A mathematical model for lot sizing and determination of optimal production rate with two different types of sequence-dependent setup

Lot-sizing and scheduling tasks are the main parts of an operative production planning and control system. Because of interrelationship between these problems, simultaneous lot sizing and scheduling is essential especially when sequence dependent setup costs and times occur. On the other, Optimizing production rate is one of the main challenges in production planning. In this paper, we try to obtain production rate and quantity of production in each period for a circular saw machine that works at different speeds. There are also two types of setups, one for switching between products and the other for switching between cutting techniques (cutting speed). Using the proposed mathematical model, the problem seeks to minimize total costs, which include inventory/backlog, setups cost, energy costs, cost of producing defective products, and production costs. This problem will be implemented according to the conditions considered and for a numerical example in GAMS software.

Keywords:

Lot-sizing and scheduling , production rate , sequence dependent setup , circular saw machine