Genetic algorithms for the scheduling of multiproduct batch plants within uncertain environment (original) (raw)
Related papers
Genetic algorithms for batch sizing and production scheduling
The International Journal of Advanced Manufacturing Technology, 2014
This paper proposes three genetic algorithms with different types of crossovers dedicated to solve the problem of short-term scheduling of batch processes. The genetic algorithms suggested are able to determine the amount of batches produced, their production sequence, machinery assignments, and a different batch size for each batch. This is a more complex variation of the batch scheduling problem where genetic algorithms are usually limited to decide the batch production sequence. A manufacturing case study is used to test the performance when minimizing the makespan, in order to compare the proposed genetic algorithms against a simulated annealing implementation, a totally random search, and a simplified genetic algorithm with no crossover (to test the crossovers' efficiency). The results show that one of the crossovers proposed has the fastest convergence in all scenarios, finding the best solutions in short searches. This crossover is slightly outperformed by the simulated annealing only in extensive searches with more iterations. The other two crossovers suggested have a good performance in certain scenarios, but show poor results in others.
2016
Due to the intrinsic uncertainty and dynamics of in dustrial environments schedulers must continually reconcile what is expected with what actually happe ns. One of the most common sources of uncertainty encountered at the operational level is the one ass ociated with variable processing times. This work c ontributes in the area of proactive scheduling by dev eloping an innovative Constraint Programming (CP) model able to cope with uncertain processing times at the decision stage, prior to scheduling and with ou resorting to the generation of scenarios. The appli cation of the model to various instances of three c ase studies shows that the approach is computationally efficient. In addition, when the obtained schedules are compared with the agendas that were reached by a deterministic CP formulation, it is shown that they absorb the variability of the processing times b tter.
Multiperiod production planning and design of batch plants under uncertainty
Computers & Chemical Engineering, 2012
A two-stage stochastic multiperiod LGDP (linear generalized disjunctive programming) model was developed to address the integrated design and production planning of multiproduct batch plants. Both problems are encompassed considering uncertainty in product demands represented by a set of scenarios. The design variables are modeled as here-and-now decisions which are made before the demand realization, while the production planning variables are delayed in a wait-and-see mode to optimize in the face of uncertainty. Specifically, the proposed model determines the structure of the batch plant (duplication of units in series and in parallel) and the unit sizes, together with the production planning decisions in each time period within each scenario. The model also allows the incorporation of new equipment items at different periods. The objective is to maximize the expected net present value of the benefit. To assess the advantages of the proposed formulation, an extraction process that produces oleoresins is solved.
Industrial & Engineering Chemistry Research, 2002
The medium-range production scheduling problem of a multi-product batch plant is studied. The methodology consists of a decomposition of the whole scheduling period to successive short horizons. A mathematical model is proposed to determine each short horizon and the products to be included. Then a novel continuous-time formulation for short-term scheduling of batch processes with multiple intermediate due dates is applied to each time horizon selected, leading to a large-scale mixed-integer linear programming (MILP) problem. Special structures of the problem are further exploited to improve the computational performance. An integrated graphical user interface implementing the proposed optimization framework is presented. The effectiveness of the proposed approach is illustrated with a large-scale industrial case study that features the production of thirty five different products according to a basic 3-stage recipe and its variations by sharing ten pieces of equipment. ¢ 7 ¢ 8 ¢ 9 ¢ 1 0 ¢ 1 1 ¢ 1 2 . However, it should be pointed out that all slot-based formulations 6 ¢ 7 ¢ 8 restrict the time representation and result by definition in suboptimal solutions. Floudas and coworkers 13 ¢ 1 4 ¢ 1 5 proposed a novel true continuous-time mathematical model for the general short-term scheduling problem of batch, continuous and semicontinuous processes, which is the basis of the work presented in this paper. Lin and Floudas 16 further extended this model to incorporate scheduling issues in the design and synthesis of multipurpose batch processes.
Iberoamerican Journal of Industrial Engineering, 2013
This paper addresses the comparison between two techniques for the optimization under parametric uncertainty of multiproduct batch plants integrating design and production planning decisions. This problem has been conceived as a two-stage stochastic Mixed Integer Linear Programming (MILP) in which the first-stage decisions consist of design variables that allow determining the batch plant structure, and the second-stage decisions consist of production planning continuous variables in a multi-period context. The objective function maximizes the expected net present value. In the first solving approach, the problem has been tackled through mathematical programming considering a discrete set of scenarios. In the second solving approach, the multi-scenario MILP problem has been reformulated by adopting a simulation-based optimization scheme to accommodate the variables belonging to different management levels. Advantages and disadvantages of both approaches are demonstrated through a case study. Results allow concluding that a simulation-based optimization strategy may be a suitable technique to afford two-stage stochastic programming problems.
Constraint handling strategies in Genetic Algorithms application to optimal batch plant design
Chemical Engineering and Processing: Process Intensification, 2008
Optimal batch plant design is a recurrent issue in Process Engineering, which can be formulated as a Mixed Integer Non-Linear Programming (MINLP) optimisation problem involving specific constraints, which can be, typically, the respect of a time horizon for the synthesis of various products. Genetic Algorithms constitute a common option for the solution of these problems, but their basic operating mode is not always wellsuited to any kind of constraint treatment: if those cannot be integrated in variable encoding or accounted for through adapted genetic operators, their handling turns to be a thorny issue. The point of this study is thus to test a few constraint handling techniques on a mid-size example in order to determine which one is the best fitted, in the framework of one particular problem formulation. The investigated methods are the elimination of infeasible individuals, the use of a penalty term added in the minimized criterion, the relaxation of the discrete variables upper bounds, dominancebased tournaments and, finally, a multiobjective strategy. The numerical computations, analysed in terms of result quality and of computational time, show the superiority of elimination technique for the former criterion only when the latter one does not become a bottleneck. Besides, when the problem complexity makes the random location of feasible space too difficult, a single tournament technique proves to be the most efficient one.
