Logistics Decision Making & Aapplied Maths

M a t h e m a t i c aB a l k a n i c a

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NewSeries Vol. 21, 2007, Fasc. 3-4

Logistics Decision Making & Aapplied Maths

George Malindretos

Presented at the MASSEE International Congress on Mathematics

MICOM - 2006, Cyprus

This article focuses on the problem of choice of method at corporation level, forperformance-based Logistics, in view of the paramount adjustment requirements to the newand ever changing technological and business environment. The research aims at erasing aseries of misconceptions, which prevent understanding of the involved costs and expected ben-efits, and, consequently, aggravate the problem. Special attention is attributed to sufficientknowledge and correct use of Maths, mathematical sets theory and Logistics models. Logisticsfollowed rapid advance and diffusion in recent years to a suite of modelling systems in strate-gic, tactical and operational planning. The articulating and modelling with use of modernmathematical techniques and the unprecedented growth in modelling, notably the NetworkInformation Technology (NIT), have contributed to the advance of Logistics in Supply ChainManagement (SCM) and furthermore in Supply Chain Re-engineering (SCR). The integratedsystem approach of Logistics and its two main components, corporation planning and through-out re-organization in processes, are presented as catalysts to value creation and competitiveadvantage. Finally, reference is made to conditions of not equal chances for introducing Logis-tics in SMEs.

Key Words: Mathematics (Maths). Logistics. Supply Chain Management (SCM).

Network Information Technology (NIT). Modern Scientific Methodology (MSM). Indepen-

dent Management Units (IMUs). Decision Support Methods (DSMs). Integrated Logistics

Approach (ILA). Logistics Systems Analysis (LSA). Models. Systems Thinking (ST). Third

Party Logistics (3PL)

Recording of the new irreversible corporation environment

TA historical challenge that the new millennium inherited is the adjust-ment to an entirely new landscape of corporation environment and new informa-tion technologies. The corporation environment has rapidly changed, especiallyduring the last quarter of the 20th century, following a shift of economic policies

260 G. Malindretos

in 70ies, a trend to globalisation of markets and trade since Eastern EuropeanCountries entered the market and the economy of China opened to foreign trade.

A widely accepted definition of Logistics as ’the process of managing theflow of materials and information through the enterprise with the aim to pro-vide the best customer service in the shortest available time and at the lowestcost’ (Rushton & Oxley 1989) reflects the difficulties in introducing Logistics,although ’most companies throughout the world have embraced them’. Scat-tered Logistics activities were used separately long back to history, mainly inpublic facilities, in warehousing of important local commodities and in freighttransportation. The rapid extension of Logistics was supported by the advance-ment of mathematical techniques, initiated by operational research, linear pro-gramming and activity analysis, increasing use of algorisms, heuristics, agilesimulation models, etc. In addition, the technological progress and particularly’Network Information Technology’ (NIT) has contributed to Logistics advanceand diffusion.

The abovementioned developments followed a new international mone-tary system established by the end of the World War II, with pegging of US$ to gold, promoted international trade, along with the creation of a series ofinternational economic organizations. Such a framework of international corpo-ration environment facilitated the ’automation technology revolution’, the ’massproduction’ and the ’consumer society’, along with a policy choice concerningincome distribution and welfare.

During 70ies, there has been a major shift in economic policy to facethe problem of ’stagflation’, with a new reform of the international monetarysystem, overall liberalization of markets and trade, emphasis to the supply side,corporate investment and innovation, absorption of the increase in oil pricesby two oil crises (1973 and 1978), etc. The policy shift to the ’supply sideeconomics’ and to ’supply management’ incorporated a different philosophy andnew ideas, characterized as ’big-bang’ in accordance with the new approach ofchaos in physics, the breaking of atom, and the continuous transformation ofmaterial/energy, the Einstein relativity rule and the quantum theory. Thesechanges altogether have contributed to the advancement of Logistics in the socalled ’Supply Chain Management’ (SCM), and further in ’Business ProcessRe-engineering’ (BPR) and ’Supply Chain Re-engineering’ (SCR), along withconvergence of macroeconomics with microeconomics (Chopra and Meindl 2001;Malindretos 2001; Bowersox, Closs, Cooper 2002; Ballou 2004).

