A cutting plane approach for integrated planning and scheduling

In this paper we propose a branch-and-cut algorithm for solving an integrated production planning and scheduling problem in a parallel machine environment. The planning problem consists of assigning each job to a week over the planning horizon, whereas in the scheduling problem those jobs assigned to a given week have to be scheduled in a parallel machine environment such that all jobs are finished within the week. We solve this problem in two ways: (1) as a monolithic mathematical program and (2) using a hierarchical decomposition approach in which only the planning decisions are modeled explicitly, and the existence of a feasible schedule for each week is verified by using cutting planes. The two approaches are compared with extensive computational testing.     

A GRASP/Path Relinking algorithm for two- and three-dimensional multiple bin-size bin packing problems

The three-dimensional multiple bin-size bin packing problem, MBSBPP, is the problem of packing a set of boxes into a set of bins when several types of bins of different sizes and costs are available and the objective is to minimize the total cost of bins used for packing the boxes. First we propose a GRASP algorithm, including a constructive procedure, a postprocessing phase and some improvement moves. The best solutions obtained are then combined into a Path Relinking procedure for which we have developed three versions: static, dynamic and evolutionary. An extensive computational study, using two- and three-dimensional instances, shows the relative efficiency of the alternatives considered for each phase of the algorithm and the good performance of our algorithm compared with previously reported results.     

A GRASP based solution approach to solve cardinality constrained portfolio optimization problems

In the current work, a solution methodology which combines a meta-heuristic algorithm with an exact solution approach is presented to solve cardinality constrained portfolio optimization (CCPO) problem. The proposed method is comprised of two levels, namely, stock selection and proportion determination. In stock selection level, a greedy randomized adaptive search procedure (GRASP) is developed. Once the stocks are selected the problem reduces to a quadratic programming problem. As GRASP ensures cardinality constraints by selecting predetermined number of stocks and quadratic programming model ensures the remaining problem constraints, no further constraint handling procedures are required. On the other hand, as the problem is decomposed into two sub-problems, total computational burden on the algorithm is considerably reduced. Furthermore, the performance of the proposed algorithm is evaluated by using benchmark data sets available in the OR Library. Computational results reveal that the proposed algorithm is competitive with the state of the art algorithms in the related literature.     

The economic lot scheduling problem: A pure genetic search approach

The economic lot scheduling problem (ELSP) is the challenge of accommodating several products to be produced on a single machine in a cyclical pattern. A solution involves determining the repetitive production schedule for N$N$ products with a goal of minimizing the total of setup and holding costs. We develop the genetic lot scheduling (GLS) procedure. This method combines an extended solution structure with a new item scheduling approach, allowing a greater number of potential schedules to be considered while being the first to explicitly state the assignment of products to periods as part of the solution structure. We maintain efficient solution feasibility determination, a problematic part of ELSP solution generation and a weakness of several other methods, by employing simple but effective sequencing rules that create “nested” schedules. We create a binary chromosomal representation of the new problem formulation and utilize a genetic algorithm to efficiently search for low cost ELSP solutions. The procedure is applied to a benchmark problem suite from the literature, including Bomberger's stamping problem [Bomberger, A dynamic programming approach to a lot scheduling problem. Management Science 1966; 12:778–84], a problem that has been under investigation since the mid 1960's. The genetic lot scheduling procedure produces impressive results, including the best solutions obtained to date on some problems.     

Parallel machine total tardiness scheduling with a new hybrid metaheuristic approach

This work proposes a hybrid metaheuristic (HMH) approach which integrates several features from tabu search (TS), simulated annealing (SA) and variable neighbourhood search (VNS) in a new configurable scheduling algorithm. In particular, either a deterministic or a random candidate list strategy can be used to generate the neighbourhood of a solution, both a tabu list mechanism and the SA probabilistic rule can be adopted to accept solutions, and the dimension of the explored neighbourhood can be dynamically modified. The considered class of scheduling problems is characterized by a set of independent jobs to be executed on a set of parallel machines with non-zero ready times and sequence dependent setups. In particular, the NP-hard generalized parallel machine total tardiness problem (GPMTP) recently defined by Bilge et al. [A tabu search algorithm for parallel machine total tardiness problem. Computers & Operations Research 2004;31:397–414], is faced. Several alternative configurations of the HMH have been tested on the same benchmark set used by Bilge et al. The results obtained highlight the appropriateness of the proposed approach.     

Heuristic algorithms for lotsize scheduling with application in the tobacco industry

We investigate a production planning problem which appears in many industries. We present an example from the tobacco industry. The basic question is how tasks of different types can be scheduled on machines in lots such that the number of changeovers is minimized. These changeovers occur if two tasks of different types are scheduled in sequence on a machine. We analyze the problem in detail and present heuristics for the single and multiple machine case. We evaluate these heuristics and give recommendations for their application to serial production systems.     

