Abstract - This paper considers a non-preemptive open shop scheduling problem (OSSP), in which machines are not available to process jobs on known periodic interval times resulted from periodic service repair, rest period, and so on. Asymmetric transportation time between machines is considered, which can be different from one job to another. The objective is to minimize the weighted mean completion time (WMCT). Since the problem is categorized into NP-hard class, two meta-heuristic algorithms including genetic algorithm (GA) and differential evolution (DE) are proposed. Meanwhile, a new initial population is introduced, which significantly improves the performance of the algorithms. Finally, the performance of the algorithms is validated through some large-sized instances and the results are discussed. Keywords - Open shop scheduling, Machine availability, Transportation time, Weighted mean completion time, Differential evolution, Genetic algorithm. I. INTRODUCTION In an open shop scheduling problem, each of n jobs is supposed to be processed by m machines in arbitrary order [1]. However, machines may be unavailable due to preventive maintenance, rest period, uncompleted jobs from the previous working shift which should be processed at the beginning of the current shift, and so on [1]. OSSP provides a wide range of applications including timetable problem, manufacturing plants, optical network, communication scheduling and so on [1]. Sheikhalishahi et al. [2] illustrated a real application of OSSP considering preventive maintenance in an automobile spare parts manufactory where 9 jobs are supposed to be processed on 9 machines (i.e., 81 operations) in a pressing and forming shop. Strusevich [3] considered a known time lag between the completion of a task and the beginning of the next task of the same job in an OSSP. Due to the actual transportation of a job between machines, he named this time lag as transportation time. Also, he referred to another interpretation of this time lag in chemical and metallurgic applications, as the cooling or heating time. Ma et al. [4] summarized scheduling problems with availability constraints caused by preventive maintenance taking into account their complexity. Accordingly, the OSSP with availability constraint even in small cases is categorized into NP-hard class. Hence, applying approximation approaches can be more effective than exact methods. Huang et al. [5] proposed four algorithms including GA, Particle Swarm Optimization (PSO), cuckoo search algorithm, and Ant Colony Optimization (ACO) for OSSP. DE is another well-known algorithm that has rarely been implemented for OSSP; however, there are some studies using this algorithm to other scheduling problems, such as parallel machines [6]. In this paper, a non-preemptive OSSP with machine availability constraint is purposed in which machines are not available to process jobs on known periodic intervals. Available/unavailable intervals are assumed to be constant and predefined for each machine while they vary from one machine to another. Asymmetric transportation times between machines is another feature of the purposed OSSP caused by considering different routes to move between machines which reduces route interception in the shop. Moreover, different jobs have different transportation times on the same route, which can be resulted from using various vehicles to carry various parts. Furthermore, the time which a job is on a machine is divided into three parts including setup, process, and removal time. Meanwhile, WMCT is considered as the objective function, which should be minimized [7]. To solve the purposed OSSP, a new initial population is introduced which significantly improves the results of both GA and DE meta-heuristics. The rest of this paper is organized as follows. In Section II, considering some assumptions the problem is defined. Then, encoding scheme and proposed initial populations are introduced in Section III. Sections IV and V contain GA and DE algorithms, respectively. Computational evaluation is presented in Section VI. Finally, the paper is concluded in Section VII. II. PROBLEM DEFENITION As shown in Fig. 1, the available times for each machine are considered like batches which jobs should be located into them while the total time of jobs does not exceed the batch time ( ௝ ). In Fig. 1, ܬ ሾ௜ሿ indicates the job in the i-th position of sequence and ܤ ௝௟ is the l-th batch of machine j. Moreover, the available ( ௝ ) and unavailable ( ݐ ௝ ) intervals are constant and predefined for each machine. Fig. 1. Job sequencing on machine j with known unavailable times Non-Preemptive Open Shop Scheduling Considering Machine Availability A. Shojaei Barjouei 1 , Abbas Barabadi 1 , R. Tavakkoli-Moghaddam 2 1 Department of Technology and Safety, UiT: The Arctic University of Norway, Tromsø, Norway 2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran (E-mail: abbas.b.abadi@uit.no)