Good day to you all ..

I built a routine to solve a machine-job allocation problem. This involves binary decision variables and an objective function to minimize the maximum completion time (makespan).The model assumes that each job, n, has a sequence of operations that must be processed in a specific order on a specific machine, m.

Consider (for example) the case of 5 machines and 3 jobs. Every job, 1, 2, and 3, visits machines 1 to 5 in order, with the processing times specified by the matrix, P. Maple successfully returns the required solutions for various combinations up to this scale.

However, when I encounter the 8-machine, 5-job problem, Maple stops (after 30 minutes of processing time) and returns the following error:

"Maximal depth, 182, of branch and bound search is too small; use depthlimit option to increase depth."

I have attempted to modify the depth limit (to a value exceeding 182) but without success ... I cannot resolve this problem. Can somebody advise on how to fix this - if possible? The worksheet in question is attached.

Thanks for reading.

MaplePrimes_Nov_16.mw

Good afternoon.

Here is (what appears to be) a simple assignment problem that involves scheduling 3 jobs through 2 machines, and I wish to minimize the total time required to complete all 3 jobs. Each job must be processed first on machine #1 before going to machine #2,and each machine can only handle one job at a time.

I have determined the optimal sequence to minimize the makespan (i.e., the completion time of the last job on machine #2) using a manual method and I was wondering if someone could review this (please see attached) and recommend a structured LP method or let me know if such a procedure exists in Maple's Optimization package.

Any help will be appreciated! 

Thanks for reading.

MaplePrimes_Nov_4.mw

Good day.

Using the iterative map routine, the location of the bifurcation points of the logistic function can be determined using the plot (see attached).

I was wondering .. is it possible to estimate and output the locations of these points and the range of the function? I would like to explore the bifurcation behavior for the modified function so, this would be a great help. 

In this case, the location of the points are: (1.00,0.00), (3.00, 0.66), (3.45, 0.44), (3.45, 0.85) and the range is [0,4]. 

Thanks for reading!

MaplePrimes_Oct_16.mw

Good day.

I am looking into the behaviour of a function, V, that depends on several parameter values; these values are fixed in the attached example. However, I have encountered an issue that is puzzling me and I was hoping that someone may be able to shine a light on this for me.

Basically,  I would like to understand how the solution, V, behaves as the value of exponent, beta, approaches infinity.

Straightforward analysis suggests that the value of V tends to -10 as beta grows infinitely large (s -> C, and beta ->infinity and so, V -> -10 ... so far, so good).

However, when the function is plotted, the solution seems to converge to a value, 6.5, as beta tends to a very large number (10^17).

Now .. here's the mystery .. there appears to be a critical value of around 7.854 x 10^17; here, the limit seems to switch from V=6.5 to -10. Does this phenomenon correspond to a discontinuity or is it related to the computational process? Are there any built-in routines in Maple to check for such potential conditions?

Thanks for reading!

MaplePrimes_Sep_19.mw

Good day.

I am constructing a 4-set Venn Diagram and I would like to know if it is possible to fix the number of decimal places in the solution.

The attached worksheet is given as an example; the default number of decimal places seems to be 2. I would like this to be either 0 or 1 (for both absolute and relative values). 

Does anyone know how to do this? 

Thanks for reading!

MaplePrimes_Venn_Diagram.mw