Family Setup Research Articles

Single machine group scheduling with family setups to minimize total tardiness

This paper considers the single machine scheduling problem with independent family (group) setup times where jobs in each family are processed together. A sequence-independent setup is required to process a job from a different family. The objective is to minimize total tardiness. A mixed-integer linear programming model capable of solving small-sized problems is described. In view of the NP-hard nature of the problem, two-phase heuristics including simulated annealing algorithms are proposed to find optimal or near-optimal schedules. Empirical results show that the proposed heuristic algorithms are quite effective in minimizing total tardiness for a single machine group scheduling problem with family setup times.

An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

Metaheuristics for scheduling a non-permutation flowline manufacturing cell with sequence dependent family setup times

The broad applications of cellular manufacturing make flowline manufacturing cell scheduling problems with sequence dependent family setup times a core topic in the field of scheduling. Due to computational complexity, almost all published studies focus on using permutation schedules to deal with this problem. To explore the potential effectiveness of treating this argument using non-permutation schedules, three prominent types of metaheuristics—a simulated annealing, a genetic algorithm and a tabu search—are proposed and empirically evaluated. The experimental results demonstrate that in general, the improvement made by non-permutation schedules over permutation schedules for the due-date-based performance criteria were significantly better than that for the completion-time-based criteria. The results of this study will provide practitioners a guideline as to when to adopt a non-permutation schedule, which may exhibit better performance with additional computational efforts.

Luxembourg

Luxembourg's fiduciary contract—or ‘fiducie’—under the Grand-Ducal Regulation of 19 July 1983 on Fiduciary Contracts with Credit Institutions was one of the first attempts to the regulation of a fiduciary relationship in the context of a civil law system and certainly a unique move within the framework of the French Code Civil. Indeed, the definition of a ‘trust’ under Article 2 of the Hague Convention on the Law Applicable to Trusts and on their Recognition of 1 July 1985 was to some extent foreseen in Luxembourg's domestic institution which predated the Hague Convention by 2 years and provided an outstanding example of a trust-like arrangement outside of the equitable jurisprudence. Under a relatively laborious Bill that took nearly 4 years to be adopted by the ordinarily swifter Luxembourg Parliament, the Grand-Duchy ratified the Hague Trusts Convention and updated the corresponding domestic institution. As a result of the Law of 27 July 2003 relating to Trusts and Fiduciary Contracts, which came into force on 1 January 2004, the previous Grand-Ducal Regulation of 1983 was repealed and a new, strengthened notion of fiduciary contract was made available to Luxembourg practitioners. In fact, to some of them only: the Luxembourg fiduciary contract, which in this respect can be seen as a model for France's recently enacted ‘fiducie’, is restricted to banks and financial intermediaries in the context of corporate transactions (as opposed to family set-ups).

Meta-heuristics for scheduling a flowline manufacturing cell with sequence dependent family setup times

This paper presents various Tabu Search (TS) based meta-heuristics for scheduling the part families and jobs within each family in a flowline manufacturing cell (also called a flowshop) with sequence dependent family setup times to minimize makespan. Concepts of Elitism and the acceptance of worse moves from simulated annealing (SA) are examined in the proposed meta-heuristics to improve intensification and diversification. The effectiveness and efficiency of the proposed TS based meta-heuristics are compared against the best meta-heuristic and heuristic algorithms reported so far for this problem on several test problems. Computational results show that the best proposed TS based meta-heuristic is quite effective in minimizing makespan in a reasonable amount of CPU time.

The single machine batching problem with identical family setup times to minimize maximum lateness is strongly NP-hard

In this paper, we consider the single machine batching problem with family setup times to minimize maximum lateness. Recently, Cheng et al. [T.C.E. Cheng, C.T. Ng, J.J. Yuan, The single machine batching problem with family setup times to minimize maximum lateness is strongly NP-hard, Journal of Scheduling 6 (2003) 483–490] proved that this problem is strongly NP-hard. This answers a long-standing open problem posed by J. Bruno and P. Downey [Complexity of task sequencing with deadlines, setup times and changeover costs, SIAM Journal on Computing 7 (1978) 393–404]. By a modification of the proof in Cheng et al. (2003), we show that this problem is still strongly NP-hard when the family setup times are identical.

