Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w_j and a profit p_j. The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.     

The Knapsack Sharing Problem: An Exact Algorithm

In this paper, we propose an exact algorithm for the knapsack sharing problem. The proposed algorithm seems quite efficient in the sense that it solves quickly some large problem instances. The problem is decomposed into a series of single constraint knapsack problems; and by applying the dynamic programming and another strategy, we solve optimally the original problem. The performance of the exact algorithm is evaluated on a set of medium and large problem instances (a total of 240 problem instances). This algorithm is parallelizable and this is one of its important feature.     

Suicide reports in the news – impact of Chief Coroner's call to open up suicide reporting

ABSTRACT

Aim: In 2010, the then Chief Coroner called for an opening up of suicide reporting in the press. We aimed to discover if this controversial action influenced the nature and extent of reporting of individual suicide cases in the newsprint media.

Method: A Factiva search of news reports from high circulation newspapers was conducted over four years. We counted the number of news reports of individual suicides and examined any mention of demographics, methods, location and contributing factors.

Results: We retrieved 291 individual suicide reports, 161 before and 130 after the Chief Coroners’ call. Reporting was more detailed after the call, with increased reporting of demographics, contributing factors and methods but less reporting of location. Most of these differences did not reach statistical significance.

Conclusion: The press did not appear to take the action of the Chief Coroner as a licence to report more frequently on individual suicide cases.     

Targeting the worst-off for free health care: a process evaluation in Burkina Faso

Effective mechanisms to exempt the indigent from user fees at health care facilities are rare in Africa. A State-led intervention (2004-2005) and two action research projects (2007-2010) were implemented in a health district in Burkina Faso to exempt the indigent from user fees. This article presents the results of the process evaluation of these three interventions. Individual and group interviews were organized with the key stakeholders (health staff, community members) to document the strengths and weaknesses of key components of the interventions (relevance and uptake of the intervention, worst-off selection and information, financial arrangements). Data was subjected to content analysis and thematic analysis. The results show that all three intervention processes can be improved. Community-based targeting was better accepted by the stakeholders than was the State-led intervention. The strengths of the community-based approach were in clearly defining the selection criteria, informing the waiver beneficiaries, using a participative process and using endogenous funding. A weakness was that using endogenous funding led to restrictive selection by the community. The community-based approach appears to be the most effective, but it needs to be improved and retested to generate more knowledge before scaling up.     

Sojourn time in an M/M/1 processor sharing queue with permanent customers

We explicitly compute the sojourn time distribution of an arbitrary customer in an M/M/1 processor sharing (PS) queue with permanent customers. We notably exhibit the orthogonal structure associated with this queuing system and we show how sieved Pollaczek polynomials and their associated orthogonality measure can be used to obtain an explicit representation for the complementary cumulative distribution function of the sojourn time of a customer. This explicit formula subsequently allows us to compute the two first moments of this random variable and to study the asymptotic behavior of its distribution. The most salient result is that the decay rate depends on the load of the system and the number K of permanent customers. When the load is above a certain threshold depending on K, the decay rate is identical to that of a regular M/M/1 PS queue.