Chemical Product and Process Modeling, 2010
This work deals with the problem of the search for optimal design of multiproduct batch chemical plants found in a chemical engineering process with uncertain demand. The aim of this work is to minimize the investment cost and find out the number and size of parallel equipment units in each stage. For this purpose, it is proposed to solve the problem in two different ways: the first way is by using Monte Carlo Method (MC) and the second way is by Genetics Algorithms (GAs). This GAs consider an effective mixed continuous discrete coding method with a four- point crossover operator, which take into account simultaneously, the uncertainty on the demand using Gaussian process modeling with two criteria maximization the Net Present Value (NPV) and Flexibility Index (FI). The results (number and size of equipment, investment cost, production time (Hi), NPV, FI, CPU time and Idle times in plant) obtained by GAs are better than the MC. This methodology can help the decision makers and const...
Short-term scheduling of multiproduct batch plants under limited resource capacity
2001
In multiproduct batch plants, the processing tasks required to complete the production of different items share manufacturing resources such as raw materials, intermediates, manpower, equipment and utilities (steam, electricity, cooling water, etc). Such resources are usually available by limited amounts that cannot be exceeded at any time of the scheduling period. This type of restriction is computationally costly when a continuous-time representation is applied to model the short-term scheduling of multiproduct batch plants. To meet such constraints, it becomes important to monitor the resource requirement profile over the entire planning horizon to exclude from the problem feasible space those schedules exceeding at least one of the resource capacities. Most of current continuous-time based methodologies ignore the resource capacity constraints. Manufacturing resources are usually classified into two major groups: renewable and nonrenewable resources. A renewable resource like units or manpower becomes again available for use after ending the processing task to which is currently assigned. Schedules involving the execution of simultaneous tasks featuring a total resource requirement larger than the available capacity is to be discarded by a proper problem representation. To this end, 0-1 decision variables and additional constraints have been defined to forbid running simultaneous processing tasks if, by doing that, some shortage in a resource capacity arises. A typical case in industry is the number of production lines running in parallel being constrained by the labor capacity. Among non-renewable resources, finite initial inventories and especially the reception of open orders of raw materials and intermediates during the period to be scheduled are challenging real-world capacity constraints to be considered by the proposed mathematical formulation. In this paper, it has been developed a new MILP mathematical formulation for the short-term scheduling of multiproduct batch plants subject to resource capacity constraints usually encountered in the manufacturing industry. The proposed model has been solved by using the modeling system GAMS and the solver OSL (IBM, 1991). A significant number of examples involving up to 15 jobs and limited availability of raw materials, utilities and manpower have been successfully solved. Results show an important reduction in the number of variables with regards to current continuous-time approaches and a good computational efficiency.
A new methodology for the optimal design and production schedule of multipurpose batch plants
Industrial & Engineering Chemistry Research, 1989
A nonlinear mathematical programming formulation for the multipurpose batch plant design problem is presented. It simultaneously provides both the optimal equipment sizes and the best series of multiproduct campaigns a t one step by taking into account the whole space of feasible production runs. By making minor changes to some problem constraints, the proposed modeling can consider the use of parallel units at certain stages. The units can be assigned to either the same or distinct products. Moreover, the proposed modeling can also handle practical situations where intermediate and salable products are to be manufactured. This algorithmic approach has been successfully applied to discover the best design and production policy in several examples. Optimal solutions to problems involving as many as 7 products and 10 stages have been determined by solving a single, small-size, nonlinear program. T h e method is computationally efficient even if the starting point is far from the optimum. Chemical batch plants are generally grouped into two classes, multiproduct and multipurpose batch facilities. In the former ones, a range of products are manufactured by running a sequence of single-product campaigns. Each of the N desired products undergoes a series of M processing tasks. These are accomplished in a set of M equipment modules or batch stages, each one carrying out a distinct physical/chemical task. A batch of product is transferred to the next stage after completion of the longest task. There is no intermediate storage between stages, and the plant is operated on the zero-wait mode. Important contributions to the mathematical problem description and the understanding of the optimal problem patterns have already been made by several authors (
Mathematical and Computer Modelling, 2007
This work considers optimal scheduling of a set of orders in a multi-product batch plant with non-identical parallel processing units where the process is single stage. The allocation of orders to the production units was formulated as an MILP problem in continuous time. Starting from the basic model proposed earlier, and adding a new constraint that was missing in previous literature, the new formulation solves the problem with a different objective function which considers the total production time or total production cost of the set of orders, without resorting to the application of any heuristic rules. A special MATLAB program has been developed for automatic creation of the optimization model, which otherwise may be a very time consuming task prone to errors. The formulation has been tested with extensive numerical, as well as one industrial, problems. The results indicate importance of the proposed modifications and effectiveness of the automated generation of the model, and present better solutions for the industrial example considered.