Corporate planning for Asia, Latin America and Africa

It is in the broad sense of “a systematic approach to general management” that strategic planning is here compared in large corporations and Government. For, just as strategic planning is today concerned

1.

1. the development and evaluation of optional strategies;     

Supply chain management in the US and Taiwan: An empirical study

This study uses an empirical survey of middle-line managers in the US and Taiwan to study the association of supply chain management components and organizational performance. Through structural equation modeling, critical components of supply chain management are found to have considerable effects on organizational performance. The findings of the study are summarized as follows:

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Supply chain competencies have positive effects on organizational performance in both the US and Taiwan. Supply chain competencies are developed around quality and service, operations and distribution, and design effectiveness. The goal of supply chain competencies is to satisfy customer requirements.     

Deciding on ISO 14001: Economics, Institutions, and Context

ISO 14001 is an international standard for environmental management systems that was introduced in September 1996. It has gained wide recognition among businesses, much like its sister standard on quality management systems, ISO 9000. As a result, managers in almost every organization will evaluate whether the organization should become ISO 14001 certified. However, most analyses of ISO 14001 that are intended to guide managers in their evaluation have focused on the merits of ISO 14001, such as improved competitiveness, management control, and regulatory compliance. Very few articles provide a balanced picture of the costs and benefits of ISO 14001—including the conditions under which adoption will be most effective. This article redresses this gap by providing an analysis of not only why firms may choose to certify based on economic and institutional considerations, but also, when certification might be appropriate based on the firm’s context.In 1998, the Jutras division of Meridian Magnesium Inc., which manufactures magnesium automotive parts, reported that it saved almost $2 million soon after its $45,000 investment on an ISO 14001 certified environmental management system (EMS).¹ The company reduced its use of electricity, natural gas, and lubricants, while producing less solid waste and contaminated water. These were not just one-time savings; they were expected to continue into perpetuity. Not all their ISO 14001 projects were winners, however. Jutras implemented ten projects for their EMS in the first year with an initial goal of saving over $460,000 in costs. Four of the projects did not result in any savings and one had disappointing but positive results. The remaining projects, however, provided larger than expected returns. The cost savings increased the competitiveness of a firm that prides itself on being the low cost leader in an increasingly competitive automotive parts industry. The benefits to the environment were a bonus. And there was yet another bonus from ISO 14001 that had not been anticipated: the preference for ISO certified suppliers by its key customers, Ford and General Motors, and the social legitimacy earned from stakeholders pressuring for greener business practices. The company now posts its ISO 14001 certification on its web site as one of its main achievements.Although this type of vignette presents ISO 14001 in a positive light, not all firms have embraced the standard with enthusiasm. While over 22,000 facilities in 98 countries were ISO 14001 certified by December 31, 2000, many firms had decided to delay certification or reject it altogether.² The significant financial rewards realized by the Jutras Division of Meridian Magnesium have not been perceived by many of its peers, even though most analyses of ISO 14001 attempt to convince the reader that such a system is of significant strategic importance and a panacea of opportunity. Writers typically tout the potential for lower costs, increased competitiveness, market share growth, higher profits, and regulatory compliance, such as those experienced by Meridian Magnesium.³The costs of ISO 14001, however, are not trivial. Managers need to undertake a careful analysis of the relevance of ISO 14001 to their firm before they decide to jump on the ISO 14001 bandwagon. While managers can estimate the direct costs of certification with the help of good internal cost accounting, evaluating the intangible costs and benefits and the indirect impacts on the firm’s performance is more difficult. In this article, we provide background perspectives and evaluation criteria for those aspects of ISO 14001 certification, looking specifically at the marginal benefit of ISO 14001 certification over an in-house EMS. This article, then, identifies why firms may certify and in which contexts, based on economic and institutional considerations. Armed with relevant decision-making criteria, we present managers with an analytical tool to assist them in determining if ISO 14001 is appropriate for their firm.The insights provided here build on three studies:

1.

an investigation of the motivations of environmental responsiveness by interviewing members of 53 firms in the UK and Japan;⁴

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an investigation of the factors that influence the adoption of ISO 14001 based on a statistical analysis of 46 matched pairs of certified and non-certified firms and interviews with members of six firms in the US;⁵ and

3.

an investigation of the contexts that explain adoption based on interviews with 16 pulp and paper companies in Canada.⁶

Details of these studies are provided in text boxes later in this paper. While these studies form the foundation of this paper, many of the anecdotes provided here are based on published sources because the interviewees were promised complete confidentiality.     

