Dirk Biskup

Single-machine scheduling with learning considerations

The focus of this work is to analyze learning in single-machine scheduling problems. It is surprising that the well-known learning effect has never been considered in connection with scheduling problems. It is shown in this paper that even with the introduction of learning to job processing times two important types of single-machine problems remain polynomially solvable.

A state-of-the-art review on scheduling with learning effects

Recently learning effects in scheduling have received considerable attention in the literature. All but one paper are based on the learning-by-doing (or autonomous learning) assumption, even though proactive investments in know how (induced learning) are very important from a practical point of view. In this review we first discuss the questions why and when learning effects in scheduling environments might occur and should be regarded from a planning perspective. Afterwards we give a concise overview on the literature on scheduling with learning effects.

Single-machine scheduling for minimizing earliness and tardiness penalties by meta-heuristic approaches

We consider the problem of scheduling a number of jobs on a single machine against a restrictive common due date. The paper consists of two parts: firstly a new and appropriate problem representation is developed. As the restrictive common due date problem is known to be intractable we decided, secondly, to apply meta-heuristics, namely evolutionary strategies, simulated annealing and threshold accepting. We demonstrate that our application of these meta-heuristics is efficient in obtaining near-optimal solutions by solving 140 benchmark problems with up to 1000 jobs. Furthermore, we compare their solution quality and find that a new variant of threshold accepting is superior to the other approaches.

Benchmarks for scheduling on a single machine against restrictive and unrestrictive common due dates

Abstract We consider the NP-hard problem of scheduling jobs on a single machine against common due dates with respect to earliness and tardiness penalties. The paper covers two aspects: Firstly, we develop a problem generator and solve 280 instances with two new heuristics to obtain upper bounds on the optimal objective function value. Secondly, we demonstrate computationally that our heuristics are efficient in obtaining near-optimal solutions for small problem instances. The generated problem instances in combination with the upper bounds can be used as benchmarks for future approaches in the field of common due-date scheduling. Scope and purpose In connection with just-in-time production and delivery, earliness as well as tardiness penalties are of interest. Thus scheduling against common due dates has received growing attention during the last decade. Many algorithms have been developed to solve the different variants of this problem. But whenever a new algorithm for scheduling against common due dates is proposed, its quality is assessed only on a few self-generated examples. Hence it is difficult to evaluate the various approaches, particularly in comparison with each other. Therefore the goal of this paper is to present numerous benchmark problems together with some upper bounds on the optimal objective function value.

Common due date scheduling with autonomous and induced learning

Abstract Up to now the few existing models, that consider learning effects in scheduling, concentrate on learning-by-doing (autonomous learning). But recent contributions to the literature on learning in manufacturing organizations emphasize the important impact of proactive investments in technological knowledge on the learning rate (induced learning). In the present paper, we focus on a scheduling problem where the processing times decrease according to a learning rate, which can be influenced by an initial cost-inducing investment. Thus we have integrated into our model both aspects of learning––autonomous and induced––thereby highlighting the managements responsibility to invest in technological knowledge enhancement. We have been able to derive some structural properties of the problem and present a polynomially bound solution procedure which optimally solves the problem by using these properties. The optimal solution to the scheduling problem contains––of course–– information on the optimal level of proactive investments in learning.

Common due date assignment for scheduling on a single machine with jointly reducible processing times

Abstract This paper focuses on analyzing the problem of assigning a common due date to a set of jobs and scheduling them on a single machine. The processing times of the jobs are assumed to be controllable but contrary to former approaches we consider a situation in which it is only possible to reduce all processing times by the same proportional amount. This situation, which is quite interesting from a practical point of view, has to the best of our knowledge never been under study before. Besides the assignment of the common due date we concentrate on two goals, namely minimizing the sum of earliness and tardiness penalties and minimizing the number of late jobs.

Single-machine scheduling against due dates with past-sequence-dependent setup times

Recently Koulamas and Kyparisis [Koulamas, C., Kyparisis, G.J., in press. Single-machine scheduling with past-sequence-dependent setup times. European Journal of Operational Research] introduced past-sequence-dependent setup times to scheduling problems. This means that the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. Koulamas and Kyparisis [Koulamas, C., Kyparisis, G.J., in press. Single-machine scheduling with past-sequence-dependent setup times. European Journal of Operational Research] were able to show for a number of single-machine scheduling problems with completion time goals that they remain polynomially solvable. In this paper we extend the analysis to problems with due dates. We demonstrated that some problems remain polynomially solvable. However, for some other problems well-known polynomially solution approaches do not guarantee optimality any longer. Consequently we concentrated on finding polynomially solvable special cases.

The effect of capital lockup and customer trade credits on the optimal lot size—a confirmation of the EPQ

Abstract The classical economic production quantity (EPQ) formula, which is obtained by balancing set-up and carrying costs, is reconsidered in this paper. Since the cost of capital tied up in stocked items is the most important part of the carrying costs, a refined approach considering different components of the capital lockup, i.e. direct labour, material, and set-up costs, is presented. Furthermore, in addition to the intensively discussed supplier trade credit, the hitherto neglected customer trade credit is introduced into the analysis. A comparison of the resulting lot-size formula and the classical one indicates that the ongoing discussion about financial refinements of the EPQ might end up at its starting point given by Harris (Oper. Res. 38 (1990) 947–50), as the classical formula can be transformed into the new one by choosing the crucial carrying cost parameter adequately. Consequently, several alternative approximations for the carrying cost parameter in the EPQ are evaluated. Scope and purpose Typically, lot-size planning takes into consideration only data from the production sector. In doing this, the interdependencies between the production and the financial sector of a firm are neglected. Consequently, a recently emerging discussion intends to overcome the separation of these two firm sectors. We extend the approaches presented up to the present date by modelling capital lockup in a more detailed way considering both the supplier and the customer trade credit as well as the time structure of the capital lockup.

Lot streaming with variable sublots: an integer programming formulation

This paper deals with the question of how to split a given lot into sublots so as to allow their overlapping production in a flow shop environment. The size of each sublot may vary over the stages. We consider an arbitrary number of stages and assume sublot availability, that is, only completed sublots are allowed to be transferred to the next stage. A mixed integer programming formulation is presented, which enables us to find optimal solutions for medium sized instances. The model is extended further to deal with different settings and objectives. Computational results confirm that the exploitation of variable sublots is advantageous and may lead to a significant increase in productivity.

On scheduling around large restrictive common due windows

This paper deals with the problem of scheduling a number of jobs on a single machine around a large, restrictive common due window. We consider individual earliness and tardiness penalties for the jobs. The objective is to find an optimal schedule which jointly minimizes the sum of the earliness and tardiness penalties. This problem is intractable and hence no efficient procedure for solving large instances is expected to be found. For this reason we first introduced a mapping of the problem which takes advantage of the structural properties inherent to optimal solutions. Secondly we solved the problem under study by using this mapping and applying three meta-heuristics, namely evolutionary strategy, simulated annealing and threshold accepting. To validate the quality of these approaches, altogether 250 benchmark problems with different window sizes and positions of up to 200 jobs are examined. Furthermore small instances are solved to optimality by a mixed integer programming formulation.