J Intell Manuf (2012) 23:811–819 DOI 10.1007/s10845-010-0437-9 Hierarchical production planning with flexibility in agroalimentary environment: a case study Ridha Erromdhani · Mansour Eddaly · Abdelwaheb Rebai Received: 19 December 2008 / Accepted: 12 July 2010 / Published online: 22 July 2010 © Springer Science+Business Media, LLC 2010 Abstract In this paper we address to the planning prob- lem in the agroalimentary domain. In such industry, several specific constraints should be taken into account for planning task such as the constraints of interdependencies between the products and variable production modes. Furthermore, we present the relationship between two large fields as the pro- duction hierarchical planning and the flexibility. Especially, we show that the flexibility planning should be made a pri- ori and then integrated in the hierarchical planning process. Indeed, we have established a mathematical model accord- ing to different production levels. While taking into account real capacities of the shop and the interdependencies between the products, the results of our formulation are satisfactory in terms of quality of solution and time requirements. It’s shown that our model is able to reach all optimal solutions for all treated models and for all system levels. Keywords Production planning · Hierarchical planning · Flexibility · Agroalimentary industries · Linear programming Introduction The agroalimentary industries constitute the link between the agriculture and the consumers. These industries can be distin- guished by their dynamic environment due to both short cycle R. Erromdhani · M. Eddaly (B ) · A. Rebai FSEGS, route de l’aéroport km 4, Sfax 3018, Tunisie e-mail: eddaly.mansour@gmail.com R. Erromdhani e-mail: erromdhaniridha@yahoo.fr A. Rebai e-mail: abdelwaheb.rebai@fsegs.rnu.tn life and the existence of unexpected command of raw materi- als and products (Erol 1999). Furthermore, the planning task in this domain is subjected to several specificities because of the high degree of incertitude and imprecision which affect the data level and the product interdependencies (Axäter and Jönsson 1984). Suhua and Wu (2000) have examined how the imprecise natures affect the planning results. Referring to Schneeweiss (2003), the flexibility can be defined by “the ability of a system to cope with unforeseen changes”. Thus, the firm which anticipates perfectly the future changes does not have need to the flexibility in its production planning. Inversely, the firm which has an infinite potential of flexibil- ity does not have need to any anticipation (Erol and Dupont 1999). Our motivation is to formulate the flexibility as a tool to overcome the punctual changes. Our work consists in study- ing the need of flexibility and locating its place in the pro- duction hierarchical planning process in the agroalimentary industry. In other words, our aim is to find a mathematical relationship for the balance between two large fields such as in the production hierarchical planning process in the agroal- imentary industry and the flexibility. The choice of the hierar- chical approach is supported by its ability in simplifying the global decision-making process. The decisions transferred to inferior level are considered as constraints to be satisfied or goals to be reached for superior level (Fontan et al. 2005). So, we propose a mathematical model which allows reducing and simplifying the real constraints in the agroalimentary envi- ronment. Thus, two kind of linear programming models were proposed. In the first one, we consider a production system consisted of several manufacturing stages with a general tree of N products in order to determine the produced quantities of each type of item. Whereas the second model consists in sharing the available capacity of an item from an inferior level into each obtained item processed from it to the immediate 123