On irreducible no-hole <Emphasis Type="Italic">L</Emphasis>(2, 1)-coloring of subdivision of graphs

An L(2, 1)-coloring (or labeling) of a graph G is a mapping \(f:V(G) \rightarrow \mathbb {Z}^{+}\bigcup \{0\}\) such that \(|f(u)-f(v)|\ge 2\) for all edges uv of G, and \(|f(u)-f(v)|\ge 1\) if u and v are at distance two in G. The span of an L(2, 1)-coloring f, denoted by span f, is the largest integer assigned by f to some vertex of the graph. The span of a graph G, denoted by \(\lambda (G)\), is min {span \(f: f\text {is an }L(2,1)\text {-coloring of } G\}\). If f is an L(2, 1)-coloring of a graph G with span k then an integer l is a hole in f, if \(l\in (0,k)\) and there is no vertex v in G such that \(f(v)=l\). A no-hole coloring is defined to be an L(2, 1)-coloring with span k which uses all the colors from \(\{0,1,\ldots ,k\}\), for some integer k not necessarily the span of the graph. An L(2, 1)-coloring is said to be irreducible if colors of no vertices in the graph can be decreased and yield another L(2, 1)-coloring of the same graph. An irreducible no-hole coloring of a graph G, also called inh-coloring of G, is an L(2, 1)-coloring of G which is both irreducible and no-hole. The lower inh-span or simply inh-span of a graph G, denoted by \(\lambda _{inh}(G)\), is defined as \(\lambda _{inh}(G)=\min ~\{\)span f : f is an inh-coloring of G}. Given a graph G and a function h from E(G) to \(\mathbb {N}\), the h-subdivision of G, denoted by \(G_{(h)}\), is the graph obtained from G by replacing each edge uv in G with a path of length h(uv). In this paper we show that \(G_{(h)}\) is inh-colorable for \(h(e)\ge 2\), \(e\in E(G)\), except the case \(\Delta =3\) and \(h(e)=2\) for at least one edge but not for all. Moreover we find the exact value of \(\lambda _{inh}(G_{(h)})\) in several cases and give upper bounds of the same in the remaining.     

Some extremal results on the colorful monochromatic vertex-connectivity of a graph

A path in a vertex-colored graph is called a vertex-monochromatic path if its internal vertices have the same color. A vertex-coloring of a graph is a monochromatic vertex-connection coloring (MVC-coloring for short), if there is a vertex-monochromatic path joining any two vertices in the graph. For a connected graph G, the monochromatic vertex-connection number, denoted by mvc(G), is defined to be the maximum number of colors used in an MVC-coloring of G. These concepts of vertex-version are natural generalizations of the colorful monochromatic connectivity of edge-version, introduced by Caro and Yuster (Discrete Math 311:1786–1792, 2011). In this paper, we mainly investigate the Erd?s–Gallai-type problems for the monochromatic vertex-connection number mvc(G) and completely determine the exact value. Moreover, the Nordhaus–Gaddum-type inequality for mvc(G) is also given.     

Nordhaus–Gaddum type result for the matching number of a graph

For a graph G, \(\alpha '(G)\) is the matching number of G. Let \(k\ge 2\) be an integer, \(K_{n}\) be the complete graph of order n. Assume that \(G_{1}, G_{2}, \ldots , G_{k}\) is a k-decomposition of \(K_{n}\). In this paper, we show that (1)

$$\begin{aligned} \left\lfloor \frac{n}{2}\right\rfloor \le \sum _{i=1}^{k} \alpha '(G_{i})\le k\left\lfloor \frac{n}{2}\right\rfloor . \end{aligned}$$

(2) If each \(G_{i}\) is non-empty for \(i = 1, \ldots , k\), then for \(n\ge 6k\),

$$\begin{aligned} \sum _{i=1}^{k} \alpha '(G_{i})\ge \left\lfloor \frac{n+k-1}{2}\right\rfloor . \end{aligned}$$

(3) If \(G_{i}\) has no isolated vertices for \(i = 1, \ldots , k\), then for \(n\ge 8k\),

$$\begin{aligned} \sum _{i=1}^{k} \alpha '(G_{i})\ge \left\lfloor \frac{n}{2}\right\rfloor +k. \end{aligned}$$

The bounds in (1), (2) and (3) are sharp. (4) When \(k= 2\), we characterize all the extremal graphs which attain the lower bounds in (1), (2) and (3), respectively.

     

Lambda number for the direct product of some family of graphs

An L(2, 1)-labeling for a graph \(G=(V,E)\) is a function f on V such that \(|f(u)-f(v)|\ge 2\) if u and v are adjacent and f(u) and f(v) are distinct if u and v are vertices of distance two. The L(2, 1)-labeling number, or the lambda number \(\lambda (G)\), for G is the minimum span over all L(2, 1)-labelings of G. When \(P_{m}\times C_{n}\) is the direct product of a path \(P_m\) and a cycle \(C_n\), Jha et al. (Discret Appl Math 145:317–325, 2005) computed the lambda number of \(P_{m}\times C_{n}\) for \(n\ge 3\) and \(m=4,5\). They also showed that when \(m\ge 6\) and \(n\ge 7\), \(\lambda (P_{m}\times C_{n})=6\) if and only if n is the multiple of 7 and conjectured that it is 7 if otherwise. They also showed that \(\lambda (C_{7i}\times C_{7j})=6\) for some i, j. In this paper, we show that when \(m\ge 6\) and \(n\ge 3\), \(\lambda (P_m\times C_n)=7\) if and only if n is not a multiple of 7. Consequently the conjecture is proved. Here we also provide the conditions on m and n such that \(\lambda (C_m\times C_n)\le 7\).     