Parallel-identical-machine job-shop scheduling with different stage-dependent buffering requirements

The neglect of buffering requirements in a classical job shop scheduling system often results in inapplicability in many complex real-world applications. To overcome this inapplicability, a new and more generalised scheduling problem is proposed under different stage-dependent buffering requirements and parallel use of identical-function machine units at each processing stage in job shop environments. The problem is formulated as a mixed integer programming model that can be exactly solved by ILOG-CPEX for small-size instances. Moreover, a hybrid metaheuristic algorithm embedded with a state-of-the-art constructive algorithm is developed. The computational experiment shows that the proposed metaheuristic can efficiently solve large-size instances. The result analysis indicates that the proposed approach can provide better configuration of real-world scheduling systems. The proposed DBPMJSS methodology has a potential to analyse, model and solve many industrial systems with the requirements of buffering conditions, particularly for manufacturing, railway, healthcare and mining industries.     

Scheduling trains as a blocking parallel-machine job shop scheduling problem

In this paper, the train scheduling problem is modelled as a blocking parallel-machine job shop scheduling (BPMJSS) problem. In the model, trains, single-track sections and multiple-track sections, respectively, are synonymous with jobs, single machines and parallel machines, and an operation is regarded as the movement/traversal of a train across a section. Due to the lack of buffer space, the real-life case should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold the train until next section on the routing becomes available. Based on literature review and our analysis, it is very hard to find a feasible complete schedule directly for BPMJSS problems. Firstly, a parallel-machine job-shop-scheduling (PMJSS) problem is solved by an improved shifting bottleneck procedure (SBP) algorithm without considering blocking conditions. Inspired by the proposed SBP algorithm, feasibility satisfaction procedure (FSP) algorithm is developed to solve and analyse the BPMJSS problem, by an alternative graph model that is an extension of the classical disjunctive graph models. The proposed algorithms have been implemented and validated using real-world data from Queensland Rail. Sensitivity analysis has been applied by considering train length, upgrading track sections, increasing train speed and changing bottleneck sections. The outcomes show that the proposed methodology would be a very useful tool for the real-life train scheduling problems.     

A sequential GRASP for the therapist routing and scheduling problem

This paper presents a new model and solution methodology for the problem faced by companies that provide rehabilitative services to clinic and home-bound patients. Given a set of multi-skilled therapists and a group of geographically dispersed patients, the objective is to construct weekly tours for the therapists that minimize the travel, treatment, and administrative costs while ensuring that all patients are seen within their time windows and that a host of labor laws and contractual agreements are observed. The problem is complicated by three factors that prevent a daily decomposition: (i) overtime rates kick in only after 40 regular hours are worked during the week, (ii) new patients must be seen by a licensed therapist on their first visit, and (iii) for some patients only the frequency and not the actual days on which they are to be seen is specified. The problem is formulated as a mixed-integer linear program but after repeated attempts to solve small instances with commercial software failed, we developed an adaptive sequential greedy randomized adaptive search procedure. The phase I logic of the procedure builds one daily schedule at a time for each therapist until all patients are routed. In phase II, several neighborhoods are explored to arrive at a local optimum. Extensive testing with both real data provided by a U.S. rehab company and datasets derived from them demonstrated the value of the purposed procedure with respect to current practice. The results indicated that cost reductions averaging over 18.09 % are possible.     

A GRASP approach for the extended car sequencing problem

This paper presents a solution procedure for a new variant of the Car Sequencing Problem (CSP) based on the GRASP metaheuristic. In this variant, called xCSP (extended CSP), the aim is to satisfy the hard constraints of the CSP while scheduling the maximum possible number of cars with specific options at specific times of the day in order to satisfy other production requirements. Additional constraint ratios are likewise considered that force at least a minimum specific number of consecutive options. An extension of the CSP is formalized in this paper and computational results are presented using available on-line instances that verify the good performance of a GRASP procedure defined for the xCSP.     

A GRASP algorithm based new heuristic for the capacitated location routing problem

Abstract

In this paper, the capacitated location-routing problem (CLRP) is studied. CLRP is composed of two hard optimisation problems: the facility location problem and the vehicle routing problem. The objective of CLRP is to determine the best location of multiple depots with their vehicle routes such that the total cost of the solution is minimal. To solve this problem, we propose a greedy randomised adaptive search procedure. The proposed method is based on a new heuristic to construct a feasible CLRP solution, and then a local search-based simulated annealing is used as improvement phase. We have used a new technique to construct the clusters around the depots. To prove the effectiveness of our algorithm, several LRP instances are used. The results found are very encouraging.     

A high performance algorithm for static task scheduling in heterogeneous distributed computing systems

Effective task scheduling is essential for obtaining high performance in heterogeneous distributed computing systems (HeDCSs). However, finding an effective task schedule in HeDCSs requires the consideration of both the heterogeneity of processors and high interprocessor communication overhead, which results from non-trivial data movement between tasks scheduled on different processors. In this paper, we present a new high-performance scheduling algorithm, called the longest dynamic critical path (LDCP) algorithm, for HeDCSs with a bounded number of processors. The LDCP algorithm is a list-based scheduling algorithm that uses a new attribute to efficiently select tasks for scheduling in HeDCSs. The efficient selection of tasks enables the LDCP algorithm to generate high-quality task schedules in a heterogeneous computing environment. The performance of the LDCP algorithm is compared to two of the best existing scheduling algorithms for HeDCSs: the HEFT and DLS algorithms. The comparison study shows that the LDCP algorithm outperforms the HEFT and DLS algorithms in terms of schedule length and speedup. Moreover, the improvement in performance obtained by the LDCP algorithm over the HEFT and DLS algorithms increases as the inter-task communication cost increases. Therefore, the LDCP algorithm provides a practical solution for scheduling parallel applications with high communication costs in HeDCSs.     

