Requires that each item i with weight w[i], be put into bin[i] such that the sum of the weights of the items in each bin does not exceed the capacity c.
Assumptions:
- forall i, w[i] >=0
- c >=0
Requires that each item i with weight w[i], be put into bin[i] such that the sum of the weights of the items in each bin b does not exceed the capacity c[b].
Assumptions:
- forall i, w[i] >=0
- forall b, c[b] >=0
Returns the load of each bin resulting from packing each item i with weight w[i] into bin[i], where the load is defined as the sum of the weights of the items in each bin.
Assumptions:
- forall i, w[i] >=0
Requires that each item i with weight w[i], be put into bin[i] such that the sum of the weights of the items in each bin b is equal to load[b].
Assumptions:
- forall i, w[i] >=0
Constrains rectangles i, given by their origins (x[i], y[i]) and sizes (dx[i], dy[i]), to be non-overlapping. Zero-width rectangles can still not overlap with any other rectangle.
Constrains k-dimensional boxes to be non-overlapping. For each box i and dimension j, box_posn[i, j] is the base position of the box in dimension j, and box_size[i, j] is the size in that dimension. Boxes whose size is 0 in any dimension still cannot overlap with any other box.
Constrains rectangles i, given by their origins (x[i], y[i]) and sizes (dx[i], dy[i]), to be non-overlapping. Zero-width rectangles can be packed anywhere.
Constrains k-dimensional boxes to be non-overlapping. For each box i and dimension j, box_posn[i, j] is the base position of the box in dimension j, and box_size[i, j] is the size in that dimension. Boxes whose size is 0 in at least one dimension can be packed anywhere.
A global non-overlap constraint for k dimensional objects. It enforces that no two objects overlap.
- k: the number of dimensions
- rect_size: the size of each box in k dimensios
- rect_offset: the offset of each box from the base position in k dimensions
- shape: the set of rectangles defining the i-th shape. Assumption: Each pair of boxes in a shape must not overlap.
- x: the base position of each object. x[i,j] is the position of object i in. dimension j.
- kind: the shape used by each object.
A global non-overlap constraint for k dimensional objects. It enforces that no two objects overlap, and that all objects fit within a global k dimensional bounding box.
- k: the number of dimensions
- rect_size: the size of each box in k dimensios
- rect_offset: the offset of each box from the base position in k dimensions
- shape: the set of rectangles defining the i-th shape. Assumption: Each pair of boxes in a shape must not overlap.
- x: the base position of each object. x[i,j] is the position of object i in dimension j.
- kind: the shape used by each object.
- l: is an array of lower bounds, l[i] is the minimum bounding box for all objects in dimension i.
- u: is an array of upper bounds, u[i] is the maximum bounding box for all objects in dimension i.
A global non-overlap constraint for k dimensional objects. It enforces that no two objects overlap, and that all objects fit within a global k dimensional bounding box. In addition, it enforces that the bounding box is the smallest one containing all objects, i.e., each of the 2k boundaries is touched by at least by one object.
- k: the number of dimensions
- rect_size: the size of each box in k dimensios
- rect_offset: the offset of each box from the base position in k dimensions
- shape: the set of rectangles defining the i-th shape. Assumption: Each pair of boxes in a shape must not overlap.
- x: the base position of each object. x[i,j] is the position of object i in dimension j.
- kind: the shape used by each object.
- l: is an array of lower bounds, l[i] is the minimum bounding box for all objects in dimension i.
- u: is an array of upper bounds, u[i] is the maximum bounding box for all objects in dimension i.
Requires that items are packed in a knapsack with certain weight and profit restrictions. Assumptions:
- Weights w and profits p must be non-negative
- w, p and x must have the same index sets
- w: weight of each type of item
- p: profit of each type of item
- x: number of items of each type that are packed
- W: sum of sizes of all items in the knapsack
- P: sum of profits of all items in the knapsack