Multiproject Resources Allocation Model under Fuzzy Random Environment and Its Application to Industrial Equipment Installation Engineering

Procedure 1

Calculate fitness value using fuzzy random simulation.

Step 1: Let 𝑛=1, 𝐹_𝑛=−∞, 𝑓(𝑐̃_𝑘𝑝)=∑^𝑁_𝑛=1𝑐𝑝_𝑛𝐷𝑇_𝑛+∑^𝑃_𝑝=1∑^𝐾_𝑘=1∑^𝑁_𝑛=1𝑐̃‌_𝑘𝑝𝑅_𝑛𝑘𝑝.

Step 2: Generate ω from Ω according to the probability measure Pr of the fuzzy random variables 𝑐̃‌_kp.

Step 3: Generate a determined vector 𝑓(𝑐̃_𝑘𝑝(𝜔)) uniformly from the α-cut of fuzzy vector 𝑓(𝑐̃_𝑘𝑝(𝜔)).

Step 4: If 𝑓(𝑐̃_𝑘𝑝(𝜔))≤𝐹_𝑛, then let 𝐹_𝑛=𝑓(𝑐̃_𝑘𝑝(𝜔)). Return to step 3, and repeat 𝑀 times.

Step 5: If 𝑛=𝑁, set 𝑁^′=𝛽𝑁 and return the 𝑁^′th least element in {𝐹₁, 𝐹₂,…, 𝐹_𝑁} as the fitness value; else go to step 2, and 𝑛=𝑛+1.