An MILP Continuous-Time Framework for Short-Term Scheduling of Multipurpose Batch Processes Under Different Operation Strategies

This work introduces a novel MILP continuous-time framework to the optimal short-term scheduling of non-sequential multipurpose batch processes with intermediate storage vessels. It is based on a problem representation that describes the batch sequence at any processing/storage unit by providing the full set of predecessors for every batch. Different operation modes can be considered by making minor changes in the problem model. The proposed framework can also handle sequence-dependent changeovers as well as multiple storage tanks available to receive material from one or several processing units. Three example problems involving up to fifteen batches and six processing tasks were successfully solved. Compared with previous work, a drastic reduction in both problem size and CPU time has been achieved.     

The effect of greenhouse gas policy on the design and scheduling of biodiesel plants with multiple feedstocks

With the increasing attention to the environmental impact of discharging greenhouses gases, there has been a growing public pressure to reduce the carbon footprint associated with the use of fossil fuels. In this context, one of the key strategies is the substitution of fossil fuels with biofuels such as biodiesel. The design of biodiesel production facilities has traditionally been carried out based on technical and economic criteria. Greenhouse gas (GHG) policies (e.g., carbon tax, subsidy) have the potential to significantly alter the design of these facilities, the selection of the feedstocks, and the scheduling of multiple feedstocks. The objective of this article is to develop a systematic approach to the design and scheduling of biodiesel production processes while accounting for the effect of GHG policies in addition to the technical, economic, and environmental aspects. An optimization formulation is developed to maximize the profit of the process subject to flowsheet synthesis and performance modeling equations. Furthermore, the carbon footprint is accounted for with the help of a life cycle analysis (LCA). The objective function includes a term which reflects the impact of the LCA of a feedstock and its processing to biodiesel. A multiperiod approach is used to discretize the decision-making horizon into time periods. During each period, decisions are made on the type and flowrate of the feedstocks, as well as the associated design and operating variables. A case study is solved with several scenarios of feedstocks and GHG policies.     

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.     

Control of manufacturing networks which contain a batch processing machine

We consider the control of a batch processing machine which is part of a larger manufacturing network of machines. Systems consisting of a batch processing machine and one or more unit-capacity machines in tandem are considered. The objective is to minimize the average time that jobs spend in the entire system. We present algorithms to determine the optimal policies for certain finite horizon, deterministic problems. We then discuss the structure of the optimal policies for infinite horizon, stochastic problems, and investigate the benefit of utilizing information about upstream and downstream unit-capacity machines in the control of the batch machine. We develop a simple heuristic scheduling policy to control the batch machine which takes into account the state of other machines in the network. Computational results demonstrate the effectiveness of our heuristic over a wide range of problem instances.     

A batch splitting method for a job shop scheduling problem in an MRP environment

The job shop scheduling problem has been a major target for many researchers. Unfortunately though, most of the previous research was based on assumptions that are different from the real manufacturing environment. Among those distorted assumptions, two assumptions about set-up time and job composition can greatly influence the performance of a schedule. First, most of the past studies ignored the impact of the before-arrival set-up time. If we know the sequence of operations in advance, we can obtain an improved schedule by preparing the setup before a job arrives. Secondly, most of the past studies assumed that a job consists of only a single part, that is a batch of size one. However, if we assume that a job consists of a batch size greater than one, as in many real manufacturing environments, then we can obtain an improved schedule because we can fill up the idle times of machines with jobs which have smaller processing times by splitting the original batches. However, the number of job orders may then increase due to the split, and the size of the scheduling problem would become too large to be solved in a practical time limit. Consequently, there may be an optimum batch size considering trade-off between better solution and tractability. The current study is the result of an attempt to find an acceptable solution when the production requirement from a MRP system for a planning period exceeds the capacity of a production system. We try to get an improved schedule by splitting the original batch into smaller batches, and consider setting up a machine before the actual arrival of jobs to that machine. Thereby we can meet the due date requirement without resorting to rescheduling of the master production schedule. For the given batch, we disaggregate it according to the algorithm we are proposing. A so-called 'modified shifting bottleneck procedure' is then applied to solve the job shop scheduling problem with a before-arrival family set-up time considering release date, transportation time and due date. The study also shows that we can adapt to unexpected dynamic events more elegantly by allowing the splitting of batches.     

