International audienceThis article deals with the combined production and maintenance plans for a manufacturing system satisfying a random demand. We first establish an optimal production plan which minimises the average total inventory and production cost. Second, using this optimal production plan, and taking into account the deterioration of the machine according to its production rate, we derive an optimal maintenance schedule which minimises the maintenance cost. A numerical example illustrates the proposed approach, this analytical approach, based on a stochastic optimisation model and using the operational age concept, reveals the significant influence of the production rate on the deterioration of the manufacturing system and consequently on the integrated production/maintenance policy
Abstract-In this paper, a forecasting problem of production and maintenance plan optimization for random demand and single machine M 1 on a finite horizon. The function rate of the machine M 1 is depending on the production rate for each period of the forecasting horizon. In order to satisfy the customer, a subcontracting assures the rest of the production through machine M 2 with transportation delay. An analytic formulation of the problem has been proposed using a sequentially computation of the optimal production plan for which an optimal preventive maintenance policy has been calculated based on minimal repair. Firstly, we find, the optimal production plans of principal and subcontracting machines, which minimizes the total production and inventory cost for the cases without and with returned products under service level and subcontracting transportation delay. Secondly, we determine a joint effective maintenance policy with the optimal production plan, which integrates the various constraints for the production rates, the transportation delay and the returned production deadline. Numerical results are presented to highlight the application of the developed approach and Sensitivity analysis shows the robustness of the model.
This paper develops and analyses a stochastic optimisation problem with a service level constraint for generating a sequentially optimal plan of production, maintenance and delivery activities in a deteriorating manufacturing system. Stochastic demand along with product returns are both assumed the latter of which allows for restocking products returned by the customer which are still new and thus in saleable condition. A constrained production/maintenance/delivery problem with service level, stochastic demand, delivery time, failure rate and product returned is formulated based on quadratic model. This quadratic formulation is adapted to provide an inventory, delivery, production and maintenance policies. The objective of this paper is to study the delivery time influence on the planning of the production, maintenance and delivery activities. Finally, we present simulation results to illustrate the exploitation of the proposed approach. IntroductionThroughout the last decades, companies are more than ever coping with decreasing profit margins due to the competitive environment, which in turn motivates them to seek improvements to their production and maintenance planning performance. We find in the literature many papers that have treated the maintenance planning problem independently of the production planning problem, despite that over the last decades we have seen the emergence of research which treats both problems simultaneously. Holt et al. (1960) developed a linear decision rule that considers only the inventory and production planning problem without maintenance and which assumed as an important contribution. The proposed analytical rule allows obtaining the optimal solution for a quadratic cost function of production, inventory and workforce levels, the principle of this method is to minimise the inventory and workforce equations. According to Bertesekas (1995), the HMMS model is assumed as one of the first models that deal the certainty equivalence principle for dynamic linear-quadratic problems. This model is usually used as a benchmarking tool in order to compare different production planning approaches and to provide managers and decision-makers with perspectives and ideas about how to manage the firm's material resources (Singhal and Singhal 1996). Hax and Candea (1984), for example, proved that this quadratic approach (HMMS) is useful to evaluate the production process. Indeed, and, for example, using the HMMS model, the quadratic inventory cost describes and takes into account both possible status of inventory: negative (shortage) and positive (overstocking). For this context Buzacott (1967) analysed the role of buffer inventory in increasing the productivity of an unreliable production system. Aghezzaf, Jamali, and Ait-Kadi (2007) developed a sequentially maintenance and production planning model for a production system subject to random failures. This model takes into account the system reliability parameters and its capacity in the development of the optimal production plan. Van der Duyn Schou...
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