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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.


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


  • continuous stationary demand for each product
  • finite production rate for each product
  • no backorders


- Nahmias (1997), Chapter 4.9

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