Heuristics for multimode scheduling problems with dedicated resources

The precedence relationships between the operations are important constraints in planning and scheduling of manufacturing systems and project management. This paper presents a method to obtain a global solution for operation sequencing with precedence constraints which are one of the most influential factors in the performance of planning and scheduling problems. An integer programming model is proposed for the operation sequencing with precedence constraints. And an adaptive evolutionary approach for the problem is developed by employing the adaptive genetic operation functions to obtain a good solution for relatively large problems in a reasonable computational time. Computational experiments for the model are performed and the results are analyzed.

Static scheduling of directed acyclic data flow graphs onto multiprocessors using particle swarm optimization

Precedence Constraints are a common restriction in scheduling, ensuring that certain tasks can only be executed after specific predecessors have been completed. Beyond scheduling, precedence constraints also appear in many other optimization problems, ranging from transportation and routing to packing problems. This dissertation investigates various combinatorial optimization problems under precedence constraints. While classical precedence constraints are typically described by partial orders, this work also considers more flexible variants. The dissertation begins with the development of a unified model for optimization under precedence constraints, representing precedence constraints as Boolean formulas. Existing models for precedence constraints emerge as special cases of this definition: For example, classical precedence constraints can be expressed as conjunctive clauses. Based on this definition, we first study a classical scheduling problem, where tasks of uniform length are processed on parallel machines. We focus on the parameterized complexity with respect to two parameters: the total number of predecessors and the total number of successors. With respect to the first parameter, the problem is shown to be FPT (fixed-parameter tractable), making it manageable when the parameter size is small. Regarding the second parameter, the dissertation analyzes the parameterized hardness of the problem under various structural restrictions on the Boolean formulas. Next, the work extends the concept of precedence constraints to two other classical combinatorial optimization problems. For the shortest-path problem, it analyzes the complexity concerning feasibility and optimality and develops a dynamic programming approach. While this algorithm generally has exponential runtime, it provides the foundation for polynomial-time solutions in certain special cases. For the maximum matching problem, precedence constraints mean that edges join the matching sequentially and can only be added once their predecessor vertices are already covered. We analyze the complexity of various special cases and develop a dynamic programming algorithm for constant treewidth. The final chapter addresses search on trees, where a target node must be located through queries to the edges. This problem is related to precedence-constrained problems because the order of queries is constrained by the tree structure. Based on linear programming, the dissertation develops a constant-factor approximation algorithm for a broad class of objective functions.

Purpose Two-stage production systems including a processing shop and an assembly stage are widely used in various manufacturing industries. These two stages are usually studied independently which may not lead to ideal results. This paper aims to deal with a two-stage production system including a job shop and an assembly stage. Design/methodology/approach Some exact methods are proposed based on branch and bound (B&B) approach to minimize the total completion time of products. As B&B approaches are usually time-consuming, three efficient lower bounds are developed for the problem and variable neighborhood search is used to provide proper upper bound of the solution in each branch. In addition, to create branches and search new nodes, two strategies are applied including the best-first search and the depth-first search (DFS). Another feature of the proposed algorithms is that the search space is reduced by releasing the precedence constraint. In this case, the problem becomes equivalent to a parallel machine scheduling problem, and the redundant branches that do not consider the precedence constraint are removed. Therefore, the number of nodes and computational time are significantly reduced without eliminating the optimal solution. Findings Some numerical examples are used to evaluate the performance of the proposed methods. Comparison result to mathematical model (mixed-integer linear programming) validates the performance accuracy and efficiency of the proposed methods. In addition, computational results indicate the superiority of the DFS strategy with regard to CPU time. Originality/value Studies about the scheduling problems for two-stage production systems including job shop followed by an assembly stage traditionally present approximate method and metaheuristic algorithms to solve the problem. This is the first study that introduces exact methods based on (B&B) approach.

In a scheduling problem, denoted by 1|prec|∑C i in the Graham notation, we are given a set of n jobs, together with their processing times and precedence constraints. The task is to order the jobs so that their total completion time is minimized. 1|prec|∑C i is a special case of the Traveling Repairman Problem with precedences. A natural dynamic programming algorithm solves both these problems in 2n n O(1) time, and whether there exists an algorithms solving 1|prec|∑C i in O(c n) time for some constant c<2 was an open problem posted in 2004 by Woeginger. In this paper we answer this question positively.

The paper deals with a single machine scheduling problem involving a general precedence structure that permits both ordinary and fuzzy precedence constraints. Feasible schedules are evaluated not only by their cost but also by the degree of satisfaction with their precedence structure. An O(mlogn+ max(n 2, Kn 2))-time algorithm is proposed for finding nondominated solutions of the resulting bi-criteria scheduling problem where n is the number of jobs, k is the number of fuzzy constrains, and m is the total number of precedence constraints.

In this paper, we discuss a scheduling problem for jobs on identical parallel machines. Ready times of the jobs, precedence constraints, and sequence-dependent setup times are considered. We are interested in minimizing the performance measure total weighted tardiness. Scheduling problems of this type are quite important in semiconductor manufacturing. We suggest a variable neighborhood search (VNS) scheme for this problem. Based on computational experiments with stochastically generated test instances we are able to show that the VNS approach clearly outperforms heuristics based on the apparent tardiness cost with setups and ready times (ATCSR) dispatching rule in many situations.

