Mixed Shop Research Articles

An adapted constraint‐programming formulation of the resource‐constrained project scheduling problem applied to the identical parallel machines group shop and mixed shop scheduling problems

AbstractIn this paper, we study the group shop and the mixed shop scheduling problems with single and identical parallel machines at each workstation with the makespan criterion. We adapted a constraint programming formulation previously presented for the classical resource‐constrained project scheduling problem. The effectiveness of our approach is evident in the fact that it achieved optimality in 107 out of 130 classical group shop scheduling problem instances and in 320 classical mixed shop scheduling problem instances. In the last set, we obtained 13 new optimal solutions.

New Ant Colony Algorithm for Solving Partial Job Shop Scheduling Problem

Scheduling problems are one of the most researched topics in the field of operational research. Scheduling problem models have evolved and branched because of the wide range of products, standards, and customer requirements. Recently, the partial job shop scheduling problem, which is a general model of shop scheduling problems, has become a new scheduling problem. Operations in this model are partially ordered, and the order varies for each job. Several problems studied independently in the literature, such as the group shop, mixed shop, job shop, and open shop scheduling problems, are considered special cases of the partial shop scheduling model. Because ant algorithms are known in the literature as effective tools for solving combinatorial optimization problems, this study proposed an ant colony (AC) algorithm for solving partial shop problems with an objective function to minimize makespan. The AC method was examined and evaluated on the renowned “Taillerd” benchmark instances. It was then compared with the hybrid scatter search (HSS) and iterated tabu search (ITS) methods. The AC algorithm’s average deviation for 80 instances ranged between 0% and 1.78%. The AC algorithm outperforms the HSS and ITS methods, according to the computational findings; where the average percentage relative deviation for AC is 0.66%, compared with 0.99% for ITS and 10.14% for HSS.

Semantic and Syntactic Anomalies of Arabic-transliterated Compound Shop Names in Saudi Arabia

This study aims to explore the denotative meaning of compound shop names in Saudi Arabia, and identify the types of semantic and syntactic anomalies in the Arabic transliterations of English compound shop names. A corpus of compound shop names was collected from 12 major cities in a Saudi Mall Directory. After eliminating international shop names, pure Arabic shop names, single-word and duplicate shop names, a sample of 168 compound shop names consisting of locally-coined English shop names and mixed shop names was subjected to further analysis. In addition, a sample of students majoring in languages and translation took a compound shop name test where they had to judge the semantic and syntactic accuracy and acceptance of compound shop names. Results showed that 69% of the Arabic transliterations of the compound shop nouns in the sample have syntactic and/or semantic anomalies. 22% have syntactic anomalies as opposed 14% semantic anomalies and 23% have both semantic and syntactic anomalies combined. Some compound shop names are meaningless because the two elements of the compound are incongruous (Operation Falafel اوبريشن فلافل; Rude Shake (روود شيك. Others have faulty word order (Mama Batata ماما بطاطا ; قوركان شيف) ; faulty use of the definite article ((المنيو دونتس; use of constituents in the compound with the same meaning from two foreign languages )THE BEAU WOW); the English plural /-s/ is added to the Arabic word ملهم in Max Molhams ماكس ملهمز; splitting words into syllables or two parts ) اكس و ريزAccessories(; كلاي ماكس(Climax); combining two words and spelling them as one lexeme شرمبشاك)). Responses to the judgment test of the semantic and syntactic anomalies in shop names showed that the students could identify more semantic than syntactic anomalies (90% vs 80% respectively). They had difficulty understanding ماكس ملهمز- قوركان شيف - أوبريشن فلافل- شرمبشاك –ماما بطاطا that have both semantic and syntactic anomalies. They found them unacceptable and difficult to comprehend. The study gives some recommendations for translating rather than transliterating English compound shop names to overcome the semantic and syntactic anomalies.

