This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a pathrelinking intensification procedure ...

In this paper, a new model of capacitated lot sizing and scheduling in a permutation flow shop is developed. In this model demand can be totally backlogged. Setups can be carryover and are sequence-dependent. It is well-known from literatures that capacitated lot sizing problem in permutation flow shop systems are NP-hard. This means the model is solved in polynomial time and metaheuristics alg...

We consider a capacitated production-inventory problem in both discreteand continuous-time, stationary settings. In the discretetime setting we analyze the infinite horizon capacitated dynamic lot-sizing problem, find the optimal solution and characterize its properties. For the continuous-time setting we formulate a new problem, which we claim to be an appropriate counterpart of the above disc...

The multi-stage lot-sizing problem with production capacities (MLSP-PC) deals with a supply chain that consists of a manufacturer with stationary production capacity and intermediaries (distribution centers or wholesalers) and a retailer to face deterministic demand. An optimal supply chain plan for the MLSP-PC specifies when and how many units each organization of the supply chain has to produ...

We address a multi-item capacitated lot-sizing problem with setup times, stock and demand shortages. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. In this paper we consider an approach based on a lagrangean relaxation of the capacity constraints to generate a lower bound of the optimal va...

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the socalled Facility Location formulation, the Shortest Route formulation, and the Inventory and Lot Sizing formulation with (`, S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integ...

We study the classical multistage lot sizing problem that arises in distribution and inventory systems. A celebrated result in this area is the 94% and 98% approximation guarantee provided by power-of-two policies. In this paper, we propose a simple randomized rounding algorithm to establish these performance bounds. We use this new technique to extend several results for the capacitated lot si...