&lt;p style='text-indent:20px;'&gt;In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.&lt;/p&gt;

A hybrid scatter search for the discrete time/resource trade-off problem in project scheduling

The rehabilitation inpatients in hospitals often complain about the service quality due to the long waiting time between the therapeutic processes. To enhance service quality, this study aims to propose an intelligent solution to reduce the waiting time through solving the rehabilitation scheduling problem. In particular, a bi-objective genetic algorithm is developed for rehabilitation scheduling via minimizing the total waiting time and the makespan. The conjunctive therapy concept is employed to preserve the partial precedence constraints between the therapies and thus the present rehabilitation scheduling problem can be formulated as an open shop scheduling problem, in which a special decoding algorithm is designed. We conducted an empirical study based on real data collected in a general hospital for validation. The proposed approach considered both the hospital operational efficiency and the patient centralized service needs. The results have shown that the waiting time of each inpatient can be reduced significantly and thus demonstrated the practical viability of the proposed bi-objective heuristic genetic algorithm.

We consider a scheduling problem with the objective of minimising the makespan under uncertain numerical input data (for example, the processing time of an operation, the job release time and due date) and fixed structural input data (for example the precedence and capacity constraints). We assume that at (before) the scheduling stage the structural input data are known and fixed but all we know about the numerical input data are their upper and lower bounds, where the uncertain numerical data become realised at the control stage as the scheduled process evolves. After improving the mixed graph model, we present an approach for dealing with our scheduling problem under uncertain numerical data based on a stability analysis of an optimal makespan schedule. In particular, we investigate the candidate set of the critical paths in a circuit-free digraph, characterise a minimal set of the optimal schedules, and develop an optimal and a heuristic algorithm. We also report computational results for randomly generated as well as well-known test problems.

The connection between the bump number problem and flow-shop scheduling with precedence constraints

Given a set of n elements V = {1, 2,..., n} and a precedence relation < P ⊆ V × V defined on V, where i < P j or (i, j) ∈ < P means that i precedes j, let us consider the complete digraph G = (V, A) with no loops and with (j, i) ∉ A if and only if i < P j. Let be assigned a cost c ij ∈ {0, 1} to each arc (i, j) ∈ A with c ij = 0 if and only if (j, i) ∉ A. Let G′ be the digraph obtained from G adding a dummy vertex s, the Traveling Salesman Problem with Precedence Constraints and Binary Costs (TSP-PC-BC) is to find a hamiltonian tour of minimum cost in G′, starting from vertex s, visiting each vertex i ∈ V after having visited every vertex j ∈ V that must precede i and returning to vertex s. In this paper we investigate the TSP-PC-BC using a different approach from those used in previous works on TSP: we replace the graph G′ with a partially ordered set P = (V, < P ), defined by < P on V and reformulate the problem as the Jump Number Problem of P. We also propose exact and heuristic solution algorithms. Computational results on a set of randomly generated test problem are discussed.

This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness Lmax for integer due dates to the scheduling problem, where along with precedence constraints given on the set V={v1,v2, …,vn} of the multiprocessor tasks, a subset of tasks must be processed simultaneously. Contrary to a classical shop-scheduling problem, several processors must fulfill a multiprocessor task. Furthermore, two types of the precedence constraints may be given on the task set V. We prove that the extended scheduling problem with integer release times ri≥0 of the jobs V to minimize schedule length Cmax may be solved as an optimal mixed graph coloring problem that consists of the assignment of a minimal number of colors (positive integers) {1,2, …,t} to the vertices {v1,v2, …,vn}=V of the mixed graph G=(V,A, E) such that, if two vertices vp and vq are joined by the edge [vp,vq]∈E, their colors have to be different. Further, if two vertices vi and vj are joined by the arc (vi,vj)∈A, the color of vertex vi has to be no greater than the color of vertex vj. We prove two theorems, which imply that most analytical results proved so far for optimal colorings of the mixed graphs G=(V,A, E), have analogous results, which are valid for the extended scheduling problems to minimize the schedule length or maximal lateness, and vice versa.

The flow set with partial order is a mixed-integer set described by a budget on total flow and a partial order on the arcs that may carry positive flow. This set is a common substructure of resource allocation and scheduling problems with precedence constraints and robust network flow problems under demand/capacity uncertainty. We give a polyhedral analysis of the convex hull of the flow set with partial order. Unlike for the flow set without partial order, cover-type inequalities based on partial order structure are a function of a lifting sequence. We study the lifting sequences and describe structural results on the lifting coefficients for general and simpler special cases. We show that all lifting coefficients can be computed in polynomial time by solving maximum weight closure problems in general. For the special case of induced-minimal covers, we give a sequence-dependent characterization of the lifting coefficients. We prove, however, if the partial order is defined by an arborescence, then lifting is sequence-independent and all lifting coefficients can be computed in linear time. Moreover, if the partial order is defined by a path (total order), then the coefficients can be expressed explicitly. We also give a complete polyhedral description of the flow set with partial order for the polynomially-solvable total order case. We show that finding an optimal lifting order for a given induced-minimal cover and a given fractional solution is a submodular optimization problem, which is solved greedily. Finally, we present preliminary computational results with a cutting-plane algorithm based on the lifting and separation results.