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.

Soft and hard tissue histologic dimensions around dental implants in the canine restored with smaller-diameter abutments: a paradigm shift in peri-implant biology

PURPOSE To evaluate the biologic width dimensions around implants with nonmatching implant-abutment diameters. MATERIALS AND METHODS Five canines had their mandibular premolars and first molars removed bilaterally and replaced with 12 implants that had nonmatching implant-abutment diameters. On one side, six implants were placed in a submerged surgical approach, and the other side utilized a nonsubmerged approach. Two of the implants on each side were placed either 1 mm above, even with, or 1 mm below the alveolar crest. Two months later, gold crowns were attached, and the dogs were sacrificed 6 months postloading. Block sections were processed for histologic and histomorphometric analyses. RESULTS The bone level, connective tissue length, epithelial dimension, and biologic width were not significantly different when the implants were initially placed in a submerged or nonsubmerged surgical approach. The bone level was significantly different around implants placed 1 mm above the crest compared to implants placed even with or 1 mm below the alveolar crest. The connective tissue dimension was not different for any implant level placement. The epithelial dimension and biologic width were significantly greater for implants placed 1 mm below the alveolar crest compared to implants placed even with or 1 mm above the alveolar crest. For five of six implant placements, connective tissue covered the implant/abutment interface. CONCLUSIONS This study reveals a fundamental change in the biologic response to implants with nonmatching implant-abutment diameters. Unlike implants with matching implant-abutment diameters, the connective tissue extended coronally past the interface (microgap). This morphologic tissue alteration represents a significant change in the biologic reaction to implant-abutment interfaces and suggests that marginal inflammation is eliminated or greatly reduced in these implant designs.

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.