Ayse Akbalik

Polynomial time algorithms for the constant capacitated single-item lot sizing problem with stepwise production cost

Abstract This paper presents two polynomial time algorithms for the constant capacitated lot sizing problem with a batch production. We give several optimality properties for the general problem. Assuming constant production capacity, constant batch size and Wagner–Whitin cost structure, we derive O ( T 4 ) and O ( T 6 ) time algorithms respectively for the case with production capacity being a multiple of the batch size and for the case with an arbitrary fixed capacity.

The single item uncapacitated lot-sizing problem with time-dependent batch sizes : NP-hard and polynomial cases}

This paper considers the uncapacitated lot sizing problem with batch delivery, focusing on the general case of time-dependent batch sizes. We study the complexity of the problem, depending on the other cost parameters, namely the setup cost, the fixed cost per batch, the unit procurement cost and the unit holding cost. We establish that if any one of the cost parameters is allowed to be time-dependent, the problem is NP-hard. On the contrary, if all the cost parameters are stationary, and assuming no unit holding cost, we show that the problem is polynomially solvable in time O(T3), where T denotes the number of periods of the horizon. We also show that, in the case of divisible batch sizes, the problem with time varying setup costs, a stationary fixed cost per batch and no unit procurement nor holding cost can be solved in time O(T3 logT).

Capacitated lot sizing problems with inventory bounds

In this paper, we study the single-item and the multi-item capacitated lot sizing problem in presence of inventory bounds (CLSP-IB). That is, in any period, both the quantity produced and the stock on hand are limited. For the single-item CLSP-IB with a stationary production capacity, time-dependent inventory bounds and concave costs, we show that the problem can be solved in time

Multi-item uncapacitated lot sizing problem with inventory bounds

O(T^4)

Lot sizing problem with multi-mode replenishment and batch delivery

O(T4) by adapting a well-known algorithm in the literature. Restricting to non-speculative costs, we propose an

Inventory replenishment planning with a full truckload cost and a full return policy

O(T^3)