# Supplier Replacement Model in a One-Level Assembly System under Lead-Time Uncertainty  
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1 University of Champagne, University of Technology of Troyes, CNRS, ICD/LOSI. 12 rue [PERSON], 10010 Troyes, France; [EMAIL_ADDRESS] (H.M.A. ); [EMAIL_ADDRESS] (F.H.) [PERSON]  
2 Department of Manufacturing Sciences and Logistics, Mines Saint-Etienne, Univ Clermont Auvergne, UMR-CNRS 6158 LIMOS, CMP, 880 route de Mimet, F-13541 Gardanne, France 2* 2* 3 3 3 3 3 3 3  
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unreliability in an assembly system? Often the suppliers are selected uniquely on their proposal of component prices. An interesting and important question is: how to integrate the purchasing price and lead time reliability in a common model to be able to evaluate suppliers on both purchasing price and lead time reliability. Such a model would be useful not only for supplier selection but also for purchasing price negotiation as a function of reliability of lead times. In the modern market, companies need to take every opportunity to reduce their costs and uncertainties to satisfy their customers. This makes negotiation of purchasing prices and conditions of delivery with suppliers, supplier selection and replacement if needed, key strategic considerations. Dynamic markets lead to the necessity to select suppliers dynamically by favoring those who are able to follow changes in company requirements [1]. Poor supply condition negotiation and supplier selection during a single period can have substantial negative impacts on a firm's long-term financial results [2]. Finding a suitable set of suppliers, definition of prices and effective replenishment rules are crucial issues. In this article, a one-level assembly system (OLAS) is considered. The assembled product is composed of \(n\) distinct components which are replenished from external suppliers with uncertain lead-times described by lead time probability distributions. Lead-time uncertainty is a crucial element in production systems and logistics. There are numerous factors causing lead time randomness: limited capacity of suppliers under random demand of their clients, substandard quality, worker absenteeism, machine failure, transport postponement and randomness, etc. The motivation for this study is based on our work experience with industrial partners from two different sectors. The first one was ZF, a gearbox producer for the automotive industry. Many of ZF's suppliers are from different countries and their lead times are often subject to random deviations. This creates problems for the assembly plant in Saint Etienne (France). To reduce the negative consequences, ZF calculates the reliability of their suppliers based on past statistics. Coefficients of reliability (greater or equal to 1) were used to calculate planned lead times for each supplier by multiplying the contractual lead time by the corresponding reliability coefficient. Nevertheless, these calculations were done for each supplier separately, thus the results were not optimal. In addition, this approach was only used to parameterize their Material Requirement Planning (MRP) system, i.e., only for replenishment planning at the operational level. The aims of ZF were to find a more efficient approach which took into account the costs, and considers all suppliers together in the same model. It was also interesting to have the possibility of using such an approach to analyze their policy of supplier selection and negotiation of purchasing prices. The second example was from retail industry, Casino Group, one of biggest retailer networks in France. Once a year the Casino Group negotiates the prices with their suppliers. There are many warehouses of the group in different regions of France, some local, some regional. Many suppliers compete to deliver the same (or similar) type of product. The lead time depends on supplier and warehouse. The Casino Group searched for models to evaluate the logistic costs of different configurations.