linprog function over multi period

Question

Scott 2022-8-24

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https://ww2.mathworks.cn/matlabcentral/answers/1785025-linprog-function-over-multi-period

评论： Torsten 2022-8-24

采纳的回答： Torsten

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For the following question.

A Company expects an increase of demand and needs to scale-up.

Using MATLAB linprog to propose a recruitment plan to meet demand and minimise cost for the next 6 years.

Expected hours of work to meet demand

Year 1 4000

Year 2 4500

Year 3 3500

Year 4 5000

Year 5 4500

Year 6 5500

When a new worker is recruited, they need to be trained by an experienced worker for one year.

After training they become experienced worker.

Each Experienced worker can do 75 hours per year.

This is reduced to 25 hours for a experienced worker who is training a new worker.

At the beginning of Year 1 there are 60 experienced workers.

5% of experienced workers choose to leave the company every year but cannot be fired.

The labour cost of an experienced worker is $ 3500 per year and It is $ 2000 for newly recruited worker during their first year.

close all 
clear all 
f=[3500;2000]; 
A=[150,-100; 150,-100;150,-100;150,-100;150,-100;150,-100]; 
b=[4000;4500;3500;5000;4500;5500];   
[x,fval,exitflag,output,lambda] = ...
linprog(f,A,b,[],[],[],[],options);

I have made a start but I was hoping someone could point me towards some documentation to guide me on solving this. I don't see how this fits with the linprog function as the Experienced workers after attrition are dependent on the decision variable of recuited workers. I didn't find any examples in the matlab help files under linprog. Do I need to consider a recursive loop and how would that work in linprog.