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Nomenclature Indices

j

= Index for operations of part p (j = 1,…,Op);

p

= Index for parts (p = 1,…,P);

m, n

= Indices for machines (m,n = 1,…, M); and

c, k

= Indices for manufacturing cells (c, k = 1,…,C).

 Input data

P

= Number of parts;

Op

= Number of operations of part P;

M

= Number of machines;

C

= Number of manufacturing cells;

Bp

= Bach size of the part P;

γ0

= Per batch, the movement cost for each unit of distance;

Lmax

= Length of the shop floor;

Wmax

= Width of the shop floor;

Lm

= Length of machine type m;

Wm

= Width of machine type m;

Hdmn

= Horizontal allowable distance between machine types m and n;

Hdck

= Horizontal allowable distance between cells c and k;

Vdmn

= Vertical allowable distance between machine types m and n;

Vdck

= Vertical allowable distance between cells c and k; and

Dm

= Allowable distance between machines and cell boundary.

 Data resulted from the cell formation stage

Dp

= Demand for part type P;

αjpm

= 1; If the operation j of part p is assigned to the machine m, 0; Otherwise; and

βmc

= 1; If the machine m is assigned to a cell c, 0; Otherwise.

 Variables Continuous

(xm, ym)

= Centroid coordinates of machine type m;

(xlcc, ylcc)

= Lower left-hand corner coordinates of cell c;

(xucc, yucc)

= Upper right-hand corner coordinates of cell c; and

dmn

= Rectilinear distance between the centroid of machines m and n.

 Binary

amnx, amny

= 1; If the machine m is located to the left/below of machine n, 0; Otherwise (right/up); and

bckx, bcky

= 1; If the cell c is located to the left/below of cell k, 0; Otherwise (right/up).

                                                                        

            

        

 

 
 

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