# How to obtain the sensitivity analysis of correlated data?

A company should supply 2 products namely A and B. The company can buy A and B in advance or in real-time, however at different prices. The demand is uncertain and prices are considered to be deterministic. Therefore, I developed a stochastic model in which uncertain demand and prices are the input and its revenue for selling the products is the output.

LA : The price of product A when buying before the delivery time.
LB : The price of product B when buying before the delivery time.

CA: The price for selling A to the customer
CB: The price for selling B to the customer

LAA : The price of product A when buying at the delivery time.
LBB : The price of product B when buying at the delivery time.

R   : Revenue of the company


Now I want to apply a sensitivity analysis based on market prices. My assumption is to gradually increase each price while keeping the others constant and see it's the effect on the revenue. Therefore, I will get 6 tables regarding the relationship between the increase in each price wrt the revenue.

For example: Let say LA = 30 while R = 50. Thus I change LA to 31 and feed it to the model. Let say the R' will be 48. I continue this routine until LA = 40. Then I can see the relationship between LA and R for a range of prices.

However, this method only considers the impact of the change in one input variable on the output. Therefore, it doesn't consider the combined variation of inputs (LA, LB). How can I perform a valid sensitivity analysis for this problem where a subset of the inputs are changed while the others are fixed? Moreover, the prices in the model are somehow correlated in reality.

• What do you mean by "correlation of prices"? Your problem description indicates that prices are deterministic. Are you assuming a relationship among them, such that if one price changes others also will change?
– prubin
Commented Aug 21, 2020 at 15:58
• I have considered the mean value of prices in the model. However I am asked to apply a sensitivity analysis on market prices wrt the revenue. But, I know that market prices depends on each others as well. Anyhow still don't know how they are correlated with each others @prubin
– SAH
Commented Aug 21, 2020 at 16:20
• it sounds like you are concerned that the price elasticity of demand is correlated across products. I.e., price elasticity of demand for product A depends on the price of product B. Is that correct? If so, you may need a multivariate model,and multivariate analysis of it. @prubin The prices may be deterministic (set by the seller), but the demand is not deterministic. Commented Aug 22, 2020 at 14:20
• Yes. How can I do so?
– SAH
Commented Aug 23, 2020 at 9:28