This paper deals with the problem of planned lead time calculation in a Material Requirement Planning (MRP) environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered: multi-level serial-production and assembly systems. For the serial production systems (one type of component at each level), a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and several numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.

In this paper, we study the sensitivity of the optimum of the knapsack problem to the perturbation of the profit of a subset of items. We propose a polynomial heuristic in order to establish both lower and upper bound limits of the sensitivity interval. The aim is to stabilize any given optimal solution obtained by applying any exact algorithm. We then evaluate the effectiveness of the proposed solution procedure on an example and a set of randomly generated problem instances.

Operating Theatre is the centre of the hospital management’s efforts. It constitutes the most expensive sector with more than 10% of the intended operating budget of the hospital. To reduce the costs while maintaining a good quality of care, one of the solutions is to improve the existent planning and scheduling methods by improving the services and surgical specialty coordination or finding the best estimation of surgical case durations. The other solution is to construct an effective surgical case plan and schedule. The operating theatre planning and scheduling is the two important steps, which aim to make a surgical case programming with an objective of obtaining a realizable and efficient surgical case schedule. This paper focuses on the first step, the operating theatre planning problem. Two planning methods are introduced and compared. Real data of a Belgian university hospital “Tivoli” are used for the experiments.

In this paper we propose a COncurrent Production Engineering System (COPES) for the flexible transfer line (FTL) layout design in a restricted area. COPES first determines the buffer size in front of the bay of each machine tool in the FTL and then initializes a computer aided design (CAD) system to draw the FTL in a restricted area. We develop a set of modules systems which have been integrated into a single framework, in accordance with the practice of concurrent engineering. Concurrent engineering involves the cooperation of these activities. It’s expected that the developed COPES can improve the cooperation between production engineers’ and the plant designer. This can be done by enabling the production engineers’ to make better decision regarding FTL buffer size.

The aim of this paper is to give an overview on models and methods used to solve tactical planning problems. The modeling and the elaboration of the well-know tactical planning problems (master planning & scheduling, material requirement planning and multi-site planning) are discussed. These problems are modeled from two “lot sizing” models called the Capacitated Lot Sizing Problem (CLSP) and Multi Level Capacitated Lot Sizing Problem (MLCLSP). From both models, a lot of extensions has been proposed in the literature. The purpose of this paper is twofold: first, classifications of the CLSP and MLCLSP as well as their extensions are given. For each model, the major scientific contributions are mentioned. These classifications made from seventy papers give an overview of “lot sizing” models dedicated to the MPS, MRP and Multi-site and show the diversity of models. Second, from a classification, an analysis of methods used for each model is given. The instance size, best gap and reference for gap computation are given for each contribution. This work can be used to elaborate an optimization tool for tactical planning problematic such as Advanced Planning System.

In this paper we consider a single machine multi-product lot scheduling problem in which defective items are produced in any production run of each product. In each cycle after the normal production of each product the machine is setup for the rework of the defectives of the same product and then the rework process starts. We assume that the setup time for the normal production process as well as the rework process is non-zero. Further we consider the waiting time cost of defectives for rework. This paper has two objectives. The first objective is to obtain the economic batch quantity (EBQ) for a single product. The second objective is to extend the result of the first objective to the multi-product case. Adopting the common cycle scheduling policy we obtain optimal batch sizes for each product such that the total cost of the system per unit time is minimized.

We consider queueing networks (QN’s) with feedback loops roamed by “intelligent” agents, able to select their routing on the basis of their measured waiting times at the QN nodes. This is an idealized model to discuss the dynamics of customers who stay loyal to a service supplier, provided their service time remains below a critical threshold. For these QN’s, we show that the traffic flows may exhibit collective patterns typically encountered in multi-agent systems. In simple network topologies, the emergent cooperative behaviors manifest themselves via stable macroscopic temporal oscillations, synchronization of the queue contents and stabilization by noise phenomena. For a wide range of control parameters, the underlying presence of the law of large numbers enables us to use deterministic evolution laws to analytically characterize the cooperative evolution of our multi-agent systems. In particular, we study the case where the servers are sporadically subject to failures altering their ordinary behavior.