ScienceDirect IFAC-PapersOnLine 48-3 (2015) 1809–1814 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2015.06.349 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Lot-sizing, sequencing, imperfect production, genetic algorithms 1. INTRODUCTION In this paper we study a lot-sizing and sequencing prob- lem under uncertainties. The production facility where appeared this problem is composed of : 1) a manufacturing line that process items of several types; 2) an automatic storage device that stocks processed items; 3) an assembly line assembling final products with stored items. We only consider the production line which manufacture several types of items by lots with sequence dependent setup times between lots. Some items processed at this line appear to be not in accordance with requirements. Such items are rejected. The machines are subject to breakdowns that involve line’s stoppages and engagement of repairs. To face the downtime caused by breakdowns, some safety time should be planned and added to the production scheduling. All items required by the assembly line should be charged into a storage system before assembly process starts. Otherwise, final products will not be delivered on time, and important backlog costs will be engaged. Thus, the objective of lot-sizing and scheduling is to increase the probability to have all items necessary for the assembly process by the due date and thus to avoid penalty costs and save the money. The manufacturing line consists of m sequentially placed machines and is a paced flow line. Every item pass through all machines in the same fixed order. Defective items are detected after the last machine and are not placed into the storage system (they are excluded from the future process because they cannot be reworked). When changing the product type, some time (set-up time ) is needed for setting up the machines. To perform this changeover, all items of the previous product should be finished and the production line should be empty. The set-up time is sequence-dependent, i.e. it depends on both - outgoing and incoming product. Thus, the sequence of products to process has an impact on the total processing time, and can increase or decrease the theoretical safety time intended for machines repairs. Decision to take daily is to determine how much items of each type (lot sizes) should be launched in the morning of the day D - 1 on the production line to obtain all items needed for assembly line by the end of the day. Because of the non quality and breakdowns, some additional items and safety time should be foreseen. We assume that the demand level and unitary processing time are known for each type of product. We consider that the probability to obtain a good quality item is given and can be different for each type of product. Each machine are subject to failures and the Mean Time to Failure (MTTF) and the Mean Time to Repair (MTTR) are also known. The original problem with probabilistic models of these uncertainties (rejects and breakdowns) was proposed in Dolgui et al. (2005). The objective was to maximize the probability of overall demand satisfying, i.e. to obtain the given number of products of all types by the end of the period (day). A decomposition based approach consisting of three levels was developed. The first level is a complete enumeration of n possible solutions. The second is the sequencing decision, equivalent to the Asymmetric Travelling Salesman Problem (ATSP). The last one is the lot-sizing decision, an extension of the Knapsack problem. Both (2 nd and 3 rd levels) are NP-hard. Dolgui et al. (2005) proposed to use a Dynamic Programming (DP) procedure to solve the lot-sizing part of the problem. In contrast, in Schemeleva et al. (2012) a genetic algorithm was used. Till now only the overall decomposition scheme * Laboratoire d’Economie des Transports, CNRS UMR 5593, University of Lyon 2, Lyon, France (e-mail: kseniya.schemeleva@let.ish-lyon.cnrs.fr) ** Ecole Nationale Sup´ erieure des Mines, FAYOL-EMSE, CNRS UMR 6158, LIMOS, Saint-Etienne Cedex, France (e-mail: delorme@emse.fr, dolgui@emse.fr) Abstract: A stochastic multi-product lot-sizing and sequencing problem is considered. Two kinds of uncertainties are integrated into the model: defectives items due to the machines’ imperfections and random lead time because of randomly arising breakdowns and uncertain repair time. There are also sequence-dependent set-up times between two items of different types. The optimization problem is to maximize the probability of overall demand satisfying. In the previous work only the lot-sizing part of the problem was considered (a decomposition approach was used). Here we study the entire problem with sequencing and lot-sizing decisions integrated. A memetic algorithm for a stochastic lot-sizing and sequencing problem Kseniya Schemeleva * Xavier Delorme ** Alexandre Dolgui **