Multi-objective Q-learning-based hyper-heuristic with Bi-criteria selection for energy-aware mixed shop scheduling

Owning to diverse customer demands and enormous product varieties, mixed shop production systems are applied in practice to improve responsiveness and productivity along with energy-saving. This work addresses a mixture of job-shop and flow-shop production scheduling problem with a speed-scaling policy and no-idle time strategy. A mixed-integer linear programming model is formulated to determine the speed level of operations and the sequence of job-shop and flow-shop products, aiming at the simultaneous optimization of production efficiency and energy consumption. Then, a multi-objective Q-learning-based hyper-heuristic with Bi-criteria selection (QHH-BS) is developed to obtain a set of high-quality Pareto frontier solutions. In this algorithm, a new three-layer encoding is designed to represent the production sequence of job-shop and flow-shop products; the Pareto-based and indicator-based selection criteria are sequentially implemented to encourage diversity and convergence; Q-learning with a multi-objective metric-based reward mechanism is applied to select an optimizer from three prominent optimizers in each iteration for better exploration and exploitation. Three conclusions are drawn from extensive experiments: (1) Bi-criteria selection is superior to single-criterion selections; (2) Q-learning-based hyper-heuristic is more effective and robust than single optimizer-based algorithms and simple hyper-heuristics; (3) QHH-BS outperforms the existing state-of-the-art multi-objective algorithms in convergence and diversity.

A COMPARATIVE STUDY OF THE USABILITY OF DIFFERENT PRODUCTION SCHEDULING ALGORITHMS AND RULES

Production scheduling optimization is a very important part of a production process. There are production systems with one service object and systems with multiple service objects. When using several service objects, there are systems with service objects arranged in a parallel or in a serial manner. We also distinguish between systems such as flow shop, job shop, open shop and mixed shop. Throughout the history of production planning, a number of algorithms and rules have been developed to calculate optimal production plans. These algorithms and rules differ from each other in the possibilities and conditions of their application. Since there are too many possible algorithms and rules it is not easy to select the proper algorithm or rule for solving a specific scheduling problem. In this article we analyzed the usability of 33 different algorithms and rules in total. Each algorithm or rule is suitable for a specific type of problem. The result of our analysis is a set of comparison tables that can serve as a basis for making the right decision in the production process decision-making process in order to select the proper algorithm or rule for solving a specific problem. We believe that these tables can be used for a quick and easy selection of the proper algorithm or rule for solving some of the typical production scheduling problems.

Graph-Based Modeling in Shop Scheduling Problems: Review and Extensions

Graphs are powerful tools to model manufacturing systems and scheduling problems. The complexity of these systems and their scheduling problems has been substantially increased by the ongoing technological development. Thus, it is essential to generate sustainable graph-based modeling approaches to deal with these excessive complexities. Graphs employ nodes and edges to represent the relationships between jobs, machines, operations, etc. Despite the significant volume of publications applying graphs to shop scheduling problems, the literature lacks a comprehensive survey study. We proposed the first comprehensive review paper which (1) systematically studies the overview and the perspective of this field, (2) highlights the gaps and potential hotspots of the literature, and (3) suggests future research directions towards sustainable graphs modeling the new intelligent/complex systems. We carefully examined 143 peer-reviewed journal papers published from 2015 to 2020. About 70% of our dataset were published in top-ranked journals which confirms the validity of our data and can imply the importance of this field. After discussing our generic data collection methodology, we proposed categorizations over the properties of the scheduling problems and their solutions. Then, we discussed our novel categorization over the variety of graphs modeling scheduling problems. Finally, as the most important contribution, we generated a creative graph-based model from scratch to represent the gaps and hotspots of the literature accompanied with statistical analysis on our dataset. Our analysis showed a significant attention towards job shop systems (56%) and Un/Directed Graphs (52%) where edges can be either directed, or undirected, or both, Whereas 14% of our dataset applied only Undirected Graphs and 11% targeted hybrid systems, e.g., mixed shop, flexible, and cellular manufacturing systems, which shows potential future research directions.

