I try to solve a manufacturing problem. I got K products over T periods of time with given demand d(t,k) for every time period and every product. I got only one machine with a given capacity in each timeperiod t c(t) Setuptimes for each product ts(k), productiontimes tp(k), Setupcosts s(k) and holdingcosts h(k). I want to minimize the costfunction:
-> Sum[1:T](Sum[1:K](s * y + h(k)*I(t,k)))
where y is a binary variable and I(t,k) is the stored amount of units which we did not used to fullfill demand. Q(t,k) will be the amount of produced products. y,I,Q are to optimize as integers using intlinprog()
I got the functions and all conditions. The only thing where i got problems is, to formulate the condition of
-> I(t-1,k) + Q(t,k) - I(t,k) = d(t,k)
which has to consider the left stock from the previous period. and i don't know how to refer to the previous persiod.
for ii = 1:T for jj = 1:K xtemp = clearer2; xtemp(ii,jj) = -1; xtemp2 = clearer3; xtemp2(ii,jj) = 1; xtemp = sparse([clearer12;xtemp(:);xtemp2(:)]'); % Change to sparse row
Aeq(counter,:) = xtemp; % Fill in row
if ii > 1 beq(counter) = d(ii,jj); % Problem -> can not subtract I(t-1,k)
else beq(counter) = d(ii,jj); % first Period no Stock
end counter = counter + 1; end end
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