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.

Long-term clinical, microbiological, and radiographic outcomes of Brånemark™ implants installed in augmented maxillary bone for fixed full-arch rehabilitation

PURPOSE The purpose of this study was to document the long-term outcome of Brånemark implants installed in augmented maxillary bone and to identify parameters that are associated with peri-implant bone level. MATERIAL AND METHODS Patients of a periodontal practice who had been referred to a maxillofacial surgeon for iliac crest bone grafting in the atrophic maxilla were retrospectively recruited. Five months following grafting, they received 7-8 turned Brånemark implants. Following submerged healing of another 5 months, implants were uncovered and restorative procedures for fixed rehabilitation were initiated 2-3 months thereafter. The primary outcome variable was bone level defined as the distance from the implant-abutment interface to the first visible bone-to-implant contact. Secondary outcome variables included plaque index, bleeding index, probing depth, and levels of 40 species in subgingival plaque samples as identified by means of checkerboard DNA-DNA hybridization. RESULTS Nine out of 16 patients (eight females, one male; mean age 59) with 71 implants agreed to come in for evaluation after on average 9 years (SD 4; range 3-13) of function. One implant was deemed mobile at the time of inspection. Clinical conditions were acceptable with 11% of the implants showing pockets ≥ 5 mm. Periodontopathogens were encountered frequently and in high numbers. Clinical parameters and bacterial levels were highly patient dependent. The mean bone level was 2.30 mm (SD 1.53; range 0.00-6.95), with 23% of the implants demonstrating advanced resorption (bone level > 3 mm). Regression analysis showed a significant association of the patient (p < .001) and plaque index (p = .007) with bone level. CONCLUSIONS The long-term outcome of Brånemark implants installed in iliac crest-augmented maxillary bone is acceptable; however, advanced peri-implant bone loss is rather common and indicative of graft resorption. This phenomenon is patient dependent and seems also associated with oral hygiene.