Improved Scheduling for the Three-Machine Proportionate Open Shop and Mixed Shop Minimum Makespan Problems

Open shop scheduling problems have many practical applications, in which the jobs can be in any order with the only restriction that their durations do not overlap with each other. In some cases, the order of a subset of jobs dictates the flow shop model while the remaining jobs can be processed in any order according to the open shop model, and the corresponding problem is called mixed shop scheduling. For every job, if its processing times on all machines are the same, then the shop is called proportionate shop. In this article we investigate the three-machine proportionate open shop and mixed shop minimum makespan problems proposed by Koulamas and Kyparisis. Our result improves the previous work in three ways. First, for both the open shop and the mixed shop scheduling problems, we derive additional sufficient conditions under which the corresponding problems are solvable in polynomial time. Second, for the non-solvable cases of the open shop scheduling problem we present an improved 13/12-approximation algorithm. Third, for the non-solvable cases of the mixed shop scheduling problem we present an improved approximation algorithm with the worst-case ratio bound of (7/6 + ϵ). All the algorithms proposed in this article run in polynomial time.

Approximation algorithms for the three-machine proportionate mixed shop scheduling

A mixed shop is a manufacturing infrastructure designed to process a mixture of a set of flow-shop jobs and a set of open-shop jobs. Mixed shops are in general much more complex to schedule than flow-shops and open-shops, and have been studied since the 1980's. We consider the three machine proportionate mixed shop problem denoted as M3|prpt|Cmax, in which by “proportionate” each job has equal processing times on all three machines. Koulamas and Kyparisis (2015) [6] showed that the problem is solvable in polynomial time in some very special cases; for the non-solvable case, they proposed a 5/3-approximation algorithm. In this paper, we first present an improved 4/3-approximation algorithm and show that this ratio of 4/3 is asymptotically tight; when the largest job is a flow-shop job, we then present a fully polynomial-time approximation scheme (FPTAS). On the negative side, while the F3|prpt|Cmax problem is polynomial-time solvable, we show an interesting hardness result that adding one open-shop job to the job set makes the problem NP-hard if this open-shop job is larger than any flow-shop job. We are able to design an FPTAS for this special case too.

Review and classification of hybrid shop scheduling

Hybrid shop scheduling has gained popularity due to the rapid rise of market demand and development of production technology. It is a combination of more than one classical shop scheduling, such as flow shop scheduling, job shop scheduling, open shop scheduling, parallel machine scheduling, and multiprocessor task scheduling. In this paper, a classification of hybrid shop scheduling problem based on the criterion of machine environment is proposed. The problem is classified into hybrid shop scheduling with parallel machines, hybrid shop scheduling with multiprocessor task, and other hybrid shop scheduling such as the mixed shop scheduling. The citation analysis method is used to give a brief review of hybrid flow shop and job shop with parallel machines. At the same time, for hybrid shop scheduling with multiprocessor task and other hybrid shop scheduling, a detailed overview is given because of its relatively few researches. Finally, some research directions for the hybrid shop scheduling are also discussed.

Improved hybrid immune clonal selection genetic algorithm and its application in hybrid shop scheduling

This paper is based on the multi-objective optimization problem of mixed shop scheduling problem, the strong coupling of the maximum flow and the minimum time, and the deficiencies of the immune genetic algorithm including high computational complexity and high spatial dimension. This paper establishes a mixed shop scheduling mathematical model with the minimization of the maximum total completion time as the target, and puts forward to use the immune clonal selection algorithm to solve the problem. In the algorithm population construction, it uses the grouping strategy, introduces the cross and delete operator, retains the excellent individuals through memory space, deletes the relatively bad individual, and improves the algorithm’s global optimization ability. In order to verify the effectiveness of the proposed algorithm, under the two experimental environments of workpiece machining and automobile shock absorber processing workshop scheduling, simulation experiments are conducted. The experimental results show that the proposed algorithm has better performance, and can achieve smaller maximum total completion time with less iteration. The algorithm can find the global optimal solution of the multi-objective problem, which has a strong practical significance.

