Priority Rule Generation with a Genetic Algorithm to Minimize Sequence Dependent Setup Costs

A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs

The determination of lot sizes and production schedules of multiple products in multiple periods is difficult when sequence-dependent set-up costs are present. By using an initial set-up cost estimator (ISCE) the joint problem can be divided and solved sequentially. A search of the literature reveals that, while there is considerable research on the individual problems of lot sizing and scheduling, there is a dearth of study on either the joint problem or on the effect of ISCE selection on the total cost solution. Using a variety of data sets, this paper evaluates the sensitivity of ISCE selection on the solution to the joint problem. Results of the study demonstrate that the choice of an ISCE can have a significant effect on the final lot sizes and schedules. Additionally, the research shows that ‘common sense’ a priori assumptions about ISCE performance may lead to the selection of an inappropriate ISCE.

A grasp for single machine scheduling with sequence dependent setup costs and linear delay penalties

The paper presents a real world application in the paper industry. Palettes arriving randomly are loaded with paper and have to be wrapped up on a single machine. A change of paper types between two consecutive pallets causes sequence-dependent set-up costs on the machine. Pallets are buffered in a line sorter. The planner has to decide in which line of the sorter a pallet is stored and from which line the next pallet that should be served on the machine is selected. The objective is to minimize set-up costs. For this optimization problem a simulation model has been implemented and different strategies for selecting a line and a pallet have been tested.

The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times

In this paper we address an uncapacitated integrated lot-sizing and scheduling problem with sequence-dependent set-up costs in which several products with associated demand are produced across multiple periods in a single facility. We develop a network-flow-based model formulation for the problem and propose facet-defining inequalities that make the formulation even tighter. We extend the model to include backordering, lost sales, and constraints for capacitated problems; these formulations with corresponding examples are provided in an appendix. In addition, we present a stochastic linear programming model and a two-stage stochastic model with a recourse policy to incorporate demand uncertainty. A Benders decomposition-based scheme is deployed to solve the models. A computational investigation is carried out that reveals the proposed method to outperform the direct solution of the model formulations by CPLEX. Few interesting managerial insights are also provided. Lastly, we summarise our work and suggest potential directions for future research.

Single machine capacitated lot-sizing and scheduling problem (SMCLSP) is one of the most famous fields of research in scheduling area. What makes this problem particularly difficult to solve is large and sequence dependent setups and also multiple criteria that must be considered. This paper formulates such a problem and presents a hybrid simulated annealing (HSA) for it. The superiority of HSA is shown compared to one the efficient recent heuristics. The average deviation of the HSA from the corresponding optimal solution for small size problems ranges from 0 to 10%.

In Chaps. 3 and 4, mathematical models have been proposed for the capacitated lot sizing problem with production carryover and setup crossover across periods. Heuristics based on both the mathematical models have also been proposed. The models and heuristics address real-life situations in process industries such as production immediately after setup and uninterrupted production carryover across periods.

SUMMARY Process planning and inventory control are important manufacturing functions; proper execution of these functions can result in large cost savings. Process planning is typically responsible for identification and sequencing of required manufacturing processes. Inventory control then uses the result of process planning activities to determine economic production quantities. Today, this sequential decision process is commonly used in industry. However, although easy to implement, it cannot guarantee that an overall minimum cost plan will be generated. An integrated approach to process planning and inventory control functions should presumably yield better results. Such an integrated approach is presented in this paper. The problem is formulated as a constrained optimization model with sequence-dependent set-up and processing costs. Dynamic programming is used to solve the model.

In this paper, we formulate the cyclic lot scheduling problem on a single facility with sequence-dependent setup costs and times and provide a heuristic solution procedure. A Lagrangian relaxation of the formulation leads to a partial separation of the embedded lot sizing and traveling salesman problems. The relaxation results in a new combinatorial problem related to the minimum spanning tree problem. The information about frequency of production, gained from the solution to this relaxation, is used to find heuristic solutions for the entire problem. Computational work on randomly generated problems shows that the problem becomes more difficult as the diversity in the sequence-dependent parameters increases.

Simultaneous lotsizing and scheduling by combining local search with dual reoptimization

Pricing, relaxing and fixing under lot sizing and scheduling

Article history: Received December 10, 2013 Received in revised format 12 March 2014 Accepted April 24 2014 Available online April 25 2014 This article addresses multi-level lot sizing and scheduling problem in capacitated, dynamic and deterministic cases of a job shop manufacturing system with sequence-dependent setup times and costs assumptions. A new mixed-integer programing (MIP) model with big bucket time approach is provided to the problem formulation. It is well known that the capacitated lot sizing and scheduling problem (CLSP) is NP-hard. The problem of this paper that it is an extent of the CLSP is even more complicated; consequently, it necessitates the use of approximated methods to solve this problem. Hence, two new mixed integer programming-based approaches with rolling horizon framework have been used to solve this model. To evaluate the performance of the proposed model and algorithms, some numerical experiments are conducted. The comparative results indicate the superiority of the second heuristic. © 2014 Growing Science Ltd. All rights reserved.

This chapter studies a two-level production planning problem where, on each level, a lot sizing and scheduling problem with parallel machines, capacity constraints and sequence-dependent setup costs and times must be solved. The problem can be found in soft drink companies where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. Models and solution approaches proposed so far are surveyed and conceptually compared. Two different approaches have been selected to perform a series of computational comparisons: an evolutionary technique comprising a genetic algorithm and its memetic version, and a decomposition and relaxation approach.

Auditor travel can significantly complicate the scheduling process and have an important impact on audit cost, especially for audits of multinational companies. This paper formulates an optimization model that specifically incorporates auditor travel time and costs in the determination of the overall optimal audit schedule. From a more theoretical perspective, this research extends the method of cost control by proposing a method by which a sequence-dependent setup cost (i.e., travel cost) and an associated variable cost (i.e., out-of-town cost) can be programmed into an optimization process for audit planning. The proposed model provides an optimal schedule considering such costs in a multiple nonidentical manpower (i.e., different auditors) environment. Previous research on manpower scheduling has not dealt with sequence-dependent travel costs. The out-of-town time and cost elements are unique for manpower scheduling and not applicable for machine scheduling. An implementation of the model to an actual empirical audit is presented.