In this paper we address to the planning problem 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 production hierarchical planning and the flexibility. Especially, we show that the flexibility planning should be made a priori and then integrated in the hierarchical planning process. Indeed, we have established a mathematical model according 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.
In this paper we suggest a new variant of Variable neighborhood search designed for solving Mixed integer programming problems. We call it Variable neighborhood formulation search (VNFS), since both neighborhoods and formulations are changed during the search. VNS deals with integer variables, while an available (commercial) solver is responsible for continues variables and the objective function value. We address the multi-item capacitated lotsizing problem with production time windows and setup times, under the non-customer specific case. This problem is known to be NP-hard and can be formulated as a mixed 0-1 program. Neighborhoods are induced from the Hamming distance in 0-1 variables, while the objective function values in the corresponding neighborhoods are evaluated using different mathematical programming formulations of the problem. The computational experiments show that our approach is more effective and efficient when compared with the existing methods from the literature.
Our research focuses on the development of two cooperative approaches for resolution of the multi-item capacitated lot-sizing problems with time windows and setup times (MICLSP-TW-ST). In this paper we combine variable neighborhood search and accurate mixed integer programming (VNS-MIP) to solve MICLSP-TW-ST. It concerns so a particularly important and difficult problem in production planning. This problem is NP-hard in the strong sense. Moreover, it is very difficult to solve with an exact method; it is for that reason we have made use of the approximate methods. We improved the variable neighborhood search (VNS) algorithm, which is efficient for solving hard combinatorial optimization problems. This problem can be viewed as an optimization problem with mixed variables (binary variables and real variables). The new VNS algorithm was tested against 540 benchmark problems. The performance of most of our approaches was satisfactory and performed better than the algorithms already proposed in the literature.
Our research focuses on the development of two algorithms based on the mathematical programming and local search procedures for resolution the Multi-Item Capacitated Lot Sizing Problem and Vehicle Routing Problem (MICLSP-VRP). It concerns so a particularly important and difficult problem in the strong sense for solving. In particular, our study is motivated by a real case study in a butcher's shop firm whose meat processing. Several production lines are considered of (turkey and chicken) items and a fleet of vehicles that is used to deliver. In this study, an effective approach based on the local search and accurate mixed integer programming model is presented to solve multi-item capacitated lot sizing problem and vehicle routing problem with delivery time windows. This consists of determining the production quantities at each site by minimizing the cost of transport and solving the sub problem. By considering an integrated approach, the computational results of a case study show a 25.33% percent decrease in the total cost production.
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