This paper addresses scheduling problems in single-stage and continuous multiproduct processes on parallel lines with intermediate due dates and especially restrictions on minimum run lengths. Whereas previous approaches require predetermined time slots or a maximum number of time slots to which only one task should be assigned, the proposed formulation does not use time slots within a time period. Therefore, the size of a model and its computation time are significantly reduced, with restrictions on several realistic situations, such as minimum run lengths, idle times of processes, and tests/maintenance, that are addressed in previous literature. Our approach is illustrated with various examples presented in the literature.

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Many researchers have studied the scheduling, planning, and design of multipurpose batch processes. However, not so many studies have treated design and scheduling or design and planning simultaneously. The complexity of these systems stems from the fact that plant configuration must be determined for the purpose of process scheduling, yet scheduling must be done to devise the plant configuration. In the present study, a new algorithm for determining the best multipurpose scheduling and plant configuration is suggested. Since the objective function of the problem is nonlinear, it is linearized using a separable programming method. The proposed method consists of a number of procedures. First, a feasible configuration is obtained. Next, both the optimum equipment size and cyclic scheduling are determined for the plant configuration obtained in the first procedure. Last, the evolutionary design method proposed by Fuchino et al.(J. Chem. Eng. Jpn. 1994, 27, 57−64) is used to find the solution that minimizes the total cost. The efficacy of the proposed approach is demonstrated in three examples. Usually, equipment sizes are considered by a continuous variable in mixed integer linear programming and task processing time is assumed to be constant. However, most types of equipment are manufactured only in discrete volume classes. In addition, processing times are dependent on batch sizes. Hence, to apply the optimization methods developed here to real industries, the method was modified such that the volumes of equipment are considered as discrete variables and the processing time is a function of batch size.

This study considers a scheduling algorithm and mathematical models for a real polyvinyl chloride (PVC) plant. According to general rules of the PVC plant, the basic PVC scheduling model is formulated as mixed integer linear programming (MILP). This model includes production, inventory management, packing, and shipment processes. The basic PVC scheduling model is customized for two PVC production processes with different characteristics, resulting in two detailed PVC scheduling models. An optimization algorithm has been developed to solve these scheduling models. This algorithm is a hybrid algorithm combining the genetic algorithm for integer programming (IP) and the interior point method for linear programming (LP). A heuristic technique has also been developed to reduce the number of solving LPs. Finally, the optimized results of the models were analyzed.

In this paper, we introduce a new blue-emitting material, CuCrS2/ZnS QDs (CCS QDs). To obtain bright and stable photoluminescent probes, we prepared a core/shell structure; the synthesis was conducted in a one-pot system, using 1-dodecanethiol as a sulfur source and co-ligand. The CCS QDs exhibited a semi-spherical colloidal nanocrystalline shape with an average diameter of 9.0 nm and ZnS shell thickness of 1.6 nm. A maximum photoluminescence emission peak (PL max) was observed at 465 nm with an excitation wavelength of 400 nm and PLQY was 5% at an initial [Cr3+]/[Cu+] molar ratio of one in the core synthesis. With an off-stoichiometric modification for band gap engineering, the CCS QDs exhibited slightly blue-shifted PL emission spectra and PLQY was 10% with an increase in initial molar ratio of 2.0 (462 nm PL max). However, when the initial molar ratio exceeded two, the CCS QDs exhibited a lower photoluminescence quantum yield of 4.5% with 461 nm of PL max at the initial molar ratio of four due to the formation of non-emissive Cr2S3 nanoflakes.