Sequence-dependent Changeover Costs Research Articles

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.

A new model and a reformulation for the crude distillation unit charging problem with oil blends and sequence-dependent changeover costs

In this paper, we address the problem of planning the crude distillation unit charging process with oil blend. It is well known that blending and splitting operations can lead together to both non-linearities and concavities in mathematical programming models. As result, many proposed models for this problem use simplifying assumptions to keep the formulation computationally tractable. However, we show the existence of splitting operations that can lead to inconsistencies in the solutions obtained by the previous MILP models from the literature. Then, we propose a way to address this issue through an aggregated inventory capacity combined with a disaggregation algorithm. Furthermore, we develop a mathematical reformulation that improves the solving efficiency of the method. Then, we report experiments that show that the reformulated MILP model presents significant gains concerning linear relaxation gaps and run times, and the disaggregation algorithm leads to feasible solutions for all the tested instances.

Multi-product valid inequalities for the discrete lot-sizing and scheduling problem

We consider a problem arising in the context of industrial production planning, namely the multi-product discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. We aim at developing an exact solution approach based on a Cut & Branch procedure for this combinatorial optimization problem. To achieve this, we propose a new family of multi-product valid inequalities which corresponds to taking into account the conflicts between different products simultaneously requiring production on the resource. We then present both an exact and a heuristic separation algorithm which form the basis of a cutting-plane generation algorithm. We finally discuss computational results which confirm the practical usefulness of the proposed inequalities at strengthening the MILP formulation and at reducing the overall computation time.

A production scheduling problem with sequence-dependent changeover costs

This paper presents a novel three-step heuristic algorithm which assigns products to parallel heterogeneous machines and determines the sequence in which the products are run on each machine. The objective is to minimise the total set-up cost, which is sequence-dependent. In the algorithm’s first step, products are assigned to machines while evaluating each potential assignment’s impact on the tentative sequence. In the second step, an optimal sequence is determined given the assignment from the first step; this is done using a dynamic constraint-generation method. The third step improves the solution through a local search heuristic. The developed algorithm is very efficient in solving large problems and has been implemented at the corresponding author’s organisation.

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.

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.

Discrete lot sizing and scheduling using product decomposition into attributes

A production planning problem, known as the discrete lot sizing and scheduling problem with sequence-dependent changeover costs, is considered. We propose a new way of modelling the production system based on the use of a multi-attribute product structure encountered in many industrial situations. The basic idea is to describe the products as combinations of physical attributes and to exploit this description to reduce the size of the mixed-integer program to be solved. The results of our computational experiments show the practical usefulness of the proposed formulation which leads to significantly improved efficiency in the solution process.

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.

Simultaneous Batching and Scheduling in Multistage Multiproduct Processes

In this article, we present a mixed-integer programming formulation for the simultaneous batching and scheduling in multiproduct multistage processes. The proposed sequence-based formulation addresses limitations of existing approaches where batching and scheduling decisions are carried out sequentially. To account for batching decisions, we use additional batch-selection and batch-size variables and introduce demand-satisfaction and unit-capacity constraints. Assignment constraints are active only for the subset of batches that are selected, and sequencing is carried out between batches that are assigned on the same processing unit. We also propose an alternate formulation to handle sequence-dependent changeover costs. Finally, to enhance the computational performance of the model, we present methods that allow us to fix a subset of sequencing variables and we develop a class of tightening inequalities based on time windows.

Sequencing with limited flexibility

We consider the problem of resequencing a set of prearranged jobs when there is limited resequencing flexibility and sequence-dependent changeover costs. Resequencing flexibility is limited by how far forward or backward a job can shift in the sequence relative to its original position. We show how the problem can be solved using dynamic programming in polynomial time with respect to the number of jobs. We also show how the same solution approach can be extended to problems where sequencing constraints are job specific and to problems where job features, which determine changeover costs, are jointly determined with the job sequence. We provide an integer programming formulation to the resequencing problem whose linear programming relaxation offers a useful lower bound. We also describe a family of decomposition heuristics that are easy to customize to provide desired levels of solution quality and solution time. We document the quality of the lower bound from the linear programming relaxation and the upper bound from the heuristic using numerical results. We also provide numerical results to support managerial insights regarding the value of flexibility. We show that the value of flexibility is of the diminishing kind with most of the benefit realized with relatively limited flexibility. We also show that a balanced allocation of flexibility among forward and backward position shifting is superior to an unbalanced one. More significantly, we show that forward and backward position shifting flexibility are complements with the value of one increasing in the amount of the other. Finally, we apply our solution approach to a real-world case from the automotive industry.

A Job-Scheduling Problem Involving Sequence-Dependent Changeover Costs

This paper studies a problem of job scheduling in a production line having various adjustable settings or ‘states’ that can process a variety of jobs. Each job can be processed when the line is in one of the several states at a cost dependent on the state used. One state is sufficient for the processing of each job. In addition, a sequence-dependent changeover cost is also incurred between states. The problem is to determine an optimal sequence of the states of the line, and allocation of jobs to states that minimizes the overall operating cost. An exact implicit enumeration algorithm, which exploits the similarity of this problem with the simple plant location problem, is proposed. Computational experience with the algorithm shows that any reasonable size problem can be solved in comparatively small computational effort.

A sequencing heuristic for dependent setups in a batch process industry

Microcomputer-based scheduling systems are dramatically enhancing the ability of manufacturing firms to respond rapidly to changing customer demands and to improve production efficiency. Pendegraft [11], Sullivan and Secrest [14], and Hodsen, Muhlemann and Price [7] provide examples of optimizing schemes that are microcomputer-based. These systems, though do not address sequencing problems with dependent setups nor do they provide efficient rescheduling capabilities required by many practical scheduling environments. This paper presents the development and application of a heuristic approach for scheduling jobs on parallel processors given sequence dependent changeover costs. The model provides for simultaneous processing of single or multiple products, the latter of particular concern in the batch process industries where machine utilization is of immediate concern. An industrial application of the sequencing heuristic at a fiberglass company indicates that cost savings arising from reduced setups can be accrued from the use of the model. The sequencing heuristic is easily understood in terms of its solution methodology and thus more likely to appeal to actual production schedulers.

MODELING AND SOLVING THE FLEXIBLE FORGING MODULE SCHEDULING PROBLEM

In this paper, an existing small scale manufacturing system called a Flexible Forging Module (FFM) is considered. For this system the sequence-dependent changeover costs have been identified. In order to obtain an optimal schedule, a network model is developed which easily incorporates both the sequence-dependent changeover costs and the precedence constraints. A branch and bound algorithm is outlined and numerical results are reported.

On the Use of A Vehicle Routing Algorithm for the Parallel Processor Problem with Sequence Dependent Changeover Costs

Abstract We consider the problem of sequencing a set of changeover dependent jobs in a parallel processor shop subject to a workload restriction where the objective is to achieve minimum total changeover cost. A heuristic algorithm, developed previously to treat the vehicle delivery model, is used on the problem. Suitable computational experience with the algorithm is provided the results of which would support its application to problems of realistic size.