During 70ies, there has been a major shift in economic policy to facethe problem of ’stagflation’, with a new reform of the international monetarysystem, overall liberalization of markets and trade, emphasis to the supply side,

Logistics Decision Making & Aapplied Maths 261

corporate investment and innovation, absorption of the increase in oil pricesby two oil crises (1973 and 1978), etc. The policy shift to the ’supply sideeconomics’ and to ’supply management’ incorporated a different philosophy andnew ideas, characterized as ’big-bang’ in accordance with the new approach ofchaos in physics, the breaking of atom, and the continuous transformation ofmaterial/energy, the Einstein relativity rule and the quantum theory. Thesechanges altogether have contributed to the advancement of Logistics in the socalled ’Supply Chain Management’ (SCM), and further in ’Business ProcessRe-engineering’ (BPR) and ’Supply Chain Re-engineering’ (SCR), along withconvergence of macroeconomics with microeconomics (Chopra and Meindl 2001;Malindretos 2001; Bowersox, Closs, Cooper 2002; Ballou 2004).

No doubt, there is some dynamic interface among science, technology,research and corporate practices. However, it is misleading to conclude thatthere is not any difficult adjustment problem, because the advance of scienceand technology offers just chances for problem solving. Only if adjustment inter-ventions were mechanical, there would be no point for alert. The vital challengeof corporation adjustment drives to revisiting of the methodology issue.

Scientific Methodology

Obviously, since the adjustment will be carried out at corporation level,the applied research and planning must be carefully approached, using all theavailable knowledge and know-how infrastructure, with interdisciplinary collab-oration of relevant scientific disciplines. It is useful for this purpose to overcomea series of misconceptions, confusion and attitudes connected with different con-ditions in the past. The new research framework has to give a drive that willbe adjustable to particular corporation conditions. No sufficient understandingof the new corporation environment prevents the right use of Maths and Lo-gistics in the initiatives of adjustment to it. Particularly, mathematical toolshave been used in solving human problems for thousands of years. Nevertheless,the formal study and application of ’quantitative techniques’ to decision-makingin economics and business is essentially a product of the 20th century. Mathsused chiefly in economic theory, originating from Leon Walras in 19th century.Main turning points in the use of Maths for corporation problems solving, werethe ’scientific management’, founded by Frederick W. Taylor in early 1900s,and the so-called ’keynesian revolution’, first appeared in 1936 (John MaynardKeynes). Construction of public infrastructure and of residential building thatrequire good technological knowledge and topology in mathematical sense wereimproved tremendously with the rapid technology and Maths advance (Winston1995).

262 G. Malindretos

It is questionable whether the dominating conventional scientific method-ology (CSM) accommodates sufficiently the new corporate research require-ments. Because, it has been observed that science, in the effort to interpretactual problems theoretically, had not paid enough attention to the methodologyitself. Thus, the compartmentization of the social science disciplines has beenfounded on conventional assumptions of single causation, partial, marginalisticapproach, etc., which are overidentified and lead in practice to indeterminacy.

It has been observed that in phases of major structural transformations,it is advisable to go back to the ’frontiers of knowledge’ (see e.g., Wilson 1952;Kuhn 1962). Therefore, research has to depart from ’zero start’, keeping in mindthe fundamentals of the actual corporate system and of structural changes, thequalitative and quantitative factors incorporated, the system integration anddynamics, etc. (Metzer & Kahn 1995; Brewerton & Millward 2001; Cooper& Schindler 2003; Saunders et al. 2003). Recording and assessing the actualnew corporate environment have to be based on genuine objective criteria, sothat to achieve unbiased estimates of the adjustment cost and the expectedbenefits, in terms of corporate performance and competitiveness (feasibilitycost/benefit analysis). The understanding of the combined utilization of knowl-edge infrastructure of Maths and of the new technologies is not that easy (Dirk& Vaart 2005).

