Sequence-dependent Changeover Times Research Articles

Integrated lot-sizing and energy supply planning with onsite generation of intermittent renewable energy

This work considers an industrial production site partially powered by a decentralised energy system based on intermittent renewable energy sources. Our objective is to simultaneous plan the industrial production and the energy supply in this site so as to minimise the total cost. A new way of modelling this combinatorial optimisation problem is proposed: it relies on the extension of a multi-product single-resource small-bucket lot-sizing model called the proportional lot-sizing and scheduling problem. This extension involves among others sequence-dependent changeover times overlapping multiple periods and energy-related constraints. Our numerical results show that the resulting mixed-integer linear programming model enables to obtain good-quality production and energy supply plans with a computational effort much smaller than the one required by a previously published large-bucket lot-sizing model.

Scheduling and batching with evolutionary algorithms in simulation–optimization of an industrial formulation plant

Industrial scheduling problems are usually characterized by a high complexity and in many, if not all cases, a detailed representation of many specific features of the production process and of the constraints is necessary to ensure that the resulting schedules are feasible when they are executed. Such detailed representations are provided by commercial discrete-event simulation programs which are often employed in the planning phase to detect bottlenecks and to validate design decisions, but usually do not provide optimized schedules. In this paper, we combine a tailored Evolutionary Algorithm with a high-fidelity simulation model in a Simulation–Optimization approach in order to obtain optimized executable production schedules.The industrial production process considered here is a formulation plant that consists of a formulation stage and a filling stage with optional intermediate storage in a set of buffer tanks. The operational constraints include limited operator availability and shift constraints, sequence-dependent changeover times in both stages, product- and line-dependent processing rates, and the need for synchronization of operations. The objective is to minimize the tardiness of a set of orders some of which have long operation times and small slack between the earliest possible end times and the due dates.The orders consist of a certain number of batches, but if all the batches of an order are processed on the same equipment, meeting the due dates is not possible. Therefore the orders have to be decomposed into sub-orders (production orders) to realize parallel processing of urgent orders on several units with the goal to meet due dates. The decision to distribute the total demand of the individual customer orders to production orders is also called batching decision in the literature.A distinctive feature of our approach is that three independent encodings of the batching, allocation and sequencing decisions are used. The batching decisions lead to variable-length chromosomes for the allocation and sequencing encodings. For the treatment of variable-length chromosomes, new crossover and mutation operators, as well as repair algorithms are presented.The results for three test cases show that the introduction of the batching decisions significantly improves the tardiness of the production schedules. A thorough tuning of the categorical parameters of the Evolutionary Algorithm has been performed and it is shown that the resulting parameter setting yields reproducible results, while outperforming simpler approaches.

Integrated production scheduling and distribution allocation for multi-products considering sequence-dependent setups: a practical application

This paper proposes an integrated multi-product production planning and distribution allocation in the supply chain network, including the detailed production sequences in each production line for a dairy manufacturing. The models are designed for manufacturers that produce multi-products. One of the concerns of the multi-products manufacturers is the sequence-dependent changeover times and costs that occur when switching from one type of product to another. The models are developed into two-stages due to different levels of decisions. The first stage models the supply chain network that determines the optimum production planning for each product type on each production line, delivery schedule, and inventory planning for the entire supply chain simultaneously to maximize the total profit. Sequentially, based on the optimal production planning, detailed production schedules are then optimized in the second stage of the model with minimizing total setup costs as the objective. The result shows that the proposed models significantly reduce the total cost and consequently increase the annual gross profit.

Heuristical Solution for Scheduling Single Stage Parallel Machines Production of Calcium Silicate Masonry Units with Sequence-Dependent Changeover Times to Improve Energy Efficiency

Determination of optimal production schedules is a complex combinatorial task and may be dependent on various objectives. Hence, many mathematical problem formulations and solving strategies have already been proposed each considering individually constrained applications in order to minimize non-value-adding times or other cost driving factors. Nevertheless, obtaining optimal solutions is still related to extensive computational resources and time efforts.As a result, heuristical approaches or combinations of heuristics and exact algorithms are of major importance when it comes to automatically creating optimal production schedules. Considering the manufacturing of calcium silicate masonry units (CS), this paper describes an advancement for the General Lot-Sizing Problem (GLSP) in order to allow sequence-dependent changeovers as well as multiple different machines and backlogging (GLSPPLB). For solving the GLSPPLB, a heuristical algorithm consisting of neighborhood search and threshold accepting techniques was implemented. To validate the results of the heuristic and compare required computational resources to accurate mathematical solvers, a test set of a realistic scenario has been used.The developed heuristic is able to create nearly optimal production schedules and thereby minimizing the trade off between energy demand regarding idle times of production machinery and stocks. It is transferable to every discrete single stage production with similar constraints and can be used as an input for further simulations to improve energy consumption.

