Yarn Resource Allocation

Say for an example,i have Color codes that are : A , B , C I want to repeat this colors so i ll put them as : 5A , 10B , 10C = 25 So now A will repeat 5 times ,B will repeat 10 times and C will repeat 10 times.

Now i have 16 hands. in which i can allocate those colors.but problem is i can not allocate it more than 16 as i have hand limits.Here i have total 25 of all colors so i need to find how many times A will be place out of 16,How many times B and how many times C.

Also one constraint is that this color should repeat exact times that are mentioned.And during one color repetition another can not start.

Take some examples here.

Previous on is simplest one but it may get complex.

The main thing is i want step reduction by allocating number of hands and reducing steps.

Complex equation: 45A18(150B98C45A)40D17(50A60D)45C

and its nearly optimized Arrangement are : 1A 4B 3C 2A 1D 2A 2D 1C=16 Steps: 1796

Can anyone guide me which Allocation algorithm i can apply to get optimized low steps and allocate hands.

I tried Permutation combination after hand allocation but 16 hands take more than hours to get all combinations.

Thanks in advance.

Notes: 16 hand means we have 16 mechanical hand that goes up down based on color pattern.

Machine is designed to move round and with moving round it controls 16 mechanical hands that are attached on each corner.

each hand has mentioned color thread that weaves color one by one by given pattern.

My input will be color pattern in form of 5A , 10B , 10C My out put need to complete this task with having 16 hand which can max support color from A to P.

Steps are number of times machine needs to circle to complete entire operation. See row in image that shows number.

columns shows 16 hand that contains color.

Colors need to be arranged and assigned in that way that it reduce steps (rows).

• Welcome to CS.SE! This sounds interesting, but I admit I'm a little confused. What is the input? What is the desired output? It sounds like maybe the input is the number of times you want each color to repeat and the number of hands; and the desired output is the arrangement? What are the rules on what arrangements are allowable? What's the relationship between the picture you're showing and the textual arrangement? What does step reduction mean? What's a step? Can you edit your question to clarify?
– D.W.
Nov 3 '16 at 8:10
• "Now i have 16 hands." I have only two, so I guess you're using the word "hand" to mean something other than its normal meaning. You seem to be assuming that we know a lot of specialist terminology, where the specialization in question is, er, knitting or something? We don't know that. Please define your terms. Nov 3 '16 at 8:46