Revising the master production schedule in a HPP framework context

This paper investigates the stability of the master production schedule (MPS) in a multi-product batch chemical plant, a typical example of manufacturing plants in the process industry. The effects of demand pattern, replanning periodicity, setup costs and unit production cost on the performance of the MPS in a rolling horizon situation are examined. Adopting the hierarchical production planning framework, a two-level mathematical model is developed to conduct the study. A comprehensive simulation work and statistical analyses are reported in this work. The results of the study show that replanning periodicity significantly influences the scheduling instability and the impact of setup cost on scheduling instability is dependent on the demand pattern and the unit production cost. Moreover, the findings indicate that replanning frequency does not affect the total cost of the system if the cost structures are not extreme. Finally, the results show that cost structures affect the batching of orders (converting production quantities into an optimal number of batches to be processed).     

基于流转批量的动态制造提前期算法研究

通过对企业资源计划(ERP)应用中生产过程的流转批量、加工批量与提前期的关系进行分析研究，以离散制造业中的批量生产为应用背景，结合批量因素提出多流转批次下的制造提前期计算方法，以流转批次反映工序间不同生产能力的相互影响，使车间作业中流转批量因素能在生产计划阶段通过提前期反映出来，以降低生产计划与车间作业计划之间的误差。并以实例应用说明该方法在生产计划制定中取得的效果。     

The impact of worker forgetting on production scheduling

Numerous articles suggest using the Japanese manufacturing strategy of minimizing inventories by producing small lot sizes. However, few studies actually have investigated the relative advantages or disadvantages of such a strategy. Worker productivity improvements during production of a batch (learning)and the loss of productivity improvements due to the breaks between batches (forgetting)both influence the optimal lot size for a product. The results of this study indicate that worker forgetting in a batch production environment can substantially increase optimal lot sizes. Since forgetting causes a type of setup cost by penalizing breaks in production, it is intuitive to expect an increase in optimal lot size for forgetting. This study confirms the expectation. What is interesting, however, is that only a small amount of forgetting is required to substantially increase the optimal lot size. The conditions under which lot sizes need to be significantly increased are discussed and illustrated. The results also suggest that special attention must be given to eliminate forgetting due to production disruption when using just-in-time scheduling techniques to reduce lot sizes. The use of automated processes in batch production may overcome the need for large lot sizes by negating the worker forgetting cost, which is a form of setup cost. Robotic technologies or flexible manufacturing systems are types of automated processes which can diminish the forgetting effect in a batch production mode, and therefore, allow efficient production of small lot sizes.     

Batch scheduling in process industries: an application of resource–constrained project scheduling

The paper deals with batch scheduling problems in process industries where final products arise from several successive chemical or physical transformations of raw materials using multi–purpose equipment. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. The production start of a batch at a given level requires the availability of all input products. We consider the problem of scheduling the production of given batches such that the makespan is minimized. Constraints like minimum and maximum time lags between successive production levels, sequence–dependent facility setup times, finite intermediate storages, production breaks, and time–varying manpower contribute to the complexity of this problem. We propose a new solution approach using models and methods of resource–constrained project scheduling, which (approximately) solves problems of industrial size within a reasonable amount of time. Received: October 15, 1999 / Accepted: March 21, 2000     

Batching and scheduling to minimize the makespan in the two-machine flowshop

In this paper, we consider a class of batching and scheduling problems in the two-machine flowshop where one of the machines is a discrete processor and the other one is a batch processor. The jobs are processed separately on the discrete processor and processed in batches on the batch processor. The processing time of a batch is equal to the total processing time of the jobs contained in it, and the completion time of a job in a batch is defined as the completion time of the batch containing it. A constant setup time is incurred whenever a batch is formed on the batch processor. The problem is to find the optimal batch compositions and the optimal schedule of the batches so that the makespan is minimized. All problems in this class are shown to be NP-complete in the ordinary sense. We also identify some polynomially solvable cases by introducing their corresponding solution methods.     