A cloud based job sequencing with sequence-dependent setup for sheet metal manufacturing

This paper presents a prototype system of sheet metal processing machinery which collects production order data, passes current information to cloud based centralized job scheduling for setup time reduction and updates the production calendar accordingly. A centralized cloud service can collect and analyse production order data for machines and suggest optimized schedules. This paper explores the application of sequencing algorithms in the sheet metal forming industry, which faces sequence-dependent changeover times on single machine systems. We analyse the effectiveness of using such algorithms in the reduction of total setup times. We describe alternative models: Clustering, Nearest Neighbourhood and Travelling Salesman Problem, and then apply them to real data obtained from a manufacturing company, as well as to randomly generated data sets. Based on the prototype implementation clustering algorithm was proposed for actual implementation. Sequence-dependency increases the complexity of the scheduling problems; thus, effective approaches are required to solve them. The algorithms proposed in this paper provide efficient solutions to these types of sequencing problems.

An MILP model for planning of batch plants operating in a campaign-mode

Fil: Fumero, Yanina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Desarrollo y Diseno. Universidad Tecnologica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseno; Argentina

Time symmetry of resource constrained project scheduling with general temporal constraints and take-give resources

The paper studies a lacquer production scheduling problem formulated as a resource constrained project scheduling problem with general temporal constraints (i.e., positive and negative time-lags). This real-world scheduling problem requires so-called take-give resources that are needed from the beginning of an activity to the completion of another activity of the production process. Furthermore, we consider sequence dependent changeover times on take-give resources. We formulate this problem by mixed integer linear programming and we suggest a parallel heuristic to solve the problem. This heuristic exploits a time symmetry mapping which allows an easy construction of a schedule in the backward time orientation. In the second part of the paper, it is proven that the time symmetry mapping is bijective and involutive even for the problem with general temporal constraints, changeover times, and take-give resources. The motivation to use this mapping is to improve the performance of the heuristic and to simplify its implementation. Finally, the performance of the heuristic algorithm is evaluated on a set of lacquer production benchmarks requiring take-give resources and on standard benchmarks for the resource constrained project scheduling problem with general temporal constraints where we found new better solutions in 16 and 12 instances out of 90 for UBO500 and UBO1000 respectively.

Simultaneous Batching and Scheduling of Batch Plants That Operate in a Campaign-Mode, Considering Nonidentical Parallel Units and Sequence-Dependent Changeovers

A mathematical modeling framework for the simultaneous batching and scheduling of multiproduct batch plants is proposed in this work. The scheduling decisions are formulated according to campaign-based operation mode. When a stable context can be assumed on the time horizon taken into account, this operation mode assures a more efficient production management. In addition, sequence-dependent changeover times and different unit sizes for parallel units in each stage are considered. Given the plant configuration and unit sizes, the total amount of each product to be produced and the product recipes, the proposed approach determines the number of batches that compose the production campaign and their sizes, the batches assignment to units, the sequencing of batches in each unit for each stage, and the timing of batches in each unit in order to minimize the campaign cycle time. A solution strategy is proposed to enhance the computational performance of the simultaneous optimization. The approach capabilities are shown through three numerical examples.

An evaluation of semidefinite programming based approaches for discrete lot-sizing problems

The present work is intended as a first step towards applying semidefinite programming models and tools to discrete lot-sizing problems including sequence-dependent changeover costs and times. Such problems can be formulated as quadratically constrained quadratic binary programs. We investigate several semidefinite relaxations by combining known reformulation techniques recently proposed for generic quadratic binary problems with problem-specific strengthening procedures developed for lot-sizing problems. Our computational results show that the semidefinite relaxations consistently provide lower bounds of significantly improved quality as compared with those provided by the best previously published linear relaxations. In particular, the gap between the semidefinite relaxation and the optimal integer solution value can be closed for a significant proportion of the small-size instances, thus avoiding to resort to a tree search procedure. The reported computation times are significant. However improvements in SDP technology can still be expected in the future, making SDP based approaches to discrete lot-sizing more competitive.

