Scheduling multiple orders per job in a single machine to minimize total completion time

This paper deals with a single-machine scheduling problem with multiple orders per job (MOJ) considerations. Both lot processing machines and item processing machines are also examined. There are two primary decisions that must be made in the proposed problem: (1) how to group the orders together, and (2) how to schedule the jobs once they are formed. In order to obtain the optimal solution to a scheduling problem, these two decisions should be made simultaneously. The performance measure is the total completion time of all orders. Two mixed binary integer programming models are developed to optimally solve this problem. Also, two efficient heuristics are proposed for solving large-sized problems. Computational results are provided to demonstrate the efficiency of the models and the effectiveness of the heuristics.     

Integrating Interval Estimates of Global Optima and Local Search Methods for Combinatorial Optimization Problems

The problem of estimating the global optimal values of intractable combinatorial optimization problems is of interest to researchers developing and evaluating heuristics for these problems. In this paper we present a method for combining statistical optimum prediction techniques with local search methods such as simulated annealing and tabu search and illustrate the approach on a single machine scheduling problem. Computational experiments show that the approach yields useful estimates of optimal values with very reasonable computational effort.     

Production scheduling with supply and delivery considerations to minimize the makespan

In this paper we study a scheduling model that simultaneously considers production scheduling, material supply, and product delivery. One vehicle with limited loading capacity transports unprocessed jobs from the supplier’s warehouse to the factory in a fixed travelling time. Another capacitated vehicle travels between the factory and the customer to deliver finished jobs to the customer. The objective is to minimize the arrival time of the last delivered job to the customer. We show that the problem is NP-hard in the strong sense, and propose an O(n) time heuristic with a tight performance bound of 2. We identify some polynomially solvable cases of the problem, and develop heuristics with better performance bounds for some special cases of the problem. Computational results show that all the heuristics are effective in producing optimal or near-optimal solutions quickly.     

A Hybrid Genetic Algorithm for the Single Machine Scheduling Problem

A hybrid genetic algorithm (HGA) is proposed for the single machine, single stage, scheduling problem in a sequence dependent setup time environment within a fixed planning horizon (SSSDP). It incorporates the elitist ranking method, genetic operators, and a hill-climbing technique in each searching area. To improve the performance and efficiency, hill climbing is performed by uniting the Wagner-Whitin Algorithm with the problem-specific knowledge. The objective of the HGA is to minimize the sum of setup cost, inventory cost, and backlog cost. The HGA is able to obtain a superior solution, if it is not optimal, in a reasonable time. The computational results of this algorithm on real life SSSDP problems are promising. In our test cases, the HGA performed up to 50% better than the Just-In-Time heuristics and 30% better than the complete batching heuristics.     

Constructive and composite heuristic solutions to the P//∑Ci scheduling problem

In this paper, we study the permutation flowshop scheduling problem with the criterion of minimising the total flow time. We propose a new constructive heuristic procedure to solve the problem. This procedure is flexible in the computational effort required, as it can be adjusted to the requirements of the problem. We combine this procedure with local search methods, whose computational requirements can also be varied, to study the efficiency and effectiveness of different ways of forming composite solution methods. Computational experiments on standard benchmark problems are carried out. The results show that the new heuristic performs significantly better than previous ones and that combining constructive and search heuristics not only further improves the solution quality but also saves computation time. Discussions on the results are provided and future research is suggested.     

An Almost Optimal Heuristic for Preemptive C max Scheduling of Dependent Tasks on Parallel Identical Machines

We consider the problem of scheduling preemptable, dependent tasks on parallel, identical machines to minimize the makespan. The computational complexity of this problem remains open if the number of machines is fixed and larger than 2. The aim of this paper is to compare two heuristic algorithms on a basis of a computational experiment. The solutions generated by the heuristics are compared with optimal solutions obtained by a branch-and-bound algorithm. Computational results show that the heuristic based on node ordering finds optimal schedules for 99.9% of instances with the maximum relative deviation from optimum of 4.8%.     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

A global MILP model for FMS scheduling

Flexible manufacturing systems (FMS) require intelligent scheduling strategies to achieve their principal benefit — combining high flexibility with high productivity. A mixed-integer linear programming model (MILP) is presented here for FMS scheduling. The model takes a global view of the problem and specifically takes into account constraints on storage and transportation. Both of these constrained resources are critical for practical FMS scheduling problems and are difficult to model. The MILP model is explained and justified and its complexity is discussed. Two heuristic procedures are developed, based on an analysis of the global MILP model. Computational results are presented comparing the performance of the different solution strategies. The development of iterative global heuristics based on mathematical programming formulations is advocated for a wide class of FMS scheduling problems.     

Rollout Algorithms for Stochastic Scheduling Problems

Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. In this paper we focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, with considerable savings in computation over optimal algorithms. We delineate circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.     

A single-machine scheduling problem with maintenance activities to minimize makespan

We study a single-machine scheduling problem with periodic maintenance activity under two maintenance stratagems. Although the scheduling problem with single or periodic maintenance and nonresumable jobs has been well studied, most of past studies considered only one maintenance stratagem. This research deals with a single-machine scheduling problem where the machine should be stopped for maintenance after a fixed periodic interval (T) or after a fixed number of jobs (K) have been processed. The objective is to minimize the makespan for the addressed problem. A two-stage binary integer programming (BIP) model is provided for driving the optimal solution up to 350-job instances. For the large-sized problems, two efficient heuristics are provided for the different combinations of T and K. Computational results show that the proposed algorithm Best-Fit-Butterfly (BBF) performs well because the total average percentage error is below 1%. Once the constraint of the maximum number of jobs (K) processed in the machine’s available time interval (T) is equal or larger than half of jobs, the heuristic Best-Fit-Decreasing (DBF) is strongly recommended.     

Optimal management of cross-trained workers in services with negligible switching costs

In this paper we consider a retail service facility with cross-trained workers who can switch between the front room and the back room depending on the size of the queue in the front room. Two problems are presented. In the first problem, given a fixed number of cross-trained workers the objective is to find optimal switching points so that the expected customer waiting time is minimized subject to a back room service level constraint. In the second problem the number of workers is also a decision variable and the objective is to minimize it subject to both front room and back room service level constraints. The paper includes an analysis of the model and based on it several heuristics are suggested. Computational analysis with the recommended heuristics is presented and comparison to optimal solutions derived by complete enumeration shows excellent results.     

Scheduling a hybrid assembly-differentiation flowshop to minimize total flow time

This study considers a hybrid assembly-differentiation flowshop scheduling problem (HADFSP), in which there are three production stages, including components manufacturing, assembly, and differentiation. All the components of a job are processed on different machines at the first stage. Subsequently, they are assembled together on a common single machine at the second stage. At the third stage, each job of a particular type is processed on a dedicated machine. The objective is to find a job schedule to minimize total flow time (TFT). At first, a mixed integer programming (MIP) model is formulated and then some properties of the optimal solution are presented. Since the NP-hardness of the problem, two fast heuristics (SPT-based heuristic and NEH-based heuristic) and three hybrid meta-heuristics (HGA-VNS, HDDE-VNS and HEDA-VNS) are developed for solving medium- and large-size problems. In order to evaluate the performances of the proposed algorithms, a lower bound for the HADFSP with TFT criteria (HADFSP-TFT) is established. The MIP model and the proposed algorithms are compared on randomly generated problems. Computational results show the effectiveness of the MIP model and the proposed algorithms. The computational analysis indicates that, in average, the HDDE-VNS performs better and more robustly than the other two meta-heuristics, whereas the NEH heuristic consume little time and could reach reasonable solutions.     

A simulated annealing algorithm for resource constrained project scheduling problems

This paper presents a simulated annealing algorithm for resource constrained project scheduling problems with the objective of minimising makespan. In the search algorithm, a solution is represented with a priority list, a vector of numbers each of which denotes the priority of each activity. In the algorithm, a priority scheduling method is used for making a complete schedule from a given priority list (and hence a project schedule is defined by a priority list). The search algorithm is applied to find a priority list which corresponds to a good project schedule. Unlike most of priority scheduling methods, in the suggested algorithm some activities are delayed on purpose so as to extend search space. Solutions can be further improved by delaying certain activities, since non-delay schedules are not dominant in the problem (the set of non-delay schedules does not always include an optimal solution). The suggested algorithm is flexible in that it can be easily applied to problems with an objective function of a general form and/or complex constraints. The performance of the simulated annealing algorithm is compared with existing heuristics on problems prepared by Patterson and randomly generated test problems. Computational results showed that the suggested algorithm outperformed existing ones.     

A Tabu search-based approach for scheduling job-shop type flexible manufacturing systems

The problem of scheduling parts in a job-shop type flexible manufacturing system (FMS) is investigated when each part can have alternative process plans and each operation required of a part can be performed on alternative machines. The mixed-(binary) integer programming model developed for the problem is proven strongly NP-hard. A higher-level heuristic solution algorithm based on a concept known as ‘tabu search’ is developed to determine the best (near-optimal) solution for problems of industrial merit. A comparison of six different versions of tabu search-based heuristics (TSH 1-TSH 6) is performed to investigate the impact of using long-term memory and the use of fixed versus variable tabu-list sizes. A carefully constructed statistical experiment, based on randomized complete-block design, is used to test the performance on four problem structures ranging from 4–14 parts. The results show that, as the problem size increases, TSH 3 with fixed tabu-list size and long-term memory is preferred over the other heuristics. Further, the branch-and-bound technique, by failing to identify as good a solution as that determined by the heuristics (TSH 1-TSH 6), let alone an optimal solution, for a small problem reinforces the need for developing efficient heuristics for solving real problems encountered in industry practice.     

A combinatorial algorithm for the TDMA message scheduling problem

In this paper, we introduce a combinatorial algorithm for the message scheduling problem on Time Division Multiple Access (TDMA) networks. In TDMA networks, time is divided in to slots in which messages are scheduled. The frame length is defined as the total number of slots required for all stations to broadcast without message collisions. The objective is to provide a broadcast schedule of minimum frame length which also provides the maximum throughput. This problem is known to be -hard, thus efficient heuristics are needed to provide solutions to real-world instances. We present a two-phase algorithm which exploits the combinatorial structure of the problem in order to provide high quality solutions. The first phase finds a feasible frame length in which the throughput is maximized in phase two. Computational results are provided and compared with other heuristics in the literature as well as to the optimal solutions found using a commercial integer programming solver. Experiments on 63 benchmark instances show that the proposed method is able to provide optimal frame lengths for all cases with near optimal throughput.     

Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations

This paper is concerned with the problem of assigning employees to gas stations owned by the Kuwait National Petroleum Corporation (KNPC), which hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. Although similar employee scheduling problems have been addressed in the literature, certain peculiarities of the problem require novel mathematical models and algorithms to deal with the specific nature and size of this problem. The problem is modeled as a mixed-integer program, and a problem size analysis based on real data reveals that the formulation is too complex to solve directly. Hence, a two-stage approach is proposed, where the first stage assigns employees to stations, and the second stage specifies shifts and off-days for each employee. Computational results related to solving the two-stage models directly via CPLEX and by specialized heuristics are reported. The two-stage approach provides daily schedules for employees for a given time horizon in a timely fashion, taking into consideration the employees’ expressed preferences. This proposed modeling approach can be incorporated within a decision support system to replace the current manual scheduling practice that is often chaotic and has led to feelings of bias and job dissatisfaction among employees.     

Scheduling preemptive open shops to minimize total tardiness

This article considers the problem of scheduling preemptive open shops to minimize total tardiness. The problem is known to be NP-hard. An efficient constructive heuristic is developed for solving large-sized problems. A branch-and-bound algorithm that incorporates a lower bound scheme based on the solution of an assignment problem as well as various dominance rules are presented for solving medium-sized problems. Computational results for the 2-machine case are reported. The branch-and-bound algorithm can handle problems of up to 30 jobs in size within a reasonable amount of time. The solution obtained by the heuristic has an average deviation of less than 2% from the optimal value, while the initial lower bound has an average deviation of less than 11% from the optimal value. Moreover, the heuristic finds approved optimal solutions for over 65% of the problems actually solved.     

Berth allocation with time-dependent physical limitations on vessels

We consider a berth allocation problem in container terminals in which the assignment of vessels to berths is limited by water depth and tidal condition. We model the problem as a parallel-machine scheduling problem with inclusive processing set restrictions, where the time horizon is divided into two periods and the processing sets in these two periods are different. We consider both the static and dynamic cases of the problem. In the static case all of the vessels are ready for service at time zero, while in the dynamic case the vessels may have nonzero arrival times. We analyze the computational complexity and develop efficient heuristics for these two cases. Computational experiments are performed to test the effectiveness of the heuristics and to evaluate the benefits of taking tidal condition into consideration when making berth allocation decisions.     

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND COMPRESSION COSTS （Part Ⅱ Heuristics for the General Case）

A single machine scheduling problem with controllable processing times and compression costs is considered. The objective is to find an optimal sequence to minimize the cost ofcompletion times and the cost of compression. The complexity of this problem is still unknown.In Part Ⅱ of this paper,the authors have considered a special case where the compression timesand the compression costs are equal among all jobs. Such a problem appears polynomiafiy solvable by developing an O(n^2) algorithm. In this part(Part Ⅱ ),a general case where the controllable processing times and the compression costs are not equal is discussed. Authors proposehere two heuristics with the first based on some previous work and the second based on the algorithm developed in Part Ⅱ . Computational results are presented to show the efficiency and therobustness of these heuristics.     

Minimizing the number of machines with limited workload capacity for scheduling jobs with interval constraints

In this paper, we consider a parallel machine scheduling problem in which machines have a limited workload capacity and jobs have deadlines and release dates. The problem is motivated by the operation of energy storage management systems for microgrids under emergency conditions and generalizes some problems that have already been studied in the literature for their theoretical value. In this work, we propose heuristic and exact algorithms to solve the problem. The heuristics are adaptations of classical bin packing heuristics in which additional conditions on the feasibility of a solution are imposed, whereas the exact method is a branch-and-price approach. The results show that the branch-and-price approach is able to optimally solve random instances with up to 250 jobs within a time limit of one hour, while the heuristic procedures provide near optimal solution within reduced running times. Finally, we also provide additional complexity results for a special case of the problem.