Search heuristics for a parallel machine scheduling problem with ready times and due dates

We consider a problem of scheduling orders on identical parallel machines. An order can be released after a given ready time and must be completed before its due date. An order is split into multiple jobs (batches) and a job is processed on one of the parallel machines. The objective of the scheduling problem is to minimize the holding costs of orders including work-in-process as well as finished job inventories. We suggest two local search heuristics, simulated annealing and taboo search algorithms, for the problem. Performance of the suggested algorithms is tested through computational experiments on randomly generated test problems.     

On-line scheduling of parallel machines to minimize total completion times

In this paper, we consider the scheduling problem on identical parallel machines, in which jobs are arriving over time and preemption is not allowed. The goal is to minimize the total completion times. According to the idea of the Delayed-SPT Algorithm proposed by Hoogeven and Vestjens [Optimal on-line algorithms for single-machine scheduling. In: Proceedings 5th international conference on integer programming and combinatorial optimization (IPCO). Lecture notes in computer science, vol. 1084. Berlin: Springer; 1996. p. 404–14], we give an on-line algorithm for the scheduling problem on m$m$ identical parallel machines. We show that this algorithm is 2-competitive and the bound is tight.     

A search heuristic for just-in-time scheduling in parallel machines

In recent years the Just-in-Time (JIT) production philosophy as been adopted by many companies around the world. This has motivated the study of scheduling models that embrace the essential components of JIT systems. In this paper, we present a search heurustic for the weighted earliness penalty problem with deadlines in parallel identical machines. Our approach combines elements of the solution methods known as greedy randomized adaptive search procedure (GRASP) and tabu search. It also uses a branch-and-bound post-processor to optimize individually the sequence of the jobs assigned to each machine.     

A simulated annealing algorithm for multi-agent systems: a job-shop scheduling application

In this paper, a parallel implementation of the modular simulated annealing algorithm for classical job-shop scheduling is presented. The implementation is for a multi agent system running on the distributed resource machine, which is a novel, scalable, distributed virtual machine based on Java technology. The problems tackled are well known, difficult benchmarks, widely used to measure the efficiency of metaheuristics with respect to both the quality of the solutions and the central processing unit time. The empirical results obtained show that the method proposed is successful in comparison with a sequential version of modular simulated annealing algorithm and other methods described in the literature.     

A bicriteria approach to minimize maximal lateness and resource consumption for scheduling a single machine

We extend the classical single-machine maximal lateness scheduling problem to the case where the job processing times are controllable by allocating a continuous and nonrenewable resource to the processing operations. Our aim is to construct an efficient trade-off curve between maximal lateness and total resource consumption using a bicriteria approach. We present a polynomial time algorithm that constructs this trade-off curve assuming a specified general type of convex decreasing resource consumption function. We illustrate the algorithm with a numerical example.     

A novel approach to resource scheduling for parallel query processing on computational grids

Advances in network technologies and the emergence of Grid computing have both increased the need and provided the infrastructure for computation and data intensive applications to run over collections of heterogeneous and autonomous nodes. In the context of database query processing, existing parallelisation techniques cannot operate well in Grid environments because the way they select machines and allocate tasks compromises partitioned parallelism. The main contribution of this paper is the proposal of a low-complexity, practical resource selection and scheduling algorithm that enables queries to employ partitioned parallelism, in order to achieve better performance in a Grid setting. The evaluation results show that the scheduler proposed outperforms current techniques without sacrificing the efficiency of resource utilisation. Recommended by: Ioannis Vlahavas     

A Road Timetable to aid vehicle routing and scheduling

Both within and between urban conurbations, the time of a journey and the corresponding shortest path in a road network from an origin to a destination may depend on the time of the day, the day of the week and the season of the year. Significant journey time differences occur mainly due to recurring instances and variations in levels of traffic congestion throughout the year. This paper examines the issues involved in constructing a database of road times for a road network that uses time-dependent data on the travel times for individual roads in the network to provide the expected times and distances between locations for journeys starting at different times. The benefits of time-dependent vehicle routing and scheduling systems are demonstrated by using real-world data for the road network in the north west of England.     

On-line service scheduling

This paper is concerned with a scheduling problem that occurs in service systems where customers are classified as ‘ordinary’ and ‘special’. Ordinary customers can be served on any service facility, while special customers can be served only on the flexible service facilities. Customers arrive dynamically over time and their needs become known upon arrival. We assume any service, once started, will be carried out to its completion. In this paper, we study the worst-case performance of service policies used in practice. In particular, we evaluate three classes of service policies: policies with priority, policies without priority, and their combinations. We obtain tight worst-case performance bounds for all service policies considered.