Methods are the most valuable riches, as Nietzsche said. Understand-ing the methodology is helpful, though there are hardly any publications onmethodological questions in the field of the supply chain management (Seuringet al. 2005). Research importance calls for more scientific attitude of decisionmakers, whereas intuition plays significant role in human thinking and actions.Methodologies to support the problem of decision making, have developed de-tailed processes with strong emphasis on planning, inspired by other engineeringdisciplines - often referred as ’engineering methodologies’. Engineering method-ologies have been around for a long time, but they have not been terribly suc-cessful. They are even less noted for being popular. The most frequent criticismof these methodologies is that they represent conventional planning and designand are bureaucratic.

As a reaction to these methodologies, a new group of methodologies haveappeared more recently. For a while these were known as lightweight method-ologies, but now the accepted term is ’agile methodologies’ (Fowler 2003). Formany people, the appeal of them is their opposition to the bureaucracy of themonumental methodologies and the CSM. The new research approaching is flex-ible and adjustable, welcome to change, people oriented and attempts a usefulcompromise between absence and exaggeration of processes, to gain a reasonable


payoff. In brief, the comparison of ordinary engineering and agile methodologyis made in terms of separation of design and construction.

The engineering methodology looks closer to the conventional researchmethodology, which does not seem to conform to the requirements of ModernScientific Methodology (Flynn et al. 1991; Metzer & Kahn 1995; Malindretos2001). MSM focuses on multiple criteria decision support methods (DSMs),etc. in converging the agile methodology and the Logistics process analysis, byheuristics, algorithms, simulation techniques, etc.

Survey Methodology focuses on the development and evaluation of tech-niques used in data collection and interpretation, and has been a source of keyinformation on statistical methods for over 30 years. Topics include: funda-mental research in survey methodology; sampling issues; design in the contextof practical constraints; use of different data sources and collection techniques;survey evaluation; time series analysis; seasonal adjustment; data configurationand analysis methods; etc.

The MSM thinking provides a state-of-the-art for supporting quantitativedecision making applied in Logistics. DSMs use computer-based techniques andtools for assist solving complex Logistics problems (Ives 1994). The research fo-cus is on building a practical and theoretical knowledge framework for rational,managerial decision making, by collective action of researchers skills, engineers,Logistics managers, and policy makers. Because, most software developmenthas been a chaotic activity, without much of an underlying plan, so that thedesign of a system is cobbled together from many short-term decisions. Thisactually works pretty well as the system is small, but as the system grows itbecomes increasingly difficult to add new features to the system. Furthermore,bugs become increasingly prevalent and difficult to fix. A typical practice isa long test drive phase after the system is ’feature complete’. Such long testphase plays havoc with schedules, as testing and debugging is difficult to sched-ule. Living with this style of development for a long time, we have had analternative: methodology. Methodologies assist a disciplined process upon soft-ware development with the aim of making it more predictable and more efficient(Fowler 2003).

Modern Logistics apply quantitative methods, including econometrics,simulation modelling, and management science analytical techniques, to evalu-ate cost tradeoffs between manufacturing, storing, and transporting raw mate-rials, component parts, and finished goods (Blanchard 1992; Dunn, Seaker, andWaller 1994; Mossman, Bankit, and Helferich 1997). The scope of the orga-nization’s strategic planning continues to be achieving ’competitive advantage’(Porter 1980). Logistics activities do support it by cost-effective value adding

264 G. Malindretos

to customers (Rushton & Oxley 1989; Gattorna 1990, 1998).

The rethinking of the methodology issue can be summarized with thefollowing points:

1. The adjustment to a totally new corporation and technology environmentrequires applied research to be carried out at supply chain level.

2. The research has to start from zero, so that to use effectively all availableknowledge infrastructure, in terms of a flexible research framework.

3. The adjustment initiative has to overcome past attitudes of extreme indi-vidualism and self-esteem, with interdisciplinary collaboration.

4. It is necessary to clarify and overcome some vagueness concerning termi-nology, methodology, methods, techniques and practices.

5. Sufficient Maths thinking and understanding of the mathematical ruleshave multiple usefulness in research, planning and implementation phases.

6. Special attention is attributable to the issues of mathematical ’systems’and ’mathematical sets theory’, for assisting the choice among objectivesin the decision support procedure.

