Showing papers on "Job shop scheduling published in 1993"

Routing and scheduling in a flexible job shop by tabu search

Abstract: A hierarchical algorithm for the flexible job shop scheduling problem is described, based on the tabu search metaheuristic. Hierarchical strategies have been proposed in the literature for complex scheduling problems, and the tabu search metaheuristic, being able to cope with different memory levels, provides a natural background for the development of a hierarchical algorithm. For the case considered, a two level approach has been devised, based on the decomposition in a routing and a job shop scheduling subproblem, which is obtained by assigning each operation of each job to one among the equivalent machines. Both problems are tackled by tabu search. Coordination issues between the two hierarchical levels are considered. Unlike other hierarchical schemes, which are based on a one-way information flow, the one proposed here is based on a two-way information flow. This characteristic, together with the flexibility of local search strategies like tabu search, allows to adapt the same basic algorithm to different objective functions. Preliminary computational experience is reported.

An approximation algorithm for the generalized assignment problem

Abstract: The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep ij and incurs a cost ofc ij ; each machinei is available forT i time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a polynomial-time algorithm that, given a valueC, either proves that no feasible schedule of costC exists, or else finds a schedule of cost at mostC where each machinei is used for at most 2T i time units. We also extend this result to a variant of the problem where, instead of a fixed processing timep ij , there is a range of possible processing times for each machine—job pair, and the cost linearly increases as the processing time decreases. We show that these results imply a polynomial-time 2-approximation algorithm to minimize a weighted sum of the cost and the makespan, i.e., the maximum job completion time. We also consider the objective of minimizing the mean job completion time. We show that there is a polynomial-time algorithm that, given valuesM andT, either proves that no schedule of mean job completion timeM and makespanT exists, or else finds a schedule of mean job completion time at mostM and makespan at most 2T.

Applying tabu search to the job-shop scheduling problem

Abstract: In this paper, we apply the tabu-search technique to the job-shop scheduling problem, a notoriously difficult problem in combinatorial optimization. We show that our implementation of this method dominates both a previous approach with tabu search and the other heuristics based on iterative improvements.

Heuristic scheduling systems : with applications to production systems and project management

Abstract: Partial table of contents: PRELIMINARIES Approaches to Scheduling Book Summary ONE-MACHINE PROBLEMS Single Machine: Foundations Mathematical Solution Methods: New Directions Single Machine: Timing MULTI-MACHINE PROBLEMS Embedded Problems Parallel Machines/Batch Machines Shop Routing FLOW SHOPS AND JOB SHOPS Scheduling Flow Shops: Makespan Scheduling Job Shops: Basic Methods PROJECT SCHEDULING AND MANAGEMENT Network Project Scheduling Resource-Constrained Project Scheduling OTHER ISSUES Model Extensions Planning, Scheduling, and Control Appendices Index

Minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem

Abstract: This paper considers minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem. After problem formulation, we present a proof to show that the general version of this problem is strongly NP-complete. We then discuss a few polynomially solvable cases of the problem and present the solution algorithms. Next, a branch and bound solution scheme is suggested. Finally, three heuristics to find approximate solutions to the general problem are proposed and their error bounds are analyzed.

Harvest scheduling with spatial constraints: a simulated annealing approach

Abstract: Simulated annealing is a stochastic approach to solving large combinatorial problems. This approach was used to model a harvest scheduling problem having block size constraints (no limit, 100–200, and 200–400 ha), a 20-year adjacency delay, and objectives to meet harvest volume targets on the minimum area possible. Spatially explicit harvest schedules complying with the constraints were successfully generated on test data sets of 6148 and 27 548 forest stands.

A practical approach to job-shop scheduling problems

Abstract: The use of Lagrangian relaxation to schedule job shops, which include multiple machine types, generic precedence constraints, and simple routing considerations, is explored. Using an augmented Lagrangian formulation, the scheduling problem is decomposed into operation-level subproblems for the selection of operation beginning times and machine types, with given multipliers and penalty coefficients. The multipliers and penalty coefficients are then updated at the higher level. The solution forms the basis of a list-scheduling algorithm that generates a feasible schedule. A procedure is also developed to evaluate the quality of this feasible schedule by generating a lower bound on the optimal cost. Numerical examples are taken from a representative industrial job shop. High-quality schedules are efficiently generated every other day over a three-week period, with costs generally within 4% of their respective lower bounds. The methodology compares favorably with knowledge-based scheduling. >

