Two-Level Lot-Sizing Problems
Integrating Production,
Transportation, Inventory, and Pricing
Decisions
Mehmet Önal and H. Edwin Romeijn
Dept. of Industrial and Systems Engineering
In classical requirements
planning problems it is usually assumed that all demands are known. However,
through pricing decisions, a firm can control the demand levels it faces and
potentially obtain higher profits. We consider a two-level uncapacitated
lot-sizing problem where production, inventory carrying, transportation, and
pricing decisions are integrated to maximize total profits. We model the
revenue in each period as a general concave function of the demand satisfied in
the period and the production costs as a concave function with a fixed-charge
structure, i.e., it has a fixed setup cost component and a variable cost
component. We then study our problem under a number of different inventory
holding and transportation cost structures. In our first model we assume that
the inventory holding and transportation cost functions are all linear. In our
second model we allow for concave transportation cost functions with a
fixed-charge structure, while in our third model we also allow the inventory
holding cost functions at both levels to be concave with a fixed-charge
structure.