Capacity planning for batch and perfusion bioprocesses across multiple biopharmaceutical facilities

Production planning for biopharmaceutical portfolios becomes more complex when products switch between fed-batch and continuous perfusion culture processes. This article describes the development of a discrete-time mixed integer linear programming (MILP) model to optimize capacity plans for multiple biopharmaceutical products, with either batch or perfusion bioprocesses, across multiple facilities to meet quarterly demands. The model comprised specific features to account for products with fed-batch or perfusion culture processes such as sequence-dependent changeover times, continuous culture constraints, and decoupled upstream and downstream operations that permit independent scheduling of each. Strategic inventory levels were accounted for by applying cost penalties when they were not met. A rolling time horizon methodology was utilized in conjunction with the MILP model and was shown to obtain solutions with greater optimality in less computational time than the full-scale model. The model was applied to an industrial case study to illustrate how the framework aids decisions regarding outsourcing capacity to third party manufacturers or building new facilities. The impact of variations on key parameters such as demand or titres on the optimal production plans and costs was captured. The analysis identified the critical ratio of in-house to contract manufacturing organization (CMO) manufacturing costs that led the optimization results to favor building a future facility over using a CMO. The tool predicted that if titres were higher than expected then the optimal solution would allocate more production to in-house facilities, where manufacturing costs were lower. Utilization graphs indicated when capacity expansion should be considered. © 2013 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 30:594–606, 2014

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al.2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

MILP-based approaches for medium-term planning of single-stage continuous multiproduct plants with parallel units

In this paper, we address the problem of medium-term planning of single-stage continuous multiproduct plants with multiple processing units in parallel. Sequence-dependent changeover times and costs occur when switching from one type of product to another. A traveling salesman problem (TSP)-based mixed-integer linear programming (MILP) model is proposed based on a hybrid discrete/continuous time representation. We develop additional constraints and variables to ensure that subtours do not occur in the solution. The model is successfully applied to an example of a polymer processing plant to illustrate its applicability. In order to solve larger model instances and planning horizons, a rolling horizon approach is developed to reduce the computational expense. Finally, the proposed model is compared to a recently published approach through literature examples, and the results show that the computational performance of the proposed model is superior.

Using composite variable modeling to achieve realism and tractability in production planning: An example from automotive stamping

Applying traditional mathematical programming techniques to problems in production planning can lead to tremendous challenges. These include non-linearities, very large numbers of constraints and weak linear programming relaxations. To ensure tractability, problems are often either simplified in scope or limited in instance size, resulting in solutions that may no longer address important real-world issues. As an alternative, this paper considers the use of models based on composite variables (variables that capture multiple decisions simultaneously) as a way to solve complex production planning problems. The scheduling of an automotive stamping facility is used as a demonstrative example, and it is shown how composite variable models and a novel corresponding algorithm can lead to high-quality, realistic solutions with acceptable run times. In the proposed approach, batch sizes, labor availability or sequencing of part types is not restricted and the number of changeovers is not fixed a priori. In addition, sequence-dependent changeover times and varying due dates are allowed. Computational results are presented using data from Ford Motor Company. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix]

A general resource-constrained scheduling framework for multistage batch facilities with sequence-dependent changeovers

This work introduces a new MILP sequential approach to the short-term scheduling of multistage batch plants that accounts for sequence-dependent changeover times, intermediate due dates and limited availability of renewable resources. It relies on a continuous-time formulation based on the general precedence notion that uses different sets of binary variables to handle allocation and sequencing decisions. To avoid resource overloading, additional constraints in terms of sequencing variables and a new set of 0-1 overlapping variables are presented. They allow tracking the set of tasks requiring the same resource and running in parallel at the start of another process operation. In this way, the proposed formulation involves a reasonable number of binary variables and constraints and features a very good computational behavior, even in the presence of hard bottleneck resources. Four illustrative examples, one of them including multiple bottleneck resources shared by several processing stages, have been efficiently solved.

On the discrete lot-sizing and scheduling problem with sequence-dependent changeover times

We consider the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs and times and propose solving it as a mixed-integer program using a commercial solver. Our approach is based on the extension of an existing tight formulation for the case without changeover times. Computational results confirm the benefits of the proposed solution procedure.