含不一致任务重量的同型熔炼炉批调度优化

为求解含不一致任务重量的同型熔炼炉批调度问题,建立了最小化最大任务完工时间优化模型,设计了一种混合粒子群算法（HPSO）。算法使用随机生成的任务序列作为粒子,采用批首次匹配（BFF）规则对任务序列分批,最长加工时间（LPT）规则将批分配到批处理机,并提出了一种最小完工时间差（MCD）规则对LPT调度结果进行优化;为避免早熟,算法引入交叉和变异操作搜索最优解。通过仿真实验与SA、GA算法对比,实验结果表明算法具有良好的性能。     

基于连续时间模型的染缸排产研究

织物的染色是一种按订单生产的批处理过程。每个订单往往被分解成几个批次生产,为了保证质量,要求不同的批次应具有相同的生产环境。因此在对布匹印染的调度过程中,需要确定每个订单的批次,在满足交期的情况下将其分配到恰当的染缸中生产。文中针对印染企业染缸排产困难和布匹浸染的订单交期延迟现象,在合理假设的基础上建立一种连续时间模型。提出了估算时间槽的一种新方法,根据求解出来的时间槽,采用LINGO软件对该模型进行求解。实例证明了该种时间槽估算方法的可行性和有效性。     

Modelling and symmetry breaking in scheduling problems on batch processing machines

Problems of scheduling batch-processing machines to minimise the makespan are widely exploited in the literature, mainly motivated by real-world applications, such as burn-in tests in the semiconductor industry. These problems consist of grouping jobs in batches and scheduling them on machines. We consider problems where jobs have non-identical sizes and processing times, and the total size of each batch cannot exceed the machine capacity. The processing time of a batch is defined as the longest processing time among all jobs assigned to it. Jobs can also have non-identical release times, and in this case, a batch can only be processed when all jobs assigned to it are available. This paper discusses four different versions of batch scheduling problems, considering a single processing machine or parallel processing machines and considering jobs with or without release times. New mixed integer linear programming formulations are proposed as enhancements of formulations proposed in the literature, and symmetry breaking constraints are investigated to reduce the size of the feasible sets. Computational results show that the proposed formulations have a better performance than other models in the literature, being able to solve to optimality instances only considered before to be solved by heuristic procedures.     

Production of biogas from municipal solid waste with domestic sewage

In this study, experiments were conducted to investigate the production of biogas from municipal solid waste (MSW) and domestic sewage by using anaerobic digestion process. The batch type of reactor was operated at room temperature varying from 26 to 36 degrees C with a fixed hydraulic retention time (HRT) of 25 days. The digester was operated at different organic feeding rates of 0.5, 1.0, 2.3, 2.9, 3.5 and 4.3kg of volatile solids (VS)/m(3) of digester slurry per day. Biogas generation was enhanced by the addition of domestic sewage to MSW. The maximum biogas production of 0.36m(3)/kg of VS added per day occurred at the optimum organic feeding rate of 2.9kg of VS/m(3)/day. The maximum reduction of total solids (TS) (87.6%), VS (88.1%) and chemical oxygen demand (COD) (89.3%) occurred at the optimum organic loading rate of 2.9kg of VS/m(3)/day. The quality of biogas produced during anaerobic digestion process was 68-72%.     

Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops

This study considers the batching and scheduling problem in two-stage hybrid flow shops in which each job with a distinct due-date is processed through two serial production stages, each of which has identical machines in parallel. Under the fundamental trade-off that large batch sizes with less frequent changeovers may reduce setup costs and hence increase machine utilisation, while small batch sizes may reduce job flow times and hence improve scheduling performance, the problem is to determine the number of batches, the batch compositions, the allocation of batches to the parallel machines at each stage, and the sequence of the batches allocated to each machine for the objective of minimising the total job tardiness. A mixed integer programming model is developed for the reduced problem in which the number of batches is given, and then, three iterative algorithms are proposed in which batching and scheduling are done repeatedly until a good solution is obtained. To show the performance of the algorithms, computational experiments were done on a number of test instances, and the results are reported. In particular, we show that the number of batches decreases as the ratio of the batch setup time to the job processing time increases.     

