A note on the lower bound for online strip packing

This note presents a lower bound of $3/2+\sqrt{33}/6 \approx 2.457$ on the competitive ratio for online strip packing. The instance construction we use to obtain the lower bound was first coined by Brown, Baker and Katseff (1980). Recently this instance construction is used to improve the lower bound in computer aided proofs. We derive the best possible lower bound that can be obtained with this instance construction

Time-constrained project scheduling

We study the Time-Constrained Project Scheduling Problem (TCPSP), in which the scheduling of activities is subject to strict deadlines. To be able to meet these deadlines, it is possible to work in overtime or hire additional capacity in regular time or overtime. For this problem, we develop a two stage heuristic. The key of our approach lies in the first stage in which we construct partial schedules with a randomized sampling technique. In these partial schedules, jobs may be scheduled for a shorter duration than required. The second stage uses an ILP formulation of the problem to turn a partial schedule into a feasible schedule, and to perform a neighbourhood search. The developed heuristic is quite flexible and, therefore, suitable for practice. We present experimental results on modified RCPSP benchmark instances. The two stage heuristic solves many instances to optimality, and if we substantially decrease the deadline, the rise in cost is only small

Time-constrained project scheduling with adjacent resources

We develop a decomposition method for the Time-Constrained Project Scheduling Problem (TCPSP) with Adjacent Resources. For adjacent resources the resource units are ordered and the units assigned to a job have to be adjacent. On top of that, adjacent resources are not required by single jobs, but by job groups. As soon as a job of such a group starts, the adjacent resource units are occupied, and they are not released before all jobs of that group are completed. The developed decomposition method separates the adjacent resource assignment from the rest of the scheduling problem. Test results demonstrate the applicability of the decomposition method. The presented decomposition forms a first promising approach for the TCPSP with adjacent resources and may form a good basis to develop more elaborated methods

Decomposition method for project scheduling with spatial resources

Project scheduling problems are in practice often restricted by a limited availability of spatial resources. In this paper we develop a decomposition method for the Time-Constrained Project Scheduling Problem (TCPSP) with Spatial Resources. Spatial resources are resources that are not required by single activities, but by activity groups. As soon as an activity of such a group starts, the spatial resource units are occupied, and they are not released before all activities of that group are completed. On top of that, the spatial resource units that are assigned to a group have to be adjacent. The developed decomposition method separates the spatial resource assignment from the rest of the scheduling problem. Test results demonstrate the applicability of the decomposition method. The presented decomposition forms a first promising approach for the TCPSP with spatial resources and may form a good basis to develop more elaborate methods

Shunting passenger trains : getting ready for departure

In this paper we consider the problem of shunting train units on a railway station. Train units arrive at and depart from the station according to a given train schedule and in between the units may have to be stored at the station. The assignment of arriving to departing train units (called matching) and the scheduling of the movements to realize this matching is called shunting. The goal is to realize the shunting using a minimal number of shunt movements. For a restricted version of this problem an ILP approach has been presented in the literature. In this paper, we consider the general shunting problem and derive a greedy heuristic approach and an exact solution method based on dynamic programming. Both methods are flexible in the sense that they allow the incorporation of practical planning rules and may be extended to cover additional requirements from practice

Pioglitazone improves cardiac function and alters myocardial substrate metabolism without affecting cardiac triglyceride accumulation and high-energy phosphate metabolism in patients with well-controlled type 2 diabetes mellitus

0.001). CONCLUSIONS: In T2DM patients, pioglitazone was associated with improvement in some measures of left ventricular diastolic function, myocardial glucose uptake, and whole-body insulin sensitivity. The functional changes, however, were not associated with myocardial substrate and high-energy phosphate metabolis