Combined strategic and operational planning – an MILP success story in chemical industry

We describe and solve a real world problem in chemical industry which combines operational planning with strategic aspects. In our simultaneous strategic & operational planning (SSDOP) approach we develop a model based on mixed-integer linear (MILP) optimization and apply it to a real-world problem; the approach seems to be applicable in many other situations provided that people in production planning, process development, strategic and financial planning departments cooperate. The problem is related to the supply chain management of a multi-site production network in which production units are subject to purchase, opening or shut-down decisions leading to an MILP model based on a time-indexed formulation. Besides the framework of the SSDOP approach and consistent net present value calculations, this model includes two additional special and original features: a detailed nonlinear price structure for the raw material purchase model, and a detailed discussion of transport times with respect to the time discretization scheme involving a probability concept. In a maximizing net profit scenario the client reports cost saving of several millions US$. The strategic feature present in the model is analyzed in a consistent framework based on the operational planning model, and vice versa. The demand driven operational planning part links consistently to and influences the strategic. Since the results (strategic desicions or designs) have consequences for many years, and depend on demand forecast, raw material availability, and expected costs or sales prices, resp., a careful sensitivity analysis is necessary showing how stable the decisions might be wit h respect to these input data.     

Development and challenges of planning and scheduling for petroleum and petrochemical production

Production planning and scheduling are becoming the core of production management, which support the decision of a petrochemical company. The optimization of production planning and scheduling is attempted by every refinery because it gains additional profit and stabilizes the daily production. The optimization problem considered in industry and academic research is of different levels of realism and complexity, thus increasing the gap. Operation research with mathematical programming is a conventional approach used to address the planning and scheduling problem. Additionally, modeling the processes, objectives, and constraints and developing the optimization algorithms are significant for industry and research. This paper introduces the perspective of production planning and scheduling from the development viewpoint.     

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.     

An MILP-based approach to the short-term scheduling of make-and-pack continuous production plants

Many fast moving consumers good manufacturing companies produce a moderate number of intermediates that are combined in many different ways to generate an enormous variety of end products. To do that, such companies usually run continuous production plants in a make-to-stock environment. The process structure includes a fabrication area yielding basic intermediates that are stocked in a large middle storage space, and a packing sector where finished products usually comprising several intermediates are manufactured. Intermediates all undergo the same sequence of processing stages and the production of any campaign is sequentially allocated to an ordered set of end products. An MILP continuous time scheduling problem formulation handling independently assignment and sequencing decisions and considering sequence-dependent setup times and specific due dates for export orders has been developed. The problem objective is to meet all end-product demands at minimum make-span. The proposed model is able to account for assorted products, multiple campaigns for a particular intermediate even at the same unit and the consecutive allocation of an intermediate campaign to different finished products. Moreover, it can easily embed powerful preordering rules to yielding reduced MILP formulations so as to tackle real-world industrial problems at low computational cost. The approach has been successfully applied to large-scale industrial examples. RID="*" ID="*" The authors acknowledge financial support from FONCYT under Grant 14-07004, and from “Universidad Nacional del Litoral” under CAI+D 121. Correspondence to: J. Cerdá     

Advanced production scheduling for batch plants in process industries

An Advanced Planning System (APS) offers support at all planning levels along the supply chain while observing limited resources. We consider an APS for process industries (e.g. chemical and pharmaceutical industries) consisting of the modules network design (for long–term decisions), supply network planning (for medium–term decisions), and detailed production scheduling (for short–term decisions). For each module, we outline the decision problem, discuss the specifi cs of process industries, and review state–of–the–art solution approaches. For the module detailed production scheduling, a new solution approach is proposed in the case of batch production, which can solve much larger practical problems than the methods known thus far. The new approach decomposes detailed production scheduling for batch production into batching and batch scheduling. The batching problem converts the primary requirements for products into individual batches, where the work load is to be minimized. We formulate the batching problem as a nonlinear mixed–integer program and transform it into a linear mixed–binary program of moderate size, which can be solved by standard software. The batch scheduling problem allocates the batches to scarce resources such as processing units, workers, and intermediate storage facilities, where some regular objective function like the makespan is to be minimized. The batch scheduling problem is modelled as a resource–constrained project scheduling problem, which can be solved by an efficient truncated branch–and–bound algorithm developed recently. The performance of the new solution procedures for batching and batch scheduling is demonstrated by solving several instances of a case study from process industries.     

Optimizing the landside operation of a container terminal

This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three-stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short-term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most 8% above a lower bound on optimal RMG utilization. Research supported by Patrick Technology and Systems, the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), and the German Research Foundation Research Center Mathematics for key technologies: Modelling, simulation, and optimization of real-world processes (Matheon).     

