Factory Planning Project (TAU 2015)

The goal of the project is given a projected set of departments and their areas, to plan the best arrangement that uses the smallest area keep short distances between related departments. The full problem is NP-Hard, and a approximization approach was presented.

The presented problem is:

Place n departments, with area given by a vector - A (10% deviance is allowed)

• Symmetric relation between department is given in Rij Matrix
• Relations are scaled between 0 (uninportant) and 3 (important to be located nearby)
• The distance is measured as rectangular distance (L1 norm) between the centers of the departments
• Goal Function is:

Minimize [ w1 x Sumall_ij(Dij x Rij) + w2 x A]

Where A is the area of minimal blocking rectangle of the whole factory, w1/w2 are input weights, R is the relation matrix and D is the distance matrix

Subject to restrictions:

• The ratio of blocking rectangle area compared to department area won't exceed 1.3
• The ratio of blocking rectangle sides of each department won't exceed 1.3

The solution approach used Python and CPLEX OPL MILP programming to reach the best planning.

Files and Directories:

• resplot.py - main python code to generate the OPL input file, run the optimization and create the output image and data
• Planning.mod - main OPL code
• input.dat - OPL data input template
• inputs - folder with 10 problems x3 (w1=0/0.5/1) in xlsx accompanied with generated OPL dat file
• png - folder with result outline images
• txt -folder with result metrics and coordinates

Mixed Integer Linear Programming Model: