A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

Comparative antibacterial efficacies of hydrodynamic and ultrasonic irrigation systems in vitro

INTRODUCTION To ensure root canal treatment success, endodontic microbiota should be efficiently reduced. The in vitro bactericidal effects of a hydrodynamic system and a passive ultrasonic irrigation system were compared. METHODS Single-rooted extracted teeth (n = 250) were contaminated with suspensions of Enterococcus faecalis ATCC 29212, mixed aerobic cultures, or mixed anaerobic cultures. First, the antibacterial effects of the hydrodynamic system (RinsEndo), a passive ultrasonic irrigation system (Piezo smart), and manual rinsing with 0.9% NaCl (the control) were compared. Colony-forming units were counted. Second, the 2 systems were used with 1.5% sodium hypochlorite (NaOCl) alone or NaOCl + 0.2% chlorhexidine (CHX). The colony-forming units in the treated and untreated roots were determined during a period of 5 days. RESULTS Both irrigation systems reduced bacterial numbers more effectively than manual rinsing (P < .001). With NaCl, ultrasonic activated irrigation reduced bacterial counts significantly better than hydrodynamic irrigation (P = .042). The NaOCl + CHX combination was more effective than NaOCl alone for both systems (P < .001), but hydrodynamic irrigation was more effective with NaOCl + CHX than the passive ultrasonic irrigation system. CONCLUSIONS Both irrigation systems, when combined with NaOCl + CHX, removed bacteria from root canals.