We propose a new algorithm to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously to minimize total production cost in a CNC environment. Most of the existing lot sizing and tool management methods solve these problems independently using a two-level optimization approach. Thus, we not only improve the overall solution by exploiting the interactions a...

We present lot-sizing heuristics that are both e cient and stable for the dynamic lot-sizing problem(DLSP) with constant or variable unit costs, including setup, inventory holding and production costs. These heuristics are myopic variants of the forward Wagner-Whitin algorithm with rolling horizons. Large scale computational experiments show that these heuristics considerably outperform other w...

We introduce a dynamic economic lot sizing problem whose production cost considers both setup and the designed-and-yet stretchable production capacity. Demands and the control on production activities drive the evolution of the production system. We give a pseudo-polynomial algorithm for the problem when future demands are known. When there is uncertainty in future demands and there is no holdi...

This paper presents a multi-period inventory lot-sizing scenario, where there are multiple products and multiple suppliers. We consider a situation where the demand of multiple discrete products is known over a planning horizon. Each of these products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applying for each period in which an order is placed on a ...

The fundamental question encountered in acquiring capacity to meet nonstationary demand over a multiperiod horizon is how to balance the trade-off between having insufficient capacity in some periods and excess capacity in others. In the former situation, part of the demand is subcontracted while, in the latter, capacity that has been paid for is rendered idle. Capacity and subcontracting decis...

We study the polyhedral structure of variants of the discrete lot–sizing problem viewed as special cases of convex integer programs. Our approach in studying convex integer programs is to develop results for simple mixed integer sets that can be used to model integer convex objective functions. These results allow us to define integral linear programming formulations for the discrete lot–sizing...

We study a two-level uncapacitated lot-sizing problem with inventory bounds that occurs in a supply chain composed of a supplier and a retailer. The first level with the demands is the retailer level and the second one is the supplier level. The aim is to minimize the cost of the supply chain so as to satisfy the demands when the quantity of item that can be held in inventory at each period is ...

In this paper, a case study is carried out concerning the lot-sizing problem involving a single item production planning in several production centers that do not present capacity constraints. Demand can be met with backlogging or not. This problem results from simplifying practical problems, such as the material requirement planning (MRP) system and also lot-sizing problems with multiple items...

Our incentive is to study the behaviour of lot-sizing rules in a multilevel context when forecast demand is subject to changes within the forecast window. To our knowledge, only Bookbinder and Heath (1988) proposed a lot-sizing study in a multi-echelon rolling schedule with probabilistic demands. But their simulation study was limited to two arborescent structures with 6 nodes. By means of an e...

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...