It is increasingly recognized that material surface topography is able to evoke specific cellular responses, endowing materials with instructive properties that were formerly reserved for growth factors. This opens the window to improve upon, in a cost-effective manner, biological performance of any surface used in the human body. Unfortunately, the interplay between surface topographies and cell behavior is complex and still incompletely understood. Rational approaches to search for bioactive surfaces will therefore omit previously unperceived interactions. Hence, in the present study, we use mathematical algorithms to design nonbiased, random surface features and produce chips of poly(lactic acid) with 2,176 different topographies. With human mesenchymal stromal cells (hMSCs) grown on the chips and using high-content imaging, we reveal unique, formerly unknown, surface topographies that are able to induce MSC proliferation or osteogenic differentiation. Moreover, we correlate parameters of the mathematical algorithms to cellular responses, which yield novel design criteria for these particular parameters. In conclusion, we demonstrate that randomized libraries of surface topographies can be broadly applied to unravel the interplay between cells and surface topography and to find improved material surfaces.

We consider a model for scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to traditional stochastic scheduling models, we assume that jobs arrive online, and there is no knowledge about the jobs that will arrive in the future. The model incorporates both stochastic scheduling and online scheduling as a special case. The particular setting we consider is nonpreemptive parallel machine scheduling, with the objective to minimize the total weighted completion times of jobs. We analyze simple, combinatorial online scheduling policies for that model, and derive performance guarantees that match performance guarantees previously known for stochastic and online parallel machine scheduling, respectively. For processing times that follow new better than used in expectation (NBUE) distributions, we improve upon previously best-known performance bounds from stochastic scheduling, even though we consider a more general setting.

We consider the problem to minimize the total weighted completion time of a set of jobs with individual release dates which have to be scheduled on identical parallel machines. Job processing times are not known in advance, they are realized on-line according to given probability distributions. The aim is to find a scheduling policy that minimizes the objective in expectation. Motivated by the success of LP-based approaches to deterministic scheduling, we present a polyhedral relaxation of the performance space of stochastic parallel machine scheduling. This relaxation extends earlier relaxations that have been used, among others, by Hall et al. [1997] in the deterministic setting. We then derive constant performance guarantees for priority policies which are guided by optimum LP solutions, and thereby generalize previous results from deterministic scheduling. In the absence of release dates, the LP-based analysis also yields an additive performance guarantee for the WSEPT rule which implies both a worst-case performance ratio and a result on its asymptotic optimality, thus complementing previous work by Weiss [1990]. The corresponding LP lower bound generalizes a previous lower bound from deterministic scheduling due to Eastman et al. [1964], and exhibits a relation between parallel machine problems and corresponding problems with only one fast single machine. Finally, we show that all employed LPs can be solved in polynomial time by purely combinatorial algorithms.

In project scheduling, a set of precedence-constrained jobs has to be scheduled so as to minimize a given objective. In resource-constrained project scheduling, the jobs additionally compete for scarce resources. Due to its universality, the latter problem has a variety of applications in manufacturing, production planning, project management, and elsewhere. It is one of the most intractable problems in operations research, and has therefore become a popular playground for the latest optimization techniques, including virtually all local search paradigms. We show that a somewhat more classical mathematical programming approach leads to both competitive feasible solutions and strong lower bounds, within reasonable computation times. The basic ingredients of our approach are the Lagrangian relaxation of a time-indexed integer programming formulation and relaxation-based list scheduling, enriched with a useful idea from recent approximation algorithms for machine scheduling problems. The efficiency of the algorithm results from the insight that the relaxed problem can be solved by computing a minimum cut in an appropriately defined directed graph. Our computational study covers different types of resource-constrained project scheduling problems, based on several notoriously hard test sets, including practical problem instances from chemical production planning.

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the processing times of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. By means of a novel time-indexed linear programming relaxation, we show how to compute in polynomial time a scheduling policy with provable performance guarantee for the stochastic version of the unrelated parallel machine scheduling problem with the weighted sum of completion times objective. Our performance guarantee depends on the squared coefficient of variation of the processing times and we show that this dependence is tight. Currently best-known bounds for deterministic scheduling problems are contained as special cases.