Scheduling of a multi-product batch process in the chemical industry (original) (raw)
Related papers
2010
In this work, a novel sequence-based mixed-integer linear programming formulation for the simultaneous batching and scheduling in multi-product multi-stage batch plants is developed. The selection of batches, the allocation of batches to processing units and the sequencing of batches in each unit constitute the discrete decisions of our model. Batch processing times and sizes are variables. Batch size increment steps are included in an attempt to accommodate our model to real-life industrial practice.
Industrial & Engineering Chemistry Research, 1991
Algorithms have been developed to solve specific scheduling and control problems that arise in multipurpose batch plants. The problems are formulated as Mixed-Integer Linear Programs (MILP). Continuous variables are the starting times of the events while integer zero-one variables are used to describe a path of operations. The solution of the problem determines the control actions that need to be taken to minimize the makespan or the cycle time of a subset of activities. The constraints include the predetermined route each product follows, the possible processing sequences in each unit, production deadlines, the times that the resources are available, setup times between processing of consecutive batches in the same unit, and the different types of intermediate storage that may be used.
A complex time based construction heuristic for batch scheduling problems in the chemical industry
European Journal of Operational Research, 2006
In this paper we investigate a heuristic for batch processing problems occurring in the chemical industry, where the objective is to minimize the makespan. Usually, this kind of problem is solved using mixed-integer linear programs. However, due to the large number of binary variables good results within a reasonable computational time could only be obtained for small instances.
Batch processes are considered to be very efficient in producing fine as well as specialty chemicals. The efficiency of batch processes is attributed to the scheduling of various tasks involved in the production of a desired product. A very common purpose of scheduling is to reduce the total completion time of the process and is referred to as makespan. One of the ways to reduce makespan is the selection of a proper production sequence i.e. a sequence in which the raw materials are processed to produce specific products. The determination of such production sequence becomes a time consuming task with increase in the number of products. The complexity further increases when dealing with various transfer policies used for the transfer of product intermediates during the production cycle. Although numerous techniques are available but most of them are based on complex mathematical equations and thus take longer CPU time to solve even for a small batch scheduling problem. Further, the search of the optimal solution is not an easy task when the number of optimal solutions increases with increase in problem size. The motivation behind current work is to reduce the mathematical complexity as well as suggesting some rule based guidelines that could speed up the solution procedure for any batch scheduling problem. A new heuristic approach is developed and applied to various problem sizes in conjunction with mathematical formulations developed in our previous work for various transfer policies. The results so obtained are very promising and shows significant contribution towards the solution of batch scheduling problems with less computational effort.
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.
Scheduling of multipurpose batch chemical plants with resource constraints
Industrial & Engineering Chemistry Research, 1993
An efficient procedure to identify the dominant multiple-product campaigns for multipurpose batch chemical plants is presented. On the basis of a linear dominance property, the dominant campaigns are identified as the noninferior extreme points of the associated multiobjective campaign formation problem. The noninferior set estimation method has been incorporated into a decomposition strategy which alternately solves an equipment group master problem to identify dominant equipment group profdes for the production lines of the campaign and a campaign formation subproblem with identifies the dominant campaigns for a particular equipment group profile. A multiperiod mixed integer linear programming production planning model for multipurpose batch plants that allots the available production time to a subset of the dominant campaigns and accounts for lost production time due to changeovers and startup times is also presented. The campaign formation and production planning procedures are illustrated with an example problem.
Optimal synthesis of multiproduct batch plants with cyclic scheduling and inventory considerations
Industrial & Engineering Chemistry Research, 1993
This paper addresses the problem of determining the optimal configuration and cyclic operation of batch plants in which all the products require the same processing sequence. In particular, the problem can be stated as follows. Given are demands of a number of products, as well as technical information on the processing tasks (size factors, processing times, clean-up times) which are not restricted to a zero-wait policy. Given are also cost data for investment and product inventories, a list of candidate equipment and a list of candidate storage vessels with standard sizes. The problem then consists in determining the following items: number, type and size of equipment, as well as their allocation to one or multiple tasks and possible parallel operation; location and size of intermediate storage vessels; the length of the production cycle including the sequence of production of the products; levels of product inventories. The objective is to maximize the net present value. The major complication of this design problem lies in the many trade-offs that are involved, as for instance the merging of tasks versus its impact on the schedule, and length of production cycle versus inventory levels. By using a novel representation for cyclic schedules and exact linearization schemes, it is shown that this problem can for formulated as a mixed-integer linear programming problem, and solved rigorously to global optimality. An efficient computational scheme is proposed for this purpose. Compared to the previous work by Birewar and Grossmann (1990), the proposed model provides a significant extension of the scope of the operational problem, while at the same time yielding an optimization problem that does not involve nonlinearities. Several example problems are presented to illustrate the capability of this method.
