This paper considers the dynamic lot sizing problem of H. M. Wagner and T. M. Whitin with the assumption that the total cost of n setups is a concave nondecreasing function of n. Such setup costs could arise from the worker learning in setups and/or technological improvements in setup methods....

We are concerned with a discrete-time undiscounted dynamic lot size model in which demand and the production setup cost are constant for an initial few periods and the holding cost of inventory is an arbitrary nondecreasing function assumed to be stationary (i.e., explicitly independent of time)...

The textbook Dantzig-Wolfe decomposition for the Capacitated Lot Sizing Problem (CLSP),as already proposed by Manne in 1958, has an important structural deficiency. Imposingintegrality constraints on the variables in the full blown master will not necessarily give theoptimal IP solution as only...

We present new lower bounds for the Capacitated Lot Sizing Problem with Set Up Times. We improve the lower bound obtained by the textbook Dantzig-Wolfe decomposition where the capacity constraints are the linking constraints. In our approach, Dantzig-Wolfe decomposition is applied to the network...

In a recent paper, Fisher et al. (2001) present a method tomitigate end-effects in lot sizing by including a valuation term for end-of-horizon inventory in the objective function of the short-horizon model. Computational tests show that the proposed method outperforms the Wagner-Whitin algorithm...

We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated, in the presence of production capacities and for different transportation cost functions. The model we study is a generalization of the traditional single-item economic...

In a multiperiod decision problem it is usually the decisions in the first or first few periods that are of immediate importance to the manager. Decision/Forecast horizon (DH/FH) research deals with the question of whether optimal decisions in the first or first few periods (known as DH) can be...

This paper calls for a change in paradigm in lot sizing and scheduling. Traditionally, a discrete time scale is chosen to model lot sizing and scheduling. As an alternative, the so-called block planning concept is proposed which is based on a continuous representation of time. A mixed-integer...

Two types of quantity discounts are treated in the literature, namely, 'all units' discounts and incremental quantity discounts. In the all units quantity discounts model. the discount applies to every unit purchased. As a result, the total purchase cost is a discontinuous function of the...