Mathematical modeling and two efficient branch and bound algorithms for job shop scheduling problem followed by an assembly stage

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.

Ant colony optimization approach based on precedence constraint matrix for flexible process planning

An innovative approach integrated into search based on ant colony optimization (ACO) is used to optimize the flexible process planning with the objective of minimizing total weight costs (TWC) against precedence constraints. First, the flexible process planning (FPP) is described as the ordering of the alternative machining operations by decomposing processing operation into several optional machining operations based on different tool access directions, and determining the precedence constraints of the alternative machining operations. Due to the determination of the set of feasible alternative machining operations of processing operation, and the use of the precedence constraint matrix to describe the precedence constraint relationship, the sequence of precedence constraint becomes the limitation of search space for seeking optimal solution. Then, the ant colony algorithm is employed to search the set sequence of the alternative machining operations based on the search space limitation method. Since each ant gets a feasible operation routing, the optimal manufacturing resource of each alternative operation is obtained from the randomly selected manufacturing resource by the minimum cost rule. Finally, compared with the existing genetic algorithm, tabu search, simulated annealing and general ant colony algorithm, the proposed algorithm is proved to be feasibility and competitiveness by instance.

AP Adjacency as a Precedence Constraint

Attributive APs precede certain other categories (PPs, genitive DPs, etc.), when the noun precedes both ( Giurgea 2009 , Adger 2012 ). This observation may suggest an analysis in terms of X-bar-style “structural layering.” However, such an account faces several problems: (a) in languages with PP-AP-N order, scrambling of the AP is permitted; (b) in languages with AP-N-PP or PP-N-AP order, there is evidence that the AP can c-command the PP, as well as the other way around; and (c) in languages with N-AP-PP order, the AP can take scope over the PP, as well as the other way around, arguably as a consequence of a structural ambiguity. We therefore develop an alternative analysis based on a striking parallel between the syntax of attributive APs and that of objects: while OV languages systematically allow adverbs to intervene between object and verb, VO languages tend to require verb-object-adverb order. This aspect of verbal syntax is familiar and can be captured in terms of a well-known linear constraint: Case Adjacency ( Stowell 1981 , Janke and Neeleman 2012 ). We propose that this constraint has a nominal counterpart that ensures N-AP adjacency in noun-initial structures. Thus, this instance of NP/VP parallelism has its source in parallel constraints, rather than parallel structural layers.

Some complexity results and an efficient algorithm for quay crane scheduling problem

This paper investigates the quay crane scheduling problem (QCSP) at container ports, subject to arbitrary precedence constraint among vessel container tasks. Differing from classic machine scheduling problems, noncrossing constraint for quay cranes must be satisfied. This is because quay cranes work in parallel and they travel on a same rail (along the berth), to perform container unloading and loading tasks for vessels. Precedence relation in an arbitrary form is rarely investigated in the literature, however, it may be originated from reefers or dangerous cargo which requires high priority of processing, and yard stacking plan. We present the computational complexity for several problem variations. In particular, we show the QCSP, even without precedence constraint, is strongly NP-hard. This complexity result improves the state-of-the-art, in which the same problem is shown to be NP-hard in the ordinary sense. Besides, we also prove that for two parallel quay cranes, if the processing times of container tasks are ones and twos, then this scheduling problem is NP-hard. This result implies that the QCSP with arbitrary precedence constraint is very difficult to solve. A genetic algorithm is proposed to obtain near-optimal solutions. Computational experiments demonstrate the efficiency.