Economic lot sizing and scheduling problem (ELSP): common cycle
We consider a single machine producing several products. The goal is to minimize
the sum a holding and setup costs with the constraint that no backorders occur.
Applying the classical production lot size model for each product in general
will not lead to a feasible production plan, as the production intervalls of
at least two products will overlap. Therefore, in addition to lot sizing the
scheduling aspect of the problem must be considered.
In this module we consider a common cycle policy.
Symbols:
| k |
index of products |
| D(k)
|
demand
rate of produkt k |
| p(k) |
production rate
produkt k |
| t(k) |
setup time for
product k |
| s(k) |
setup cost for
product k |
| h(k) |
holding cost
for product k |
| q(k) |
isolated optimal
lot size for product k (computed with the economic
production quantity formula) |
| Tmin |
lower bound
for the common cycle |
| Topt |
optimum common
production cycle |
Assumptions:
- continuous stationary demand for each product
- finite production rate for each product
- no backorders
Literatur:
- Nahmias (1997), Chapter 4.9
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