An effective heuristic algorithm for the partial shop scheduling problem

In a partial shop scheduling problem the operations of each job have to respect a partial order, which can be different for each job. We study the problem of finding a solution of minimal makespan in partial shops. This problem generalizes many problems which have been studied independently in the literature, such as the group shop scheduling problem, the mixed shop scheduling problem, and the open shop scheduling problem. In this paper we propose an algorithm which is able to find solutions for the partial shop scheduling problem. In computational experiments we find that the proposed single heuristic can compete with the state-of-the-art heuristics for the partial shop, group shop, mixed shop, and open shop, and in many cases, improves the state of the art. The main contribution of this paper is the demonstration that a single algorithm can solve effectively many special cases of the partial shop without taking into consideration their particular structure. We highlight the contribution of the main novel components of the algorithm, namely the initial solution generator, neighbourhood structure, and the lower bound for new solutions generated by such neighbourhood.

An Experimental Analysis on Dispatching Rules for the Train Platforming Problem in Busy Complex Passenger Stations

This paper presents the scheduling models for trainplatforming problem (TPP) by using mixed integer linear programming and job shop scheduling theory. First, the operation procedures and scheduled time adjustment costs of different train types specific to busy complex passenger stations are explicitly represented. Second, a multi-criteria scheduling model (MCS) for TPP without earliness and tardiness time window (ETTW) and a time window scheduling model (TWS) with ETTW for TPP are proposed. Third, various dispatching rules were designed by incorporating the dispatcher experiences with modern scheduling theory and a rule-based metaheuristic to solve the above model is presented. With solution improvement strategies analogous to those used in practice by dispatchers, the realistic size problems in acceptable time can be solved.

An Efficient Solution to the Mixed Shop Scheduling Problem Using a Modified Genetic Algorithm

The mixed job shop scheduling problem is one in which some jobs have fixed machine orders and other jobs may be processed in arbitrary orders. In past literature, optimal solutions have been proposed based on adaptations of classical solutions such as by Johnson, Thompson and Giffler among many others, by pseudopolynomial algorithms, by simulation, and by Genetic Algorithms (GA). GA based solutions have been proposed for flexible Job shops. This paper proposes a GA algorithm for the mixed job shop scheduling problem. The paper starts with an analysis of the characteristics of the so-called mixed shop problem. Based on those properties, a modified GA is proposed to minimize the makespan of the mixed shop schedule. In this approach, sample instances used as test data are generated under the constraints of shop scheduling problems. A comparison of our results based on benchmark data indicate that our modified GA provides an efficient solution for the mixed shop scheduling problem.

Hybrid stage shop scheduling

The proposed hybrid stage shop scheduling (HSSS) model, inspired from a real case in the high-fashion industry, aims to fully exploit the potential of parallel resources, splitting and overlapping concurrent operations among teams of multifunctional machines and operators on the same job.The HSSS formally extends mixed shop scheduling (a combination of flowshop and open shop), which is able to model routing flexibility, and hybrid shop scheduling, which provides resource flexibility. To also include operational flexibility through alternative plans obtained by reordering operations linked by undefined or arbitrary (immaterial) precedence constraints, the proposed model integrates process planning and group shop scheduling.A mixed integer linear programming model and a theory based on disjunctive graphs have been proposed to explore the composite relations between nodes involving immaterial relations and deploying their routing rules.A constructive O(resources×jobs2) algorithm to generate a feasible plan/schedule in the most general case has been developed and applied to a case study.

A modified ABC algorithm for the stage shop scheduling problem

Stage shop problem is an extension of the mixed shop as well as job shop and open shop. The problem is also a special case of the general shop. In a stage shop, each job has a number of stages; each of which includes one or more operations. As a subset of operations of a job, the operations of a stage can be done without any precedence consideration of each other, whereas the stages themselves should be processed according to a preset sequence. Due to the NP-hardness of the problem, a modified artificial bee colony (ABC) algorithm is suggested. In order to improve the exploitation feature of ABC, an effective neighborhood of the stage shop problem and PSO are used in employed and onlooker bee phases, respectively. In addition, the idea of tabu search is substituted for the greedy selection property of the artificial bee colony algorithm. The proposed algorithm is compared with the traditional ABC and the state-of-the-art CMA-ES. The computational results show that the modified ABC outperforms CMA-ES and completely dominates the traditional ABC. In addition, the proposed algorithm found high quality solutions within short times. For instance, two new optimal solutions and many new upper bounds are discovered for the unsolved benchmarks.