Scheduling of manufacturing systems using the Lagrangian relaxation technique

Abstract: The practical solutions for three manufacturing scheduling problems are examined. As each problem is formulated, constraints are added or modified to reflect increasing real world complexity. The first problem considers scheduling single-operation jobs on identical machines. The second problem is concerned with scheduling multiple-operation jobs with simple fork/join precedence constraints on identical machines. The third problem is the job shop problem in which multiple-operation jobs with general precedence constraints are scheduled on multiple machine types Langrangian relaxation is used to decompose each of the scheduling problems into job- or operation-level subproblems. The subproblems are easier to solve than the original problem and have intuitive appeal. This technique results in algorithms which generate near-optimal schedules efficiently, while giving a lower bound on the optimal cost. In resolving the scheduling problem from one time instant to the next, the Lagrange multipliers from the last schedule can be used to initialize the multipliers, further reducing the computation time. >

Structure of a simple scheduling polyhedron

Abstract: In a one-machine nonpreemptive scheduling problem, the feasible schedules may be defined by the vector of the corresponding job completion times. For given positive processing times, the associated simple scheduling polyhedronP is the convex hull of these feasible completion time vectors. The main result of this paper is a complete description of the minimal linear system definingP. We also give a complete, combinatorial description of the face lattice ofP, and a simple, O(n logn) separation algorithm. This algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems.

Engineering and analysis of fixed priority schedulers

Abstract: Scheduling theory holds great promise as a means to a priori validate timing correctness of real-time applications. However, there currently exists a wide gap between scheduling theory and its implementation in operating system kernels running on specific hardware platforms. The implementation of any particular scheduling algorithm introduces overhead and blocking components which must be accounted for in the timing correctness validation process. This paper presents a methodology for incorporating the costs of scheduler implementation within the context of fixed priority scheduling algorithms. Both event-driven and timer-driven scheduling implementations are analyzed. We show that for the timer-driven scheduling implementations the selection of the timer interrupt rate can dramatically affect the schedulability of a task set, and we present a method for determining the optimal timer rate. We analyzed both randomly generated and two well-defined task sets and found that their schedulability can be significantly degraded by the implementation costs. Task sets that have ideal breakdown utilization over 90% may not even be schedulable when the implementation costs are considered. This work provides a first step toward bridging the gap between real-time scheduling theory and implementation realities. This gap must be bridged for any meaningful validation of timing correctness properties of real-time applications. >

Operational rationality through compilation of anytime algorithms

Abstract: An important and largely ignored aspect of real-time decision making is the capability of agents to factor the cost of deliberation into the decision making process. I have developed an efficient model that creates this capability. The model uses as basic components {\em anytime algorithms} whose quality of results improves gradually as computation time increases. The main contribution of this work is a {\em compilation} process that extends the property of gradual improvement from the level of single algorithms to the level of complex systems. In standard algorithms, the fixed quality of the output allows for composition to be implemented by a simple call-return mechanism. However, when algorithms have resource allocation as a degree of freedom, there arises the question of how to construct, for example, the optimal composition of two anytime algorithms, one of which feeds its output to the other. This scheduling problem is solved by an off-line compilation process and a run-time monitoring component that together generate a utility maximizing behavior. The crucial meta-level knowledge is kept in the {\em anytime library} in the form of {\em conditional performance profiles}. These profiles characterize the performance of each elementary anytime algorithm as a function of run-time and input quality. The compilation process therefore extends the principles of procedural abstraction and modularity to anytime computation. Its efficiency is significantly improved by using {\em local compilation} that works on a single program structure at a time. Local compilation is proved to yield global optimality for a large set of program structures. Compilation produces {\em contract} algorithms which require the determination of the total run-time when activated. Some real-time domains require {\em interruptible} algorithms whose total run-time is unknown in advance. An important result of this work is a general method by which an interruptible algorithm can be constructed once a contract algorithm is compiled. Finally, the notion of gradual improvement of quality is extended to sensing and plan execution and the application of the model is demonstrated through a simulated robot navigation system. The result is a modular approach for developing real-time agents that act by performing anytime actions and make decisions using anytime computation.

