A common problem in process design is the selection of optimal operating condition, which involves considering simultaneously multiple response (output) variables. This type of problem is known as multiple response optimisation (MRO) problems. Multiple response problems are quite prevalent across various disciplines of science and engineering. In this context, responses are the quality characteristics which attribute to the quality of process or product. In this context, responses may be catogorised into three different types, viz. larger-the -better(LTB), smaller-the-better(STB) and nominal-the-best(NTB).

For LTB type of response, the value of response is expected to be higher than the lower specification bound (target) on response. For smaller the better type response, the value should be lower than the upper bound on response. In case of nominal the best type of response, the value of response should be at spcefied target value with minimum variance.Response are affected by the set of input process conditions (variables)

However,set of optimal input condition for a a particular response may not be optimal for some other response. Thus, a trade-off solution is inhabitable in MRO problem.

In case of manufacturing or service processes, MRO problems are quite prevalent. Manufacturing problems. Multiple response problems are prevalent. Manufacturing product or service delivery may be a single-stage or multi-stage processes. In single isolated stage process, desired finished product or service is attained  after passing through multiple interdependent stages. The most challenging a spect for (STB), MRO problem is attaining optimal (or tion
multiple stage. Researchers had  demonstrated that optimising each stage in isolation may not assure optimality of entire multi-stage process due to cascade effect. An interdependent multistage process shown in the figure.

Our research group works to determine multi- objective trade-off near optimal solutions for multi-stage MRO problems in manufacturing and service environment.