The three-machine proportionate open shop and mixed shop minimum makespan problems

Abstract We first consider the ordinary NP-hard three-machine proportionate open shop minimum makespan O 3| prpt | C max problem and show that it is solvable in O ( n log n ) time when certain conditions on the total machine load are met. When these conditions are not met, we derive an approximate solution by implementing the optimal solution for the O 3| prpt | C max problem when the two longest jobs are of equal length. In that case, both absolute and ratio worst-case bounds are derived. We also consider the more general mixed shop problem M 3| prpt | C max in which a given job subset must be processed as in a flow shop while the remaining jobs can be processed as in the O 3| prpt | C max problem. We show that our open shop solution techniques can be implemented to derive exact and approximate solutions for the M 3| prpt | C max problem. Finally, we discuss the applicability of our open shop results to the proportionate open shop problem with unequal machine speeds.

A possibilistic programming approach for capacitated lot-sizing problem in mixed assembly shops

This paper develops a fuzzy multi-objective linear programme (FMOLP) model for solving the bi-objective capacitated lot-sizing problem (CLSP). The proposed model attempts to simultaneously minimise total cost consist of total production variation cost, inventory cost, backlog cost and total setup cost while maximising the resource utilisation. According to the structure of the mixed assembly shops, a multi-product model with multi-item that should be produced during multi-level has been designed. Based on the vagueness and imprecision of the real case, the production, holding and backorder costs and demand of the products were considered as fuzzy number that have their membership function during planning horizon in each period. An interactive fuzzy solution method is developed by combining a number of efficient solution algorithms from the recent literature in order to solve the proposed possibilistic model. In order to demonstrate the significance and applicability of the proposed model as well as the usefulness of the proposed solution approach, numerical experiments are conducted and the results are provided.

A Tabu Search Algorithm for the Stage Shop Problem

This paper presents stage shop problem which is a special case of the general shop. The stage shop is a more realistic generalization of the mixed shop problem. In the stage shop problem, each job has several stages of operations. In order to solve the stage shop problem with makespan objective function, a tabu search algorithm is developed. In addition, an existing lower bound of the job shop is adapted to the new problem and the computational results have been compared to it. The proposed TS algorithm has reached the optimal solutions for about half of the problem instances

Optimal scheduling in walk-in outpatient clinics: a mixed hybrid flow shop problem approach

One of the major challenges most outpatient clinics are facing is how to cope with the increasing demand pressure due to population growth and ageing. This paper studies how to improve the scheduling practise in a generic walk-in outpatient clinic with complex patient flows. Mathematical programming is applied to model the outpatient clinic as a mixed hybrid flow shop problem. Optimal schedule of the outpatient clinic is achieved by solving the mathematical programming model. Computational results prove that better scheduling helps to improve the performance of outpatient clinics without additional resources.

A Complete 4-parametric complexity classification of short shop scheduling problems

We present a comprehensive complexity analysis of classical shop scheduling problems subject to various combinations of constraints imposed on the processing times of operations, the maximum number of operations per job, the upper bound on schedule length, and the problem type (taking values "open shop," "job shop," "mixed shop"). It is shown that in the infinite class of such problems there exists a finite basis system that allows one to easily determine the complexity of any problem in the class. The basis system consists of ten problems, five of which are polynomially solvable, and the other five are NP-complete. (The complexity status of two basis problems was known before, while the status of the other eight is determined in this paper.) Thereby the dichotomy property of that parameterized class of problems is established. Since one of the parameters is the bound on schedule length (and the other two numerical parameters are tightly related to it), our research continues the research line on complexity analysis of short shop scheduling problems initiated for the open shop and job shop problems in the paper by Williamson et al. (Oper. Res. 45(2):288---294, 1997). We improve on some results of that paper.