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 WagnerWhitin cost structure, we derive O(T ) and O(T ) time algorithms respectively for the case with production capacity multiple of the batch siz...

This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, therefore efficiently avoiding the weaknesses asso...

We present an ant-based algorithm to solve multi-level capacitated lot sizing problems. We apply a hybrid approach where we use the ant system to optimize the decomposition of the problem into smaller subproblems. These subproblems containing only a few items and periods are solved using CPLEX. Then the overall solution is derived by consolidating the partial solutions. This hybrid approach pro...

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 WagnerWhitin cost structure, we derive O(T 4) and O(T 6) time algorithms respectively for the case with production capacity multiple of the batch s...

The aim of lot sizing problems is to determine the periods where production takes place and the quantities to be produced in order to satisfy the customer demand while minimizing the total cost. Due to its importance on the efficiency of the production and inventory systems, Lot sizing problems are one of the most challenging production planning problems and have been studied for many years wit...

The capacitated lot sizing policy is pivotaltostochastic production planning. This paper attempts to formulate a general lot sizing model for a stochastic MTS (make-to-stock) manufacturing environment under demand uncertainty. To better reflect real-world manufacturing, general distributions are used as a substitute for unrealistic theoretical assumptions on involved random variables. Instead o...

This paper deals with the multi-item capacitated lot-sizing problem with setup times and lost sales. Because lost sales, demands can be partially or totally lost. To find a good lower bound, we use a Lagrangian relaxation of the capacity constraints, when single-item uncapacitated lot-sizing problems with lost sales have to be solved. Each subproblem is solved using an adaptation of the O(T ) d...

Starting from the seminal intuitions that led to the developments of the Economic Order Quantity model and of the formulation of the Dynamic Lot Sizing Problem, inventory models have been widely employed in the academic literature and in corporate practice to solve a wide range of theoretical and real-world problems, as, through simple modifications to the original models, it is possible to acc...