An integrated system solution for supply chain optimization in the chemical process industry

This paper considers a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries. RID="*" ID="*" The authors would like to thank Hans-Otto Günther and Roland Heilmann for helpful comments on draft versions of this paper.     

面向订单的生产计划与调度的综合优化

研究了一个多订单环境下的生产计划与调度集成优化问题,以实现准时生产为目标,综合考虑产品装配结构约束的订单任务计划与订单产品零部件的加工调度,采用直接面向客户订单的工序调度模式建立了计划和调度的综合优化整数规划模型.设计了带精英策略的蚁群算法作为该数学模型的求解方法,并通过对比试验为该算法选取最佳的搜索参数.实例仿真结果表明,所建模型的正确性以及蚁群算法求解该问题的可行性和有效性.     

揭开先进计划系统的神秘面纱

适应当今市场对计划与决策支持系统更加复杂的需求、功能强大的先进计划(Advanced Planning and Scheduling,APS)系统在国外受到了众多企业组织的青睐,并且给传统的EPP软件厂商带来了强烈冲击。然而该系统在我国还没有受到相应的重视,人们对该系统还缺乏深入了解。由此,本文具体介绍了APS系统的逻辑模型、主要功能特点及常采用的数学模型、网络模型与模拟方法等计划方法和技术。     

物料需求计划不稳定性的模拟研究

介绍物料需求计划不稳定性的基本概念和模拟研究方法。在不确定性需求的流动式计划环境下,研究冻结参数和计划算法在不同生产条件下对物料需求计划不稳定性的影响。通过设计模拟实验和大量模拟计算及统计分析表现：费用结构、预测模式、冻结比例、计划周期和计划算法对物料需求计划不稳定性有较大影响,且交互作用显著。研究结果对减小物料需求计划的不稳定性有一定指导意义。     

More MILP models for integrated process planning and scheduling

The integration of process planning and scheduling is important for an efficient utilisation of manufacturing resources. In general, there are two types of models for this problem. Although some MILP models have been reported, most existing models belong to the first type and they cannot realise a true integration of process planning and scheduling. Especially, they are completely powerless to deal with the cases where jobs are expressed by network graphs because generating all the process plans from a network graph is difficult and inefficient. The network graph-specific models belong to the other type, and they have seldom been deliberated on. In this research, some novel MILP models for integrated process planning and scheduling in a job shop flexible manufacturing system are developed. By introducing some network graph-oriented constraints to accommodate different operation permutations, the proposed models are able to express and utilise flexibilities contained in network graphs, and hence have the power to solve network graph-based instances. The established models have been tested on typical test bed instances to verify their correctness. Computational results show that this research achieves the anticipant purpose: the proposed models are capable of solving network graph-based instances.     

LP-based heuristics for scheduling chemical batch processes

A mixed-integer linear programming (MILP) model for scheduling chemical batch processes is presented. Since computational times are prohibitive for most problems of realistic size, a two-stage solution procedure is suggested. In the first stage, an initial solution is derived by use of a LP-based heuristic. The proposed heuristic defines a time grid that includes only a limited number of feasible periods in which a processing task is allowed to start. Thus, the size of the original multi-period MILP model is reduced in a controlled manner and optimal solutions to the relaxed model are obtained within reasonable computational time. The second stage consists of an improvement step that aims to compress the initial schedule by left-shifting operations over the time-axis. In order to evaluate the applicability of the heuristics a number of numerical experiments were performed. It is shown that near-optimal solutions are obtained for largesize problems with only modest computational effort.     

Cyclic lot scheduling with sequence-dependent set-ups: a heuristic for disassembly processes

The importance of material and product recovery is steadily increasing, mainly due to customer expectations and take-back obligations. Disassembly is a major operation in material and product recovery, since returned products are often disassembled to separate materials and components. The paper considers the problem of scheduling several items on a single disassembly facility. It develops a cyclic lot-scheduling heuristic for disassembly processes with sequence- dependent set-ups, resulting in disassembly frequencies for the items. Additionally, the way the problem is formulated allows calculation of the profitable use of the facility. The disassembly frequencies and the profitable use of the facility are used to create a cyclic schedule.     

A note on 'deliberately slowing down output in a family production context'

In this paper, we consider the economic lot scheduling problem with controllable production rates and imperfect quality. The problem is to schedule the production of several different items in the same facility on a repetitive basis. The facility is such that only one item can be produced at a time and the demand rate for each item is constant over an infinite planning horizon. We focus on the case where quality is imperfect and yield rates decrease with increased production rates and lot sizes. We show that the resulting lot sizes under the proposed extension are smaller. Also, we show that the production rates for some products can be considerably different from the case of perfect quality.     

