MATERIALS HANDLING SYSTEM DESIGN - Environmentally Conscious Materials Handling - page 23

The first part of objective function's three terms indicates the manufacturing
operation costs, the machine setup costs, and the MH operation costs, respec-
tively. The second part of the objective function computes the overall compat-
ibility of the MH equipment. As a result, the formulation of the problem is a
multiobjective model seeking to strike a balance between the two objectives.
There are nine constraints in this model:
1. Each part type can use only one process plan:
P(i)

Z(ip) = 1 ∀ i. (3)

p = 1

2. For a given part type i under process plan p , each operation of the selected
process plan is assigned to only one of the available machines:

Y sj (ip) = Z(ip) ∀ i, p, s.

(4)

j ∈ J ips

3. Once a machine is selected for operation s of part type i under process
plan p , then all the ( h h ) combinations corresponding to ( sj )mustbe
performed:

i, p, s, j, h, h. (5)
4. Each h h combination can be assigned to only piece of available and
capable MH equipment:

Y sj (ip) = A sj h h (ip) ∀

i, p, s, j, h, h. X ijph he = A ijph h ∀

(6)

e ∈ E jhh

5. At least one operation must be allocated to a selected machine:

H

P(i) S(ip)

n H

X ijph he ≥ M j ∀ j. (7)

i = 1 p = 1 s = 1 h = 1 h e ∈ E jhh

= 1

6. The allocated operations cannot exceed the corresponding machine's
capacity:

H

n P(i) S(ip) H

d i t sj (ip)X ijph he ≤ b j M j ∀ j.

(8)

e ∈ E jhh

i = 1 p = 1 s = 1 h = 1 h

= 1

7. A specific MH equipment can be selected only if the corresponding type
of equipment is selected:

D e ≤ D e ∀ e, e. (9)