Optimal operation of a distributed energy generation system for a sustainable palm oil-based eco-community

The palm oil industry potentially can be environmentally sustainable through utilizing the vast availability of biomass residues from palm oil mills as renewable energy sources. This work addresses the optimal operation of a combined bioenergy and solar PV distributed energy generation system to meet the electricity and heat demands of an eco-community comprising a palm oil mill and its surrounding residential community. A multiperiod mixed-integer linear programming planning and scheduling model is formulated on an hourly basis that optimally selects the power generation mix from among available biomass, biogas, and solar energy resources with consideration for energy storage and load shifting. A multiscenario approach is employed that considers scenarios in the form of many possible weather conditions and various energy profiles under varying mill operation modes and residential electricity consumption. The proposed approach is demonstrated on a realistic case study for a palm oil mill in the Iskandar Malaysia economic development region. The computational results indicate that biomass-based resource is the preferred renewable energy to be implemented due to the high cost associated with solar PV. As well, load shifting and energy storage can be feasibly deployed for demand peak shaving particularly for solar PV systems.     

Single-machine batch delivery scheduling and common due-date assignment with a rate-modifying activity

We consider batch delivery scheduling on a single machine, where a common due-date is assigned to all the jobs and a rate-modifying activity on the machine may be scheduled, which can change the processing rate of the machine. Thus the actual processing time of a job is variable depending on whether it is processed before or after the rate-modifying activity. The objective is to determine the optimal job sequence, the optimal partition of the job sequence into batches, the optimal assigned common due-date, and the optimal location of the rate-modifying activity simultaneously to minimize the total cost of earliness, job holding, weighted number of tardy jobs, due-date assignment, and batch delivery. We derive some structural properties of the problem, based on which we design polynomial-time algorithms to solve some special cases of the problem.     

Optimizing production smoothing decisions via batch selection for mixed-model just-in-time manufacturing systems with arbitrary setup and processing times

This paper is concerned with the production smoothing problem that arises in the context of just-in-time manufacturing systems. The production smoothing problem can be solved by employing a two-phase solution methodology, where optimal batch sizes for the products and a sequence for these batches are specified in the first and second phases, respectively. In this paper, we focus on the problem of selecting optimal batch sizes for the products. We propose a dynamic programming (DP) algorithm for the exact solution of the problem. Our computational experiments demonstrate that the DP approach requires significant computational effort, rendering its use in a real environment impractical. We develop three meta-heuristics for the near-optimal solution of the problem, namely strategic oscillation, scatter search and path relinking. The efficiency and efficacy of the methods are tested via a computational study. The computational results show that the meta-heuristic methods considered in this paper provide near-optimal solutions for the problem within several minutes. In particular, the path relinking method can be used for the planning of mixed-model manufacturing systems in real time with its negligible computational requirement and high solution quality.     

Production scheduling of single-stage multi-product batch chemical processes with fixed batch sizes

We address the problem of scheduling a single-stage multi-product batch chemical process with fixed batch sizes. We present a mixed-integer nonlinear programming model to determine the schedule of batches, the batch size, and the number of overtime shifts that satisfy the demand at minimum cost for this process. We introduce a polynomial-time algorithm to solve the problem when the processing times of all batches are identical and the setup and cleaning times are sequence-independent. The solution procedure is based on recognizing that the optimal fixed batch size is a member of a set whose cardinality is polynomial. Given a batch size, the problem may be formulated as an assignment problem. Thus, an optimal solution may be found by iteratively solving a polynomial number of assignment problems. This work was motivated by a pesticide manufacturing company in the design of a new plant where the assumptions of a single bottleneck machine, fixed batch sizes, sequence-independent setup times, and identical batch processing times are all valid. An example is developed for this application.     

Multi-stage,multi-facility,batch production system with deterministic demand over a finite time horizon

Researches on multi-stage production systems, so far, have tended to schedule production according to the overall optimal batch size of the entire shop with little consideration of the influence of the individual stages of production on the batch sizes that are considered optimal. The authors have attempted, in this paper, to investigate the effects of scheduling according to the optimality of the respective production stages. The results are compared with those of the more common case of overall optimal batch scheduling