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)...

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...

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...

This work aims at investigating the influence of picking batch size to average time in system of orders in a one-aisle warehouse under the assumption that order arrivals follow a Poisson process and items are uniformly distributed over the aisle's length. We model this problem as an M/G[k]/1...

Two heuristics based on branch and bound (B&B) are developed to solve closed-loop material requirements planning (MRP) lot-sizing problems that have general product structures and variable costs. A “look ahead method'’(LAM) heuristic allows for variable production/purchasing costs and uses a...

The research on lot sizing is extensive; however, no author in the literature reviewed to date provides an optimal solution algorithm to a prevalent problem which is found in manufacturing. A multi-level, general product-structure, variable-cost model is presented which follows the procedure of a...