Satisfying due-dates in the presence of sequence dependent family setups with a special comedown structure

This paper addresses a static, n-job, single-machine scheduling problem with sequence dependent family setups. The setup matrix follows a special structure where a constant setup is required only if a job from a smaller indexed family is an immediate successor of one from a larger indexed family. The objective is to minimize the maximum lateness (Lmax). A two-step neighborhood search procedure and an implicit enumeration scheme are proposed. Both procedures exploit the problem structure. The enumeration scheme produces optimum solutions to small and medium sized problems in reasonable computational times, yet it fails to perform efficiently in larger instances. Computational results show that the heuristic procedure is highly effective, and is efficient even for extremely large problems.

Single machine batch scheduling problem with family setup times and release dates to minimize makespan

In this paper we consider the single machine batch scheduling problem with family setup times and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an $$O(n (\frac{n}{m}+1)^m)$$ time dynamic programming algorithm and an $$O(mk^{k}P^{2k-1})$$ time dynamic programming algorithm for the problem, where n is the number of jobs, m is the number of families, k is the number of distinct release dates and P is the sum of the setup times of all the families and the processing times of all the jobs. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme (PTAS) for the problem.

Customer order scheduling on a single machine with family setup times: Complexity and algorithms

We consider a situation where C customers each order various quantities (possibly zero in some cases) of products from P different families, which can be produced on a continuously available machine in any sequence (requiring a setup whenever production switches from one family to another). We assume that the time needed for a setup depends only on the family to be produced immediately after it, and we follow the item availability model (which implies that all units are ready for dispatch as soon as they are produced). However, an order is shipped only when all units required by a customer are ready. The time from the start (time zero) to the completion of a customer order is called the order lead time. The problem, which restates the original description of the customer order scheduling problem, entails finding a production schedule that will minimize the total order lead time. While this problem has received some attention in the literature, its complexity status has remained vexingly open. In this note, we show for the first time that the problem is strongly NP-hard. We proceed to give dynamic programming based exact solution algorithms for the general problem and a special case (where C is fixed). These algorithms allow us to solve small instances of the problem and understand the problem complexity more fully. In particular, the solution of the special case shows that the problem is solvable in polynomial time when C is fixed.

The Multiple-Family ELSP with Safety Stocks

The multiple-family economic lot scheduling problem with safety stocks (MFELSP-SS) with normally distributed, time-stationary demand is considered in a manufacturing setting where the relevant costs include family setup costs, item setup costs, and inventory holding costs for both cycle and safety stocks. A family is a subset of the items that share a common family setup with its associated setup cost and setup time. Each item within the family may have its own setup time and setup cost. The families form a partition of the set of items manufactured on a single facility. The safety stock level for any item is a function of the time interval between production runs for the item, the service level specified, and the variance of its demand. We consider safety stocks explicitly in the formulation, as their holding costs vary nontrivially with the model’s decision variables. The MFELSP-SS differs from multilevel inventory models with family setups in that the former assumes noninstantaneous inventory replenishment and considers the cost of holding safety stocks; the latter assumes instantaneous replenishment and does not directly assess the impact of safety stock levels on the total cost. An efficient solution procedure is developed for this model. Properties of the nonconvex feasible space are identified and used in the solution approach. The solution to the mathematical model comprises the basic period length, the family multipliers, and the item multipliers that give the lowest total cost of setups and carrying inventory. The family multipliers and item multipliers are restricted to integer powers of two.

Minimizing sum of completion times on a single machine with sequence-dependent family setup times

This paper presents a branch-and-bound (B&B) algorithm for minimizing the sum of completion times in a single-machine scheduling setting with sequence-dependent family setup times. The main feature of the B&B algorithm is a new lower bounding scheme that is based on a network formulation of the problem. With extensive computational tests, we demonstrate that the B&B algorithm can solve problems with up to 60 jobs and 12 families, where setup and processing times are uniformly distributed in various combinations of the [1,50] and [1,100] ranges.

Minimizing flow time in a flow-line manufacturing cell with family setup times

This paper considers the problem of scheduling part families and jobs within each part family in a flowline manufacturing cell with independent family setup times where parts (jobs) in each family are processed together. The objective is to minimize total flow time. A branch-and-bound algorithm capable of solving moderate sized problems is developed. Several heuristic algorithms are proposed and empirically evaluated as to their effectiveness and efficiency in finding optimal permutation schedules. These results show that several heuristic algorithms generate solutions that are better than those generated by an existing genetic algorithm.

