Ok, I see you must be using ANSWER-TIMES.
In ANSWER-TIMES the specification of parameters for PAST years is, indeed, a bit limited.
However, you still have reasonable ways of specifying e.g. the investment costs for past investments.
- All the costs parameters are by default extrapolated backwards. Therefore, if you specify a cost for the year 2000 (and this is your first datayear), it will be applied to the past investments of that process as well (unless you use an interpolation option that prevents backwards extrapolation).
- ANSWER supports datayear and modelyear independence. Therefore, you could add one or two past datayears into your TS spread, while still keeping 2000 as the first Milestone year (called Result Year in ANSWER) in your model. So, you could add 1990 as an additional datayear into the model database, and then you could specify the costs directly for the year 1990.
I am not sure what you mean by "depreciation costs" here. But TIMES of course takes into account the discount factor for the 1990 investments when adding the investment costs into the objective function. And in a certain sense it also takes into account depreciation, by taking into account the value of the remaining lifetime falling within the model horizon.
As an example, assume that your model horizon starts in 2000, and also the base year for discounting is 2000, and the discount rate is 5%. Now assume that you have specified NCAP_PASTI(1990)=1 with a lifetime of 20 years, and you specify NCAP_COST(2000)=100. The costs will be extrapolated backwards, and so we will also have NCAP_COST(1990)=100. When discounted forward, the 1990 investment has a value of 100*1.05^10 = 162.9 in terms of 2000 money value. However, because the plant has only 10 years of remaining lifetime within the model horizon, the depreciated value is 162.9*0.3804 = 62.0, which is the cost entered into the objective function. (The coefficient 0.3804 is the discounted value of the remaining lifetime as a fraction of the total discounted lifetime).
However, note that the costs of the past investments represent sunk costs that actually have no impact on the model solution, because they are a constant term in the objective. Threfore, it actually does not matter how the costs of the past investments are accounted in the objective function.