Herman Crauwels

Local search heuristics for single machine scheduling with batch set-up times to minimize total weighted completion time

Local search heuristics are developed for a problem of scheduling a single machine to minimize the total weighted completion time. The jobs are partitioned into families, and a set-up time is necessary when there is a switch in processing jobs from one family to jobs of another family. Four alternative neighbourhood search methods are developed: multi-start descent, simulated annealing, threshold accepting and tabu search. The performance of these heuristics is evaluated on a large set of test problems, and the results are also compared with those obtained by a genetic algorithm. The best results are obtained with the tabu search method for smaller numbers of families and with the genetic algorithm for larger numbers of families. In combination, these methods generate high quality schedules at relatively modest computational expense.

Local search heuristics for single-machine scheduling with batching to minimize the number of late jobs

Abstract Local search heuristics are developed for a problem of scheduling jobs on a single machine. Jobs are partitioned into families, and a set-up time is necessary when there is a switch in processing jobs from one family to jobs of another family. The objective is to minimize the number of late jobs. Four alternative local search methods are proposed: multi-start descent, simulated annealing, tabu search and a genetic algorithm. The performance of these heuristics is evaluated on a large set of test problems. The best results are obtained with the genetic algorithm; multi-start descent also performs quite well.

Branch and bound algorithms for single-machinescheduling with batch set-up times to minimizetotal weighted completion time

This paper presents several branch and bound algorithms for a single-machine scheduling problem with batching. Jobs are partitioned into families, and a set-up time is necessary when there is a switch from processing jobs of one family to jobs of another family. The objective is to minimize the total weighted completion time. A lower bound based on Lagrangian relaxation of the machine capacity constraint is derived. Also, a multiplier adjustment method to find values of the multipliers is proposed. Computational experience with instances having up to 50 jobs shows that the lower bounds are effective in restricting the search.

Branch and Bound Algorithms for Single Machine Scheduling with Batching to Minimize the Number of Late Jobs

This paper considers the problem of scheduling a single machine to minimize the number of late jobs in the presence of sequence-independent family set-up times. The jobs are partitioned into families, and a set-up time is required at the start of each batch, where a batch is a maximal set of jobs in the same family that are processed consecutively. We design branch and bound algorithms that have several alternative features. Lower bounds can be derived by relaxing either the set-up times or the due dates. A first branching scheme uses a forward branching rule with a depth-first search strategy. Dominance criteria, which determine the order of the early jobs within each family and the order of the batches containing early jobs, can be fully exploited in this scheme. A second scheme uses a ternary branching rule in which the next job is fixed to be early and starting a batch, to be early and not starting a batch, or to be late. The different features are compared on a large set of test problems, where the number of jobs ranges from 30 to 50 and the number of families ranges from 4 to 10.

The development and application of an integrated production planning methodology for sheet metal working SMEs

Sheet metal working remains an important industry. It is argued that, to be competitive, the complete production chain needs to be optimised. Therefore, this article focuses on the optimisation of the production plan. The sheet metal shop is configured as a two-stage flow shop with laser cutting and air bending. In the literature, theoretical production planning models can be found for both individual processes. Unfortunately, those planning models have a low applicability in sheet metal working small and medium sized enterprises (SMEs) due to the fact that they only focus on one single production step while in reality the planning decisions taken at the cutting stage affect the production plan for the air bending stage. An integrated production planning methodology is proposed to overcome this problem of individual optimisation by taking into account relevant bending information already at the cutting stage. An integer program is presented, incorporating some important practical requirements: (1) the planning model is suited for normal workpieces, rush orders, special workpieces and multiple-machine sheet metal shops and (2) the computational times to generate the production plan are limited. Ten real-life industrial test cases are used to evaluate the proposed methodology. The integrated production planning methodology results in schedules with a reduced makespan and a reduced set-up time at the press brake compared to the current way of planning. All planning models are developed in close cooperation with sheet metal working SMEs to facilitate the implementation process.

Sheet-Metal Shop Scheduling Considering Makespan and Flow Time Criteria~!2009-06-01~!2010-05-12~!2010-06-22~!

Sheet-metal parts typically follow a unidirectional flow in the sheet-metal shop. In the first cutting stage, a large sheet is cut to different unfolded parts with a laser cutting machine. To avoid waste material different parts are combined on a sheet. Next, the 2D parts are transformed to 3D products with air bending. In this bending stage, time- consuming set-ups between production layouts are reduced as much as possible. Separate optimisation of cutting and air bending causes the optimisation benefits to counteract one another. Integrated models have been proposed for both single- and multiple-machine classes, but calculation times are too high and avoidable changeovers still occur. In this paper, by applying variable neighbourhood search with a number of different starting solutions, local optima of good quality are determined for minimising the makespan and the total flow time for both the single-machine and the multi-machine classes. Because the two performance measures are important for a good production plan, bicriteria optimisation by means of a simultaneous and a hierarchical approach, is also considered. Compared to the mathematical programming models for the combined cutting and bending operations, both quality and required computation time are improved for several real-life instances.

Integrated production planning for the multiple-machine sheet metal shop with laser cutting and air bending

To compete with alternative production methods, sheet metal working firms need to improve continuously. Improvement efforts do not solely focus on the production processes, but also on other aspects of the production chain. Production planning is one of those aspects that need to be optimized. The presented research focuses on production planning optimization for sheet metal shops with a cutting stage and a bending stage. The combination of the production plans of the individual processes does not result in a globally optimal production plan. Consequently, both processes need to be integrated for production planning. In this paper, an integer programming formulation is presented for the multiple-machine two-stage sheet metal shop production planning problem. Numerous real-life test cases are used to benchmark the approach against the current way of planning. To limit the computational time, a dedicated variable neighborhood search procedure is presented.