MILP model for scheduling and design of a special class of multipurpose batch plants
Computers & Chemical Engineering, 1996
In this paper we propose a method for the integrated scheduling and design for a special class of multipurpose batch processes. The type of plants considered are the ones where not all the products use the same processing stages, and manufacturing of the products can be characterized through production routes. A novel representation for cyclic schedules is proposed that has the effect of aggregating the number of batches for each product. It is shown that the no-wait characteristics of subtrains can be exploited with a reduction scheme that has the effect of greatly decreasing the dimensionality of the problem. This reduction scheme can be complemented with a tight formulation of the underlying disjunctions in the MILP to reduce the computational expense. The proposed MILP model for scheduling is extended to design problems in which the potential existence of intermediate storage in the production paths is also considered. In addition to the rigorous scheduling of the process, the sizes of the equipment constituting the various production stages are determined. By using exact linearization schemes it is shown that the problem can be reformulated as an MILP model and solved rigorously to global optimality. Application of the proposed model is illustrated with several example problems. Literature review Because of its relative simplicity, the preliminary design of multiproduct plants has been in focus by many researchers. Rippin (1993) reviews most of the work in this area in recent years. In this review the need for a comprehensive algorithm that will automatically consider and select from all structural possibilities considered simultaneously is recognized. Voudouris and Grossmann (1993) developed a comprehensive MILP model for multiproduct batch plants that considers all the structural possibilities, and even further, considers final product inventories within a periodic scheduling approach. For multipurpose plants the mixed integer approaches for design and scheduling can be categorized in thrce broad arcas. The main difference between these approaches is the way with which the scheduling subproblem is dealt with. The first approach is based on a simplified campaign planning scheme as for instance with the work by Vaselenak et al (1987). In this approach a central issue is the production campaign formation. Namely, during a production campaign which consists of batches of the same product, two products are allowed to be produced in the same campaign only if their production paths do not share any processing equipment. Faqir and Karimi (1990) generalized this approach by allowing more than one path for the production of a particular product The model they developed was a nonconvex MINLP which was later reformulated as an MILP by Voudouris and Grossmann (1992). Papageorgaki and Reklaitis (1990) also developed a nonconvex MINLP model which incorporated many additional aspects like flexible task-to-equipment allocation, but still was based on a campaign planning mode. A variant of this campaign approach is proposed by Shah and Pantelides (1992) where the assumption of simultaneously utilizing production paths with noncommon equipment for the formation of production campaigns is applied to production stages instead of production paths. The main problem with these approaches is that the scheduling problem is solved based on a simplifying assumption, thus allowing underutilization of time, the generation of relatively large idle times for the processing equipment, and significant overdesign of the plant when the design subproblem is integrated. The second approach tries to tackle the problem of time underutilization. For this reason it is recognized that a rigorous scheduling of production paths has first to be performed and to serve as a lower level subproblem to the capacity allocation problem. The work by Wellons and Reklaitis (1991) is representative of this approach. Unfortunately the resulting models are highly intractable mainly because of the nonlinearities that arc involved. Furthermore, an arbitrary selection of the total number of batches that are considered may lead to suboptimai solutions.
A GENERAL ALGORITHM FOR SHORT-TERM SCHEDULING OF BATCH OPERATIONS-I. MILP FORMULATION
A general framework for handling a wide range of scheduling problems arising in multi-product/multipurpose batch chemical plants is presented. Batch processes involving a variety of complexities are represented using a state-task network. The novel feature of this representation is that both the individual batch operations (" tasks ") and the feedstocks, intermediate and final products (" states ") are included explicitly as network nodes. Processes involving sharing of raw materials and intermediates, batch splitting and mixing and recycles of material, can be represented unambiguously as such networks. The short-term scheduling problem is formulated as a mixed integer linear program (MILP) based on a discrete time representation. Flexible equipment allocation, variable batchsizes and mixed intermediate storage policies involving both dedicated and multipurpose storage vessels are taken into account. Limited availability of raw materials, both at the start and during the time horizon of interest, is accommodated. Product deliveries may take place at any time during the horizon, and the amounts involved may be either fixed or variable. The use of utilities by the various tasks may vary over the task processing time, and may be constant or proportional to the batchsize. The availability and/or cost of utilities may vary over the time horizon of interest. The objective function is the maximization of a profit function involving the value of the products, and the cost of raw materials, utilities and material storage. The formulation may result in MILPs involving large numbers of binary variables. Issues pertaining to the efficient solution of these problems are discussed in Part II of this paper.
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.