Makespan minimisation on parallel batch processing machines with non-identical job sizes and release dates

The problem we study in this paper arises from the washing step of hospital sterilisation services. Washers in the washing step are capable of handling more than one medical device set as long as their capacity is not exceeded. The medical device set sizes and arrival times to the sterilisation service may be different, but they all have the same washing duration. Thus, we model the washing step as a batch scheduling problem where medical device sets are treated as jobs with non-identical sizes and release dates, but equal processing times. The main findings we present in this paper are the following. First, we study two special cases for which polynomial algorithms are presented. We then develop a 2-approximation algorithm for the general problem. Finally, we develop a MILP model and compare it with another MILP model from the literature. Computational results show that our MILP model outperforms the model from the literature.     

A Constraint Programming model for food processing industry: a case for an ice cream processing facility

This paper presents a Constraint Programming (CP) scheduling model for an ice cream processing facility. CP is a mathematical optimisation tool for solving problems either for optimality (for small-size problems) or good quality solutions (for large-size problems). For practical scheduling problems, a single CP solution model can be used to optimise daily production or production horizon extending for months. The proposed model minimises a makespan objective and consists of various processing interval and sequence variables and a number of production constraints for a case from a food processing industry. Its performance was compared to a Mixed Integer Linear Programming (MILP) model from the literature for optimality, speed, and competence using the partial capacity of the production facility of the case study. Furthermore, the model was tested using different product demand sizes for the full capacity of the facility. The results demonstrate both the effectiveness, flexibility, and speed of the CP models, especially for large-scale models. As an alternative to MILP, CP models can provide a reasonable balance between optimality and computation speed for large problems.     

A spread-sheet model for efficient production and scheduling of a manufacturing line/cell

In this paper we develop an efficient spread-sheet production planning/scheduling model for a resource-constraint production line or a manufacturing cell that produces several products but one at a time with significant changeover time and changeover cost. There are also management and physical constraints related to the operating hours, production capacity and amount of inventory allowed. The production line/cell supplies several products to customers who pull the products according to their own operating policy (working hours) that may be different from manufacture's operating hours. We also show several real-world applications and highlight the benefits and merits of the model.     

Mathematical modelling of a robust inspection process plan: Taguchi and Monte Carlo methods

This study develops a new optimisation framework for process inspection planning of a manufacturing system with multiple quality characteristics, in which the proposed framework is based on a mixed-integer mathematical programming (MILP) model. Due to the stochastic nature of production processes and since their production processes are sensitive to manufacturing variations; a proportion of products do not conform the design specifications. A common source of these variations is maladjustment of each operation that leads to a higher number of scraps. Therefore, uncertainty in maladjustment is taken into account in this study. A twofold decision is made on the subject that which quality characteristic needs what kind of inspection, and the time this inspection should be performed. To cope with the introduced uncertainty, two robust optimisation methods are developed based on Taguchi and Monte Carlo methods. Furthermore, a genetic algorithm is applied to the problem to obtain near-optimal solutions. To validate the proposed model and solution approach, several numerical experiments are done on a real industrial case. Finally, the conclusion is provided.     

A multi-objective optimisation model to integrating flexible process planning and scheduling based on hybrid multi-objective simulated annealing

Process planning and production scheduling play important roles in manufacturing systems. In this paper we present a mixed integer linear programming (MILP) scheduling model, that is to say a slot-based multi-objective multi-product, that readily accounts for sequence-dependent preparation times (transition and set up times or machine changeover time). The proposed scheduling model becomes computationally expensive to solve for long time horizons. The aim is to find a set of high-quality trade-off solutions. This is a combinatorial optimisation problem with substantially large solution space, suggesting that it is highly difficult to find the best solutions with the exact search method. To account for this, the hybrid multi-objective simulated annealing algorithm (MOHSA) is proposed by fully utilising the capability of the exploration search and fast convergence. Two numerical experiments have been performed to demonstrate the effectiveness and robustness of the proposed algorithm.     

The Scheduling of Lots on a Single Facility

The problem of scheduling the production of lots of n products on a single facility is treated with the objective of minimizing the combined costs of setup, inventory, and backorder over a specified planning horizon. The discussion extends one of Elmaghraby's models (4) by developing a branch-and-bound algorithm which incorporates a dominance rule, a global precedence relation, and several local precedence relations.