Minimizing the number of tardy jobs in two-machine settings with common due date

We consider two-machine scheduling problems with job selection. We analyze first the two-machine open shop problem and provide a best possible linear time algorithm. Then, a best possible linear time algorithm is derived for the job selection problem on two unrelated parallel machines. We also show that an exact approach can be derived for both problems with complexity \(O(p(n) \times \sqrt{2}^n)\), p being a polynomial function of n.     

The thickness of the complete multipartite graphs and the join of graphs

The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is known for relatively few classes of graphs, compared to other topological invariants, e.g., genus and crossing number. For the complete bipartite graphs, Beineke et al. (Proc Camb Philos Soc 60:1–5, 1964) gave the answer for most graphs in this family in 1964. In this paper, we derive formulas and bounds for the thickness of some complete k-partite graphs. And some properties for the thickness for the join of two graphs are also obtained.     

Hamiltonian numbers in oriented graphs

A hamiltonian walk of a digraph is a closed spanning directed walk with minimum length in the digraph. The length of a hamiltonian walk in a digraph D is called the hamiltonian number of D, denoted by h(D). In Chang and Tong (J Comb Optim 25:694–701, 2013), Chang and Tong proved that for a strongly connected digraph D of order n, \(n\le h(D)\le \lfloor \frac{(n+1)^2}{4} \rfloor \), and characterized the strongly connected digraphs of order n with hamiltonian number \(\lfloor \frac{(n+1)^2}{4} \rfloor \). In the paper, we characterized the strongly connected digraphs of order n with hamiltonian number \(\lfloor \frac{(n+1)^2}{4} \rfloor -1\) and show that for any triple of integers n, k and t with \(n\ge 5\), \(n\ge k\ge 3\) and \(t\ge 0\), there is a class of nonisomorphic digraphs with order n and hamiltonian number \(n(n-k+1)-t\).     

An optimal online algorithm for the parallel-batch scheduling with job processing time compatibilities

We consider the online (over time) scheduling on a single unbounded parallel-batch machine with job processing time compatibilities to minimize makespan. In the problem, a constant \(\alpha >0\) is given in advance. Each job \(J_{j}\) has a normal processing time \(p_j\). Two jobs \(J_i\) and \(J_j\) are compatible if \(\max \{p_i, p_j\} \le (1+\alpha )\cdot \min \{p_i, p_j\}\). In the problem, mutually compatible jobs can form a batch being processed on the machine. The processing time of a batch is equal to the maximum normal processing time of the jobs in this batch. For this problem, we provide an optimal online algorithm with a competitive ratio of \(1+\beta _\alpha \), where \(\beta _\alpha \) is the positive root of the equation \((1+\alpha )x^{2}+\alpha x=1+\alpha \).     

Executive remuneration standards and the “conformity gap” at controlled corporations

In this paper we analyze the relationship between conformity to executive remuneration standards, corporate ownership, and the level and structure of CEO compensation for large European listed companies in the years 2007 and 2010. We show that controlled corporations conform to executive remuneration standards less than widely held firms. We also show that weaker compliance is associated with lower CEO pay and more cash-based incentive structures. We interpret this “conformity gap” from the perspective of individual firms and from a societal perspective, with the aim to contribute to frame the policy questions concerning executive pay at controlled corporations. Different policy implications depend on whether the conformity gap reflects a lower need for managerial incentives, given the monitoring by controlling shareholders, or the latter’s willingness to extract private benefits of control. We argue in this paper that the former hypothesis prevails, so that regulators should abstain from increasing the level of enforcement of executive remuneration standards.     

A lower bound for the adaptive two-echelon capacitated vehicle routing problem

Adaptive two-echelon capacitated vehicle routing problem (A2E-CVRP) proposed in this paper is a variant of the classical 2E-CVRP. Comparing to 2E-CVRP, A2E-CVRP has multiple depots and allows the vehicles to serve customers directly from the depots. Hence, it has more efficient solution and adapt to real-world environment. This paper gives a mathematical formulation for A2E-CVRP and derives a lower bound for it. The lower bound is used for deriving an upper bound subsequently, which is also an approximate solution of A2E-CVRP. Computational results on benchmark instances show that the A2E-CVRP outperforms the classical 2E-CVRP in the costs of routes.     

The no-wait job shop with regular objective: a method based on optimal job insertion

The no-wait job shop problem (NWJS-R) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is prescribed. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The problem consists in finding a schedule that minimizes a general regular objective function. We study the so-called optimal job insertion problem in the NWJS-R and prove that this problem is solvable in polynomial time by a very efficient algorithm, generalizing a result we obtained in the case of a makespan objective. We then propose a large neighborhood local search method for the NWJS-R based on the optimal job insertion algorithm and present extensive numerical results that compare favorably with current benchmarks when available.     

The Global Wave of Refugees and Migrants: Complex Challenges for European Policy Makers

This article reviews the burdensome problem posed by the arrival in the European countries of large number of refugees and migrants from countries at war or with little economic opportunities. It differentiates the issues of migrants (for economic reasons) and refugees (humanitarian grounds). This wave of refugees currently poses huge challenges to European policy makers. The article suggests some policy initiatives that could solve or at least control the present chaos, disorder, and uncertainty created by the arrival of this unprecedented number of refugees.     

‘Strong Personalities’ and ‘Strong Institutions’ Mediated by a ‘Strong Third Force’: Thinking ‘Systems’ in Corruption Control

Corruption in public sector is a complex, ‘messy’ and ‘fuzzy’ phenomenon which involves calculus machinations between actors and constantly growing in sophistication. Consequently, an attempt to prevent, control or fight it requires systems thinking that ranges from public officials with integrity and personal ethics [strong personalities]; administrative rules and procedures as well as governments adopting, enforcing and monitoring appropriate systems [strong institutions]. This paper provides a systems approach to enhancing public sector ethics through ‘a corruption control tripod’ in preventing, controlling and combating corruption in all its forms. This framework discusses three overarching pillars and argues that adopting a reductionist approach in corruption control would yield futility; there is a need for synthesis so that each one would reinforce the other.     

Strategic Planning in the Malawi Public Sector: Potential Tool for Progress or Regression?

The process of developing strategic plans in the public sector is regarded as one indicator of positive reform in the system. The assumption is that strategic planning ensures that (just like in the private sector) public sector organizations’ operations should cost less but deliver better service. Ultimately the argument is that public sector institutional governance and responsiveness to the citizenry is not only seen but felt. However, strategic planning has to be done in an appropriate manner for it to deliver. For instance an analysis of the underlying motives, the role of leadership in the process as well as the relevance or viability of the guiding strategic planning model significantly affect the nature of expected results. In the early 2000s, the Malawi public sector embarked on a serious drive towards strategic planning process as part of its reform package. In order to ascertain it’s potential to transform the Malawi public service, this paper focuses at critically analyzing the strategic planning process in the Malawi public sector by among other things asking: who initiated and led the process? What approach determined the process? What is the possible potentiality of the adopted strategic planning approach in enhancing the reform agenda in Malawi? Based on interviews with senior officers in key Malawi public sector institutions, the paper concludes that the strategic planning process is ‘transitional and fluid’ hence lacks the clout to effectively enhance reforms in this sector. Another finding is that lack of effective leadership has largely contributed to the status quo.