I am doing a linear program problem about motor cars.
I need to write a constraint to say that the stock for ten models of cars at the end of each month, is the initial stock for the next month?
I've only been given the initial stock for the beginning of January, which is:
M1: 500, M2: 1000, M3: 1550, M4: 1500, M5: 2000, M6: 2000, M7: 1800, M8: 1470, M9: 750, M10: 940
Also that the initial stock for December for each model needs to be greater than 500 and the total amount which can be stocked for each model is 2000.
Usually we model this with an inventory balance equation. Something like: $$ Inv_{t} = Inv_{t-1} + Prod_t - Sales_t $$ i.e. inventory at end of period is inventory at end of previous period plus production minus sales during the period. ($Inv$ is a stock variable and $Prod$ and $Sales$ are flow variables). I don't see immediately why you need inventory at beginning of $t$ and end of $t-1$ (that is essentially the same quantity). $Inv_0$ can be initial inventory and you can put a constraint on the final inventory $Inv_T$ if needed. You can also put restrictions on the intermediate inventories (for example storage capacity).