A comparison of branch-and-bound algorithms for a family scheduling problem with identical parallel machines

This paper investigates branch-and-bound algorithms for the problem of scheduling jobs with family setups on identical parallel machines to minimize the weighted sum of completion times. In particular, we propose a new branching scheme that appears to substantially outperform current procedures in terms of computation time and search tree size.

Scheduling on a single machine with family setups to minimize total tardiness

This paper considers the problem of scheduling on a single machine to minimize total tardiness when family setup times exist. The paper proposes optimal branch-and-bound procedures for the case where the group technology assumption is used and for the case when the group technology assumption is removed. A heuristic procedure is also proposed to solve larger problems with the group technology assumption removed. The procedures were tested on problems of various sizes and parameters. An important finding of the tests is total tardiness can be significantly reduced by removing the group technology assumption when scheduling.

Learners Without Adult Care at Home Who Succeed in School

Observations in the townships of South Africa lead to the realization that child-headed families or households are becoming commonplace. These families can be large and sometimes begging becomes their way of life. In some instances, the community, especially the neighbours, are forced to look after these children. In cases of the school going children, the teachers are the ones who are left with the responsibility of ensuring their wellbeing. Due to this new family set-up, the rights of the children are being violated as they are in most cases forced, for example, to do cheap labour in order to survive. This happens despite the fact that parental roles in the upbringing of children are highly emphasised in the constitution and in the education literature (SA Constitution, 1996; Kok, 1988:7). Parents have a critical role to play in the well being of their children. Not only are they expected to provide materially, but they are also entrusted with provision of safety, emotional stability, and guidance according to norms and values for their children. Parents are also expected to give support to the children's learning and school education. This paper highlights the very decisive role of teachers (guidance teachers in particular), positive and supportive peers, caring neighbours and extended family, school feeding schemes and inherent learner potential. Without these such achieving respondents would not have had any hope for their future and could have become a loss to society and personal disasters.

Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups

This paper considers the problem of scheduling part families and jobs within each part family in a flowshop manufacturing cell with sequence dependent family setups times where it is desired to minimize the makespan while processing parts (jobs) in each family together. Two evolutionary algorithms-a Genetic Algorithm and a Memetic Algorithm with local search-are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules. The proposed algorithms use a compact representation for the solution and a hierarchically structured population where the number of possible neighborhoods is limited by dividing the population into clusters. In comparison to a Multi-Start procedure, solutions obtained by the proposed evolutionary algorithms were very close to the lower bounds for all problem instances. Moreover, the comparison against the previous best algorithm, a heuristic named CMD, indicated a considerable performance improvement.

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.

Le revenu minimum d’insertion avant la décentralisation

The RMI (minimum income) before decentralisation. Since the 1st January 2004, the RMI, in effect for 15 years, has become the responsibility of each French département. At the end of 2003, statistics from the French Child Benefit Office (CNAF) point to large regional differences in the population entitled to the support, and those who are longtime beneficiaries of the support (over five years). In broad terms, the départements along the Mediterranean and the industrialised north, such as the Nord -Pas-de-Calais, with a high percentage of the population entitled to the RMI, differ from the areas to the West, the Eastern border and the Alps regions, where there is a low percentage of RMI beneficiaries. High unemployment in the former départements is combined with, on average, a large number of long-term beneficiaries of the provision. If unemployment has been a long-term factor in RMI dynamics, regional differences are not limited solely to differences in unemployment. This is what analysis of the percentage of beneficiaries, who combine the allocation with a paid job, gives as an example. Apart from the connection between the probability of no longer needing the benefit and the context of local unemployment, the study of the itineraries of women, who benefit from the RMI, confirms that there is a significant link with the family set-up : for women, alone or in couples, the presence of children means that there is less chance of their doing without the social minima.

Scheduling with product family set-up times: an application in TFT LCD manufacturing

The development of a scheduling methodology for module processing in thin film transistor liquid crystal display manufacturing is presented. The problem is a parallel machine-scheduling problem with family set-up times and due dates. Two objectives are considered: total tardiness and the number of family set-ups. Two heuristics are developed based on the MULTIFIT method and tabu search. The experimental results show that the proposed algorithms give schedules that are very efficient in terms of both total tardiness and the number of family set-ups.

Minimizing L max for the single machine scheduling problem with family set-ups

A procedure for the single machine-scheduling problem of minimizing the maximum lateness for jobs with sequence independent set-ups is presented. The procedure provides optimal/near-optimal solutions over a wide range of problems. It performs well compared with other heuristics, and it is effective in finding solutions for large problems.