On the b-coloring of tight graphs

A coloring c of a graph \(G=(V,E)\) is a b -coloring if for every color i there is a vertex, say w(i), of color i whose neighborhood intersects every other color class. The vertex w(i) is called a b-dominating vertex of color i. The b -chromatic number of a graph G, denoted by b(G), is the largest integer k such that G admits a b-coloring with k colors. Let m(G) be the largest integer m such that G has at least m vertices of degree at least \(m-1\). A graph G is tight if it has exactly m(G) vertices of degree \(m(G)-1\), and any other vertex has degree at most \(m(G)-2\). In this paper, we show that the b-chromatic number of tight graphs with girth at least 8 is at least \(m(G)-1\) and characterize the graphs G such that \(b(G)=m(G)\). Lin and Chang (2013) conjectured that the b-chromatic number of any graph in \(\mathcal {B}_{m}\) is m or \(m-1\) where \(\mathcal {B}_{m}\) is the class of tight bipartite graphs \((D,D{^\prime })\) of girth 6 such that D is the set of vertices of degree \(m-1\). We verify the conjecture of Lin and Chang for some subclass of \(\mathcal {B}_{m}\), and we give a lower bound for any graph in \(\mathcal {B}_{m}\).     

On the <Emphasis Type="Italic">L</Emphasis>(2, 1)-labeling conjecture for brick product graphs

Let \(G=(V, E)\) be a graph. Denote \(d_G(u, v)\) the distance between two vertices u and v in G. An L(2, 1)-labeling of G is a function \(f: V \rightarrow \{0,1,\ldots \}\) such that for any two vertices u and v, \(|f(u)-f(v)| \ge 2\) if \(d_G(u, v) = 1\) and \(|f(u)-f(v)| \ge 1\) if \(d_G(u, v) = 2\). The span of f is the difference between the largest and the smallest number in f(V). The \(\lambda \)-number \(\lambda (G)\) of G is the minimum span over all L(2, 1)-labelings of G. In this paper, we conclude that the \(\lambda \)-number of each brick product graph is 5 or 6, which confirms Conjecture 6.1 stated in Li et al. (J Comb Optim 25:716–736, 2013).     

Edge-disjoint spanning trees and the number of maximum state circles of a graph

Motivated by the connection with the genus of unoriented alternating links, Jin et al. (Acta Math Appl Sin Engl Ser, 2015) introduced the number of maximum state circles of a plane graph G, denoted by \(s_{\max }(G)\), and proved that \(s_{\max }(G)=\max \{e(H)+2c(H)-v(H)|\) H is a spanning subgraph of \(G\}\), where e(H), c(H) and v(H) denote the size, the number of connected components and the order of H, respectively. In this paper, we show that for any (not necessarily planar) graph G, \(s_{\max }(G)\) can be achieved by the spanning subgraph H of G whose each connected component is a maximal subgraph of G with two edge-disjoint spanning trees. Such a spanning subgraph is proved to be unique and we present a polynomial-time algorithm to find such a spanning subgraph for any graph G.     

A note on (<Emphasis Type="Italic">s</Emphasis>, <Emphasis Type="Italic">t</Emphasis>)-relaxed <Emphasis Type="Italic">L</Emphasis>(2, 1)-labeling of graphs

Let \(G=(V, E)\) be a graph. For two vertices u and v in G, we denote \(d_G(u, v)\) the distance between u and v. A vertex v is called an i-neighbor of u if \(d_G(u,v)=i\). Let s, t and k be nonnegative integers. An (s, t)-relaxed k-L(2, 1)-labeling of a graph G is an assignment of labels from \(\{0, 1, \ldots , k\}\) to the vertices of G if the following three conditions are met: (1) adjacent vertices get different labels; (2) for any vertex u of G, there are at most s 1-neighbors of u receiving labels from \(\{f(u)-1,f(u)+1\}\); (3) for any vertex u of G, the number of 2-neighbors of u assigned the label f(u) is at most t. The (s, t)-relaxed L(2, 1)-labeling number \(\lambda _{2,1}^{s,t}(G)\) of G is the minimum k such that G admits an (s, t)-relaxed k-L(2, 1)-labeling. In this article, we refute Conjecture 4 and Conjecture 5 stated in (Lin in J Comb Optim. doi: 10.1007/s10878-014-9746-9, 2013).     

Planar graphs without 4-cycles and close triangles are (2, 0, 0)-colorable

For a set of nonnegative integers \(c_1, \ldots , c_k\), a \((c_1, c_2,\ldots , c_k)\)-coloring of a graph G is a partition of V(G) into \(V_1, \ldots , V_k\) such that for every i, \(1\le i\le k, G[V_i]\) has maximum degree at most \(c_i\). We prove that all planar graphs without 4-cycles and no less than two edges between triangles are (2, 0, 0)-colorable.