer Selected Answer: False Correct Answer: False

Math540 Quiz 5 Essay

1075 words - 5 pages | | | | | Selected Answer: |  False | Correct Answer: |  False | | | | | Question 6 0 out of 2 points | | | The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function.  Answer | | | | | Selected Answer: |  False | Correct Answer: |  True | | | | | Question 7 2 out of 2 points | | | If we are solving a 0-1 integer programming problem, the