I have data (Annual generation, availability, O&M expenses) of three hydropower plants for a period of ten years. I want to apply data envelopment analysis to determine relative efficiency of these power plants. I am considering every power plant as a separate DMU (Decision making unit) for every year. This makes my total DMUs as 3 x 10 = 30. I want to know that for using O&M (Operation & maintenance expenses) in the DEA model, do I need to consider time value of money or write the ten year O&M values as they are obtained from the plants? If yes, how do I incorporate time value of money?
Yes, over ten years, the value of money will change most surely.
Depending on the historical context, money value may change every day significantly.
In any case, over ten years, it most surely will.
You may also ask your self with what relevant output power unit you plot your system.
Think of digital systems: from one year to the next the "customer accepted" memory size may go from 1 MB to 8 MB, 64MB, 256 MB, 1GB etc.
What is the demand curve for energy: maybe people need to have light, then a fridge, then a washing machine, ... then recharge an electrical motorbike
Thank you Renaud Di Francesco Sir for your reply. Sir, are you implying that I should calculate the rate of change for time value of money based on future demand curve or should I go for some standard inflation rates or WPI/ CPI available?
Thank you Saeed Assani Sir for you reply. I agree with your point but I am not able to put it to right words, there is still confusion with me, of not including time value.
Sir, I have 3 power plants, my aim is input reduction (O&M expenses and plant unavailability) with output energy generation fixed. For every year for each DMU, a relative efficiency value is calculated.
Does it not imply that every efficiency value is calculated using its data for that year (I think this is absolute efficiency),?
or, it implies that,
every efficiency value calculated is dependent on all other values justified by the BCC or CRS model equations? But the question arises to me that even in the relative calculation, a power plant "A" with less O&M in 2010 shall turn out to be more efficient than "A" in 2018 with more O&M expenses? Of course generation and unavailability values will also vary too in 2010 and 2018.
Please help me with this confusion.
Thank you Ahmed Mohamed Habib
. Can I not use an "input-oriented non-discretionary model for my analysis, considering every power plant as a separate DMU in all the ten years?
Saeed Assani Can you please guide me as to how I should evaluate increasing/ decreasing returns to scale in my case? Which model should I use?
Thank you.
Thank you Saeed Assani . Yes, I have read the 2004 returns to scale paper. It is an excellent read. Also I will go through your paper for scale efficiency.
Is it necessary to evaluate ratio of CCR and BCC models to obtain scale inefficiency?, as we can obtain the RTS directly from models described in the 2004 paper.
In many papers I have found that CCR model is used for power plant efficiencies along with BCC model, although the input and output factors do not change proportionally, so I was considering leaving the CCR model. As per your expert opinion, when should CCR and BCC model be used or both should be used?
Regards
Sanchit
Saeed Assani I have obtained CCR and BBC efficiency along with values of scale efficiency. Regarding Returns to scale, I am able to solve the simple example given in 2004 Banker et al. paper.
However, my model is input oriented which contains a non-discretionary (ND) input. As per 2004 paper, what mathematical model (in BCC and CCR) will represent the returns to scale with ND input?
I believe an equation for ND input is supposed to be added in the given models?
Saeed Assani
1. On solving the input oriented CCR and BBC non-discretionary models, [Softwares: Springer DEA Solver LV8 and DEAOS (Online DEA)] the result includes slacks even for the non discretionary input. I am unable to understand the logic behind this? If it is ND, why slacks are appearing as we cannot change the input values of ND input.
2. Additionally , For return to scale,
I have prepared non-discretionary models based on the 2004 Banker et al, paper on returns to scale.
I am attaching the mathematical models in a word file. I humbly request you to check whether I have correctly incorporated the non-discretionary part in objectives and constraints.
Again, I thank you for giving your valuable time and expertise for my help.
Sincerely,
Sanchit S Agarwal
Saeed Assani Are you suggesting to avoid using models 4 and 6? Should I use only 2 and 5 for every DMU and determine the RTS.
But, as per theory models 4 and 6 are used to avoid having to explore all optimum solutions. May I know what that means?
Tme value of money is taken into account by discounting the value for O&M (Operation & maintenance expenses) by a discount rate. Discount rate is the company's average cost of borrowing money from equity or from banks.
Renaud Di Francesco I had replied you on March 11, without realizing I did not tag your name. Here I am posting my query again!
Thank you Renaud Di Francesco Sir for your reply. Sir, are you implying that I should calculate the rate of change for time value of money based on future demand curve or should I go for some standard inflation rates or WPI/ CPI available?
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