Project Scheduling Problems: A Survey

Abstract: A survey of project scheduling problems since 1973 limited to work done specifically in the project scheduling area (although several techniques developed for assembly line balancing and job‐shop scheduling can be applicable to project scheduling): the survey includes the work done on fundamental problems such as the resource‐constrained project scheduling problem (RCPSP); time/cost trade‐off problem (TCTP); and payment scheduling problem (PSP). Also discusses some recent research that integrates RCPSP with either TCTP or PSP, and PSP with TCTP. In spite of their practical relevance, very little work has been done on these combined problems to date. The future of the project scheduling literature appears to be developing in the direction of combining the fundamental problems and developing efficient exact and heuristic methods for the resulting problems.

Developing conflict-free routes for automated guided vehicles

Abstract: Automated guided vehicles AGVs are a highly sophisticated and increasingly popular type of material handling device in flexible manufacturing systems. This paper details solution methodologies for the static routing problem in which demand assignment of the AGVs are known; the focus is to obtain an implementable solution within a reasonable amount of computer time. The objective is to minimize the makespan, while routing AGVs on a bidirectional network in a conflict-free manner. This problem is solved via column generation. The master problem in this column generation procedure has the makespan and vehicle interference constraints. Columns in the master problem are routes iteratively generated for each AGV. The subproblem is a constrained shortest path problem with time-dependent costs on the edges. An improvement procedure is developed to better the solution obtained at the end of the master-subproblem interactions. Several methods of iterating between the master and subproblem are experimented with in-depth computational experiments. Our empirical results indicate that the procedure as a whole usually generates solutions that are within a few percent of a proposed bound, within reasonable computer time.

A modified shifting bottleneck procedure for job-shop scheduling

Abstract: We propose a modified version of the Adams et al. shifting bottleneck (SB) procedure for job-shop scheduling. By modifying Carlier's algorithm extensively used in the SB procedure, we eliminate some drawbacks. Computational results are reported with good performances, particularly on the classical 10-10 and 5-20 problems.

An on-line scheduling heuristic with better worst case ratio than Graham's list scheduling

Abstract: The problem of on-line scheduling a set of independent jobs on m machines is considered. The goal is to minimize the makespan of the schedule. Graham’s List Scheduling heuristic [R. L. Graham, SIAM J. Appl. Math., 17(1969), pp. 416–429] guarantees a worst case performance of $2 - \frac{1} {m}$ for this problem. This worst case bound cannot be improved for $m = 2$ and $m = 3$. For $m \geqslant 4$, approximation algorithms with worst case performance at most $2 - \frac{1}{m} - \varepsilon _m $ are presented, where $\varepsilon _m $ is some positive real depending only on m.

Heuristics for flowshop scheduling problems minimizing mean tardiness

Abstract: Several heuristics are presented for the flowshop scheduling problem with the objective of minimizing mean tardiness. We consider the cases in which job sequences on all machines are the same (permutation flowshop) and in which they may be different. For the former case, the various methods that have been devised for minimizing the makespan are modified for our objective, while the list scheduling algorithm is used for the latter case. These heuristics are tested and compared with each other on randomly-generated test problems.

Single-machine scheduling with early and tardy completion costs

Abstract: We address a single-machine scheduling problem in which penalties are assigned for early and tardy completion of jobs. These penalties are common in industrial settings where early job completion can cause the cash commitment to resources in a time frame earlier than needed, giving rise to early completion penalties. Tardiness penalties arise from a variety of sources, such as loss of customer goodwill, opportunity costs of lost sales, and direct cash penalties. Accounting for earliness cost makes the performance measure nonregular, and this nonregularity has apparently discouraged researchers from seeking solutions to this problem. We found that it is not much more difficult to design an enumerative search for this problem than it would be if the performance measure were regular. We present and demonstrate an efficient timetabling procedure which can be embedded in an enumerative algorithm allowing the search to be conducted over the domain of job permutations.© 1993 John Wiley & Sons, Inc.

Heuristic algorithms for the multiple depot vehicle scheduling problem

Abstract: We consider the NP-hard Multiple Depot Vehicle Scheduling Problem, in which a given set of time-tabled trips have to be assigned to vehicles stationed at different depots, so as to minimize the number of vehicles used and the overall operational cost. The problem arises in the management of transportation companies. In this paper some structural properties of the problem are studied and used to design a new polynomial-time heuristic algorithm which always guarantees the use of the minimum number of vehicles. Several effective refining procedures are also proposed. Extensive computational results on test problems involving up to 1,000 trips and 10 depots are reported, showing that the new approach always produces very tight approximate solutions in small computing times and outperforms other heuristics from the literature.

