(15) Consider the Part Type Selection problem we covered in class. This problem helps us determine which parts we will produce in a new FMS. The problem assumes that we have candidate parts ii = 1,2, ... NN, that the total savings achieved by producing part ii in the FMS is ssii and that we know that there is a key bottleneck in the FMS, which has PP available time units. Each part ii requires a total processing time ppii in the key bottleneck. In class we saw that a way to solve this problem is the following Greedy Heuristic: Step 1: Order parts [1] to [N] such that ss[1] pp[1] ss[2] pp[2] ss[NN] pp[NN]

Define remaining available time TT = PP Step 2: For ii = 1 ... NN select part [ii] and add the part to the FMS if ppii < TT and ssii > 0. Each time you add a new part ii, update remaining available time as TT = TT ppii. Now suppose you had 3 key bottlenecks (that is 3 resources that each might be the bottleneck depending on the parts you choose to produce in the FMS). These resources have PP,QQ and RR time units available respectively. And each part ii requires a total processing time ppii, qqii and rrii in each of the three, respectively. Modify the algorithm above to solve the 3-bottleneck version of the problem