I am trying to solve an assignment problem where all the variables are continuous. I have a set of sources S, and another set of destinations D. Each source and destination have capacity/demand expressed as continuous variables. There is a distance associated with each source-destination. I need to find the ideal allocation while minimizing the total distance in the network. A source can supply to multiple destinations, and the reverse holds true as well. The caveat is that the allocation has to be split among multiple sources for every destination. For example, we have 3 sources S1, S2, S3 with capacities 1081.52, 3810.48, 950.64 respectively. There are 2 destinations D1, D2 with demands 1759.38, and 3993.21. My final assignment looks like this:
|Destinations||Sources||Supply||Total Demand at Destination|
What type of algorithm should I be looking at for such problems? I also want to place constraints on how many times a source can be used.