set up linear programming model and explain Suppose you are helping to create a
ID: 672253 • Letter: S
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set up linear programming model and explain Suppose you are helping to create a student schedule for a peer tutoring lab. The need for service fluctuates during work hours (8 a m. to 5 p.m.). The minimum number of students needed is 2 between 8 a.m. 10 a.m., 3 between 10 a.m. and 11 a.m., 4 between 11 a.m. and 1 p.m. and 3 between 1 p.m. and 3 p.m. Each student is allotted 3 consecutive hours (except for those starting at 3 p.m. who work for 2 hours, and those who start at 4 p.m. who work for one hour) Because of their flexible schedules, the student workers can usually report to work at any hour during the work day, except that no student worker wants to start working at lunch time (noon). Determine the minimum number of students the department should employ and specify the time of the day at which they should each report to work. Complete this problem as follows: Set up a linear programming model for this scenario so that the number of students is minimized. Make sure you define your variables well, and create your model in a clear and complete manner. Solve your model on Lindo. Interpret your results: Give a complete and practical interpretation of your results (state it in a way that your non-technical colleagues will understand) Put all results into a single file as stated in the directions at the top of the pageExplanation / Answer
>Every network flow model has a linear programming model, that is a model with algebraic linear expressions describing the objective function and constraints
>The linear programming model is an algebraic description of the objective to be minimized and the constraints to be satisfied by the variables. The variables are the flows in each arc designated by x1 through x17. The network flow problem is to minimize total cost while satisfying conservation of flow at each node.
>The variables must also satisfy the simple upper and lower bounds on arc flow.
>Mathematical technique used in computer modeling (simulation) to find the best possible solution in allocating limited resources (energy, machines, materials, money, personnel, space, time, etc.) to achieve maximum profit or minimum cost. However, it is applicable only where all relationships are linear (see linear relationship), and can accommodate only a limited class of cost functions
>Linear programming can be applied to a wide variety of fields of study, and has proved useful in planning, routing, scheduling, assignment, and design, such as in transportation or manufacturing industries.
>Linear programming models are found in almost every field of business model
>Workforce Planning
Problem Definition.
Consider a restaurant that is open seven days a week. Based on past experience, the number of workers needed on a particular day is given as follows:
Day Mon Tue Wed Thu Fri Sat Sun
Number 14 13 15 16 19 18 11
Every worker works have consecutive days, and then takes two days o , repeating this pattern indefinitely.
Q)How can we minimize the number of workers that sta the restaurant?
Ans:
>A natural (and wrong!) first attempt at this problem is to let xi be the number of people working on day i.
>Note that suchavariable definition does not match up with what we need to and. It does us no good to know that 15 people work Monday, 13 people Tuesday, and so on because it does not tell us how many workers are needed. Some workers will work both Monday and Tuesday, some only one day, some neither of those days. Instead, let the days be numbers 1 through 7 and
>let xi be the number of workers who begin their have day shift on day i.
>Our objective is clearly:
x1 + x2 + x3 + x4 + x5 + x6 + x7
>Consider the constraint for Monday's stang level of 14. Who works on Mondays? Clearly those who start their shift on Monday (x1). Those who start on Tuesday (x2) do not work on Monday, nor do those who start on Wednesday (x3).
>Those who start on Thursday (x4) do work on Monday, as do those who start on Friday, Saturday, and Sunday.
This gives the constraint:
x1 + x4 + x5 + x6 + x7 >=14
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