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.

Accuracy and reproducibility of aortic annulus sizing using a dedicated three-dimensional computed tomography reconstruction tool in patients evaluated for transcatheter aortic valve replacement

Aims: To evaluate the accuracy and reproducibility of aortic annulus sizing using a multislice computed tomography (MSCT) based aortic root reconstruction tool compared with conventional imaging among patients evaluated for transcatheter aortic valve replacement (TAVR). Methods and results: Patients referred for TAVR underwent standard preprocedural assessment of aortic annulus parameters using MSCT, angiography and transoesophageal echocardiography (TEE). Three-dimensional (3-D) reconstruction of MSCT images of the aortic root was performed using 3mensio (3mensio Medical Imaging BV, Bilthoven, The Netherlands), allowing for semi-automated delineation of the annular plane and assessment of annulus perimeter, area, maximum, minimum and virtual diameters derived from area and perimeter (aVD and pVD). A total of 177 patients were enrolled. We observed a good inter-observer variability of 3-D reconstruction assessments with concordance coefficients for agreement of 0.91 (95% CI: 0.87-0.93) and 0.91 (0.88-0.94) for annulus perimeter and area assessments, respectively. 3-D derived pVD and aVD correlated very closely with a concordance coefficient of 0.97 (0.96-0.98) with a mean difference of 0.5±0.3 mm (pVD-aVD). 3-D derived pVD showed the best, but moderate concordance with diameters obtained from coronal MSCT (0.67, 0.56-0.75; 0.3±1.8 mm), and the lowest concordance with diameters obtained from TEE (0.42, 0.31-0.52; 1.9±1.9 mm). Conclusions: MSCT-based 3-D reconstruction of the aortic annulus using the 3mensio software enables accurate and reproducible assessment of aortic annulus dimensions.

Scheduling of continuous and discontinuous material flows with intermediate storage restrictions

This paper deals with scheduling batch (i.e., discontinuous), continuous, and semicontinuous production in process industries (e.g., chemical, pharmaceutical, or metal casting industries) where intermediate storage facilities and renewable resources (processing units and manpower) of limited capacity have to be observed. First, different storage configurations typical of process industries are discussed. Second, a basic scheduling problem covering the three above production modes is presented. Third, (exact and truncated) branch-and-bound methods for the basic scheduling problem and the special case of batch scheduling are proposed and subjected to an experimental performance analysis. The solution approach presented is flexible and in principle simple, and it can (approximately) solve relatively large problem instances with sufficient accuracy.

Scheduling the production of rolling ingots: Industrial context, model, and solution method

We study a real-world scheduling problem arising in the context of a rolling ingots production. First we review the production process and discuss peculiarities that have to be observed when scheduling a given set of production orders on the production facilities. We then show how to model this scheduling problem using prescribed time lags between operations, different kinds of resources, and sequence-dependent changeovers. A branch-and-bound solution procedure is presented in the second part. The basic principle is to relax the resource constraints by assuming infinite resource availability. Resulting resource conflicts are then stepwise resolved by introducing precedence relationships among operations competing for the same resources. The algorithm has been implemented as a beam search heuristic enumerating alternative sets of precedence relationships.