A TSP-based MILP Model for Medium-Term Planning of Single-Stage Continuous Multiproduct Plants

In this paper, we consider the problem of medium-term planning of single-stage continuous plants with a single processing unit that manufactures several products over a planning horizon of several weeks. Sequence-dependent changeover times and costs occur when switching from one type of product to another. To overcome the computational expensiveness of traditional slot-based models for large instances, a novel TSP-based (traveling salesman problem) mixed-integer linear programming (MILP) model is proposed that relies on a hybrid discrete/continuous time representation. The model is applied to an example of a real world polymer processing plant to illustrate its applicability. Finally, the proposed model is compared to recently published approaches through literature examples, and the results show that the computational performance of the proposed model is superior.

Medium-Term Planning of Single-Stage Single-Unit Multiproduct Plants Using a Hybrid Discrete/Continuous-Time MILP Model

The objective of this work is to develop an optimization model for the medium-term planning of single-stage continuous multiproduct plants with a single processing unit. Several types of stock keeping units (SKUs) are produced. Customers place orders that represent multiples of SKUs that must be delivered at the end of each week. When different SKU types are processed, sequence-dependent changeover times and costs are incurred. The problem is formulated as a mixed-integer linear programming (MILP) model with a hybrid time representation. The objective is to maximize profit that involves sales revenues, production costs, product changeover costs, inventory costs, and late delivery penalties. The proposed optimization-based model is validated in a real-world polymer processing plant. To improve its computational efficiency, integer cuts are developed and added in the model. The model is then applied to two literature examples, and the results are compared with other models of similar nature.

Optimal Short-Term Scheduling of Multi-Purpose Batch Processes Considering Sequence-Dependent Constraints and Mixed Intermediate Storage Policies

A simple mathematical model for efficient short-term scheduling of non-sequential multi-product-multi-unit batch processes with unit- and sequence-dependent setup/changeover times and mixed intermediate storage policies is proposed. The scheduling objective is to minimize the makespan or the earliness of the completion of orders. When some of the sequence-dependent changeover times are relatively large compared to the processing times, a rigid formulation is provided to achieve optimality, which is seldom attended to in previous studies. Several intermediate storage policies for the batch processes are considered, including unlimited intermediate storage (UIS), no intermediate storage (NIS), finite intermediate storage (FIS), zero wait (ZW), and mixed intermediate storage (MIS). The problem is then formulated as a mixed-integer linear program (MILP). Two numerical examples are supplied to demonstrate the efficiency and the wide applicability of the proposed scheduling model in face of various different environments.

Enhanced Continuous-Time Unit-Specific Event-Based Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies

An enhanced continuous-time formulation is presented for the short-term scheduling of multipurpose batch plants with intermediate due dates. The proposed formulation is based on the continuous-time formulation introduced by Ierapetritou and Floudas (Ind. Eng. Chem. Res. 1998, 37, 4341 and 4360) and incorporates and elaborates on several features that include (i) various storage policies (UIS, FIS, NIS, and ZW), (ii) resource constraints, (iii) variable batch sizes and processing times, (iv) batch mixing and splitting, and (v) sequence-dependent changeover times. The key features of the proposed formulation include a continuous-time representation utilizing a necessary number of event points of unknown location corresponding to the activation of a task. Also, tasks are allowed to continue over several event points, enabling resource quantities to be correctly determined at the beginning of each resource utilization. Several examples are presented to illustrate the effectiveness of the proposed formulation, and comparisons with other approaches are provided.

New General Continuous-Time State−Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants

A new continuous-time MILP model for the short-term scheduling of multipurpose batch plants is presented. The proposed model relies on the state-task network (STN) approach and addresses the general problem of batch scheduling, accounting for resource (utility) constraints, variable batch sizes and processing times, various storage policies (UIS, FIS, NIS, ZW), batch mixing/splitting, and sequence-dependent changeover times. The key features of the proposed model are the following: (a) a continuous-time representation is used, common for all units; (b) assignment constraints are expressed using binary variables that are defined only for tasks, not for units; (c) start times of tasks are eliminated, so that time-matching constraints are used only for the finish times of tasks; and (d) a new class of valid inequalities that improves the LP relaxation is added to the MILP formulation. Compared to other general continuous time STN formulations, the proposed model is faster. Compared to event-driven formulations, it is more general, as it accounts for resources other than equipment and gives solutions in comparable computational times. The application of the model is illustrated through four example problems.