An investigation of heuristic decomposition to tackle workforce scheduling and routing with time-dependent activities constraints

This paper presents an investigation into the application of heuristic decomposition and mixed-integer programming to tackle workforce scheduling and routing problems (WSRP) that involve timedependent activities constraints. These constraints refer to time-wise dependencies between activities. The decomposition method investigated here is called repeated decomposition with con ict repair (RDCR) and it consists of repeatedly applying a phase of problem decomposition and sub-problem solving, followed by a phase dedicated to con ict repair. In order to deal with the time-dependent activities constraints, the problem decomposition puts all activities associated to the same location and their dependent activities in the same sub-problem. This is to guarantee the satisfaction of time-dependent activities constraints as each sub-problem is solved exactly with an exact solver. Once the assignments are made, the time windows of dependent activities are fixed even if those activities are subject to the repair phase. The paper presents an experimental study to assess the performance of the decomposition method when compared to a tailored greedy heuristic. Results show that the proposed RDCR is an effective approach to harness the power of mixed integer programming solvers to tackle the diffcult and highly constrained WSRP in practical computational time. Also, an analysis is conducted in order to understand how the performance of the different solution methods (the decomposition, the tailored heuristic and the MIP solver) is accected by the size of the problem instances and other features of the problem. The paper concludes by making some recommendations on the type of method that could be more suitable for different problem sizes

Existence and uniqueness of solutions for first-order nonlinear differential equations with two-point and integral boundary conditions

In this article, we study the existence of solutions to boundary-value problems for ordinary differential equations with two-point and integral boundary conditions. Existence and uniqueness results are obtained by using well known fixed point theorems. Some illustrative examples are also discussed

Improved calculation of the slot leakage inductance of different slot shapes

The slot leakage inductance calculation is an important element of the electric machine’s design. The empirical definitions are described in the literature and widely used until today. The crucial parameter is the slot permeance factor which defines the influence of slot dimensions on the leakage inductance. The traditional approach to the slot leakage inductance calculation is used in this paper, but improved flux line length and active slot area calculation are presented. The main objective of the paper is the definition of relatively simple relation to the calculation of the slot permeance factor and comparison with the finite element calculation and literature-based equations. Therefore, an overview of different slot types is presented in this paper, and obtained results are in general more reliable than literature-related relations based on the finite element validation

Effect of scattered-site housing using rent supplements and intensive case management on housing stability among homeless adults with mental illness: A randomized trial

IMPORTANCE Scattered-site housing with Intensive Case Management (ICM) may be an appropriate and less-costly option for homeless adults with mental illness who do not require the treatment intensity of Assertive Community Treatment. OBJECTIVE To examine the effect of scattered-site housing with ICM services on housing stability and generic quality of life among homeless adults with mental illness and moderate support needs for mental health services. DESIGN, SETTING, AND PARTICIPANTS The At Home/Chez Soi projectwas an unblinded, randomized trial. From October 2009 to July 2011, participants (N = 1198) were recruited in 4 Canadian cities (Vancouver, Winnipeg, Toronto, and Montreal), randomized to the intervention group (n = 689) or usual care group (n = 509), and followed up for 24 months. INTERVENTIONS The intervention consisted of scattered-site housing (using rent supplements) and off-site ICM services. The usual care group had access to existing housing and support services in their communities. MAIN OUTCOMES AND MEASURES The primary outcome was the percentage of days stably housed during the 24-month period following randomization. The secondary outcome was generic quality of life, assessed by a EuroQoL 5 Dimensions (EQ-5D) health questionnaire. RESULTS During the 24 months after randomization, the adjusted percentage of days stably housedwas higher among the intervention group than the usual care group, although adjusted mean differences varied across sites. The mean change in EQ-5D score from baseline to 24 months among the intervention group was not statistically different from the usual care group (60.5 [95%CI, 58.6 to 62.5] at baseline and 67.2 [95%CI, 65.2 to 69.1] at 24 months for the intervention group vs 62.1 [95% CI, 59.9 to 64.4] at baseline and 68.6 [95%CI, 66.3 to 71.0] at 24 months for the usual care group, difference in mean changes, 0.10 [95%CI, −2.92 to 3.13], P=.95). CONCLUSIONS AND RELEVANCE Among homeless adults with mental illness in 4 Canadian cities, scattered site housing with ICM services compared with usual access to existing housing and community services resulted in increased housing stability over 24 months, but did not improve generic quality of life.This research has been made possible through a financial contribution from Health Canada