Managing genetic search in job shop scheduling

Abstract: The Vanderbilt Schedule Optimizer Prototype (VSOP), which uses genetic algorithms as search methods for job shop scheduling problems, is discussed A job shop is a facility that produces goods according to prespecified process plans, under several domain-dependent and common sense constraints The scheduling of orders in a job shop is a multifaceted problem VSOP uses domain-specific chromosome representations, recombination operators, and local enumerative search to increase efficiency Experimental results from a fully implemented VSOP package are presented >

Optimal generation scheduling with ramping costs

Abstract: In this paper, a decomposition method is proposed which relates the unit ramping process to the cost of fatigue effect in the generation scheduling of thermal systems. The objective of this optimization problem is to minimize the system operation cost, which includes the fuel cost for generating the required electrical energy and starting up decommitted units, as well as the rotor depreciation during ramping processes, such as starting up, shutting down, loading, and unloading. According to the unit fatigue index curves provided by generator manufacturers, fixed unit ramping-rate limits, which have been used by previous studies, do not reflect the physical changes of generator rotors during the ramping processes due to the fatigue effect. By introducing ramping costs, the unit on/offstates can be determined more economically by the proposed method. The Lagrangian relaxation method is proposed for unit commitment and economic dispatch, in which the original problem is decomposed into several subproblems corresponding to the optimization process of individual units. The network model is employed to represent the dynamic process of searching for the optimal commitment and generation schedules of a unit over the entire study time span. The experimental results for a practical system demonstrate the effectiveness of the proposed approach in optimizing the power system generation schedule. >

Scheduling medical residents to rotations: solving the large-scale multiperiod staff assignment problem

Abstract: The resident scheduling problem is a specific case of the multiperiod staff assignment problem where individuals are assigned to a variety of tasks over multiple time periods. As in many staffing and training situations, numerous limitations and requirements may be placed on those assignments. This paper presents a procedure for addressing two major problems inherent in the determination of a solution to this type of problem: infeasibilities that naturally occur in the scheduling environment but are obscured by complexity; and the intractable nature of large-scale models with this structure. The procedure developed describes a systematic approach that allows decision makers to resolve system-inherent infeasibilities, and a heuristic based on rounding to develop good feasible solutions to the model. The procedure is illustrated via a case example of resident assignments for teaching and training modules in a university affiliated teaching hospital.

Schedulers for larger classes of pinwheel instances

Abstract: The pinwheel is a hard-real-time scheduling problem for scheduling satellite ground stations to service a number of satellites without data loss. Given a multiset of positive integers (instance)A={a1,..., an}, the problem is to find an infinite sequence (schedule) of symbols from {1,2,...,n} such that there is at least one symboli within any interval of ai symbols (slots). Not all instancesA can be scheduled; for example, no “successful” schedule exists for instances whose density,ρ(A)=∑ (l/ai), is larger than 1. It has been shown that all instances whose densities are less than a 0.5 density threshold can always be scheduled. If a schedule exists, another concern is the design of a fast on-line scheduler (FOLS) which can generate each symbol of the schedule in constant time. Based on the idea of “integer reduction,” two new FOLSs which can schedule different classes of pinwheel instances, are proposed in this paper. One uses “single-integer reduction” and the other uses “double-integer” reduction. They both improve the previous 0.5 result and have density thresholds of 13/20 and2/3, respectively. In particular, if the elements inA are large, the density thresholds will asymptotically approach In 2 and 1/R2, respectively.

A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times

Abstract: In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) with setup times is considered. DLSP is the problem of determining the sequence and size of production batches for multiple items on a single machine. The objective is to find a minimal cost production schedule such that dynamic demand is fulfilled without backlogging. DLSP is formulated as a Set Partitioning Problem (SPP). We present a dual ascent and column generation heuristic to solve SPP. The quality of the solutions can be measured, since the heuristic generates lower and upper bounds. Computational results on a personal computer show that the heuristic is rather effective, both in terms of quality of the solutions as well as in terms of required memory and computation time.