7. The dominance of the CSM expresses the ’hypothesis testing’ which hasmarginalistic, abstract and partial character, in divergence from moderncorporate environment conditions and the MSM with holistic and multi-criteria approaching.

8. An integrated system Logistics approach is definitely an outlet at appliedresearch, planning, implementation and construction level.

9. Critical importance has the effective use of information flow, data col-lection, configuration, computing at real-time and reporting the results,with modern agile techniques, smart algorithms, simulations and heuristictechniques, at planning, tactical and operational level.

10. Advanced Logistics are supported by modern NIT in combination withequipment automation and manpower planning. Because effective useof technology is based on human training and development, in line withsocial psychology, for accruing mutual benefits to the individual and thecompany.


11. The complicated operational interrelationships among various processesat supply chain level (e.g. transport and warehousing facilities) needsclearing-up, taking into account the trade-offs in and between corpora-tions.

12. The new research framework methodology has to be directly applicable atcompany level.

Maths Decision Making Support

According to the MSM, the applied research for the introduction of Lo-gistics at corporation level has to begin from zero basis in the decision makingprocess going to the fundamentals and using of all knowledge infrastructure. Theconstruction of public and private projects always required good technologicaland geographical knowledge and today mathematical studies and combinationalanalysis and topology in mathematical sense are usefully applied. In addition,the IT ’revolution’ has been based on Maths, but confinement in the use ofsoftware facilities leaves gaps for wrong decision making. The arrangement of asyllabus in a school or university may be so difficult that we have to recourseto electronic means because of a vast number of restrictions and specifications.The design of building a dam as well as the preparation of a production line mayrequire participation of many people performing hundreds of actions, specifica-tion, construction and drawing up of complex graphs to represent mathematicalmodels with points and lines denoting restrictions on their timing, in which thePERT (Progress Evaluation and Review Technique) method foreshadows (Bag-uley 1995). Planning and implementation face many difficulties especially withstructural changes, in a highly exogenously given and irreversible new world.Descartes laid down rules for helping ’inventive reflection’, introducing the roleof heuristics, intervening attitude and emotion - a mixture of inventive intu-ition and logic. The great mathematician G. Polya considers that the heuristicattitude is fundamental to the discoverer, the explorer. Heuristics, accordingto Descartes and after him Leibnitz and Bolzano, lay down rules for mixinginventive intuition and logic that is important in the conduct of research andcreativity and generally for the behaviour of men (Kaufmann 1968). Talent,experience and intense desire and spirit for the truth are not just subtlety oreven cunning. The marriage of intuition and logic can be promoted throughunderstanding and proper use of mathematical methods.

In support of decision making, it is required ’intelligent design’ (ID) andsome preference ordering. ID is based on the premise that ’certain featuresof the universe and living things are best explained by an intelligent cause,

266 G. Malindretos

not an undirected process such as natural selection’. It is a matter of nature,philosophy, culture and religion, namely questions to be answered for footing ascientific theory encompassing evolution and origin of life.

Besides the doubts whether ID is a science, there has to be an implicitpreference of the today world from the past, that is identified by transformationof the business environment and the human society at large. New productsand new ways of doing them, new professions and specialties away from thework conditions in the past; the walker became a driver, the clerk has givenplace to the planner, the craftsman has become a manufacturing technician, theshopkeeper is now a distributor, etc.

Further support in decision making and formulation of a ’design theory’is offered by the mathematical sets theory and the combinatorics branch ofmathematics (Hausdorff, F. 1957; Graham et al. eds 1996). The aggregateof possible items is broken down into perceptibly smaller sets, from which achoice can be made. This is a practical simplified and logical method that helpsspecifying and quantifying the increasingly complexity of the modern world,though it does not preclude subjective preference orderings and severalty.

The combinatorics branch of mathematics contains a series of rules oncombinations and permutations. The rules of combinations correspond brieflyto:

(1) C(n, 1) = n

(2) C(n, 2) =n(n − 1)

2!

(3) C(n, 3) =n(n − 1)(n − 2)

3!

(4) C(n, 3) =n(n − 1)(n − 2)...(n − r + 1)

r!

Similarly, we have for permutations:

(5) P (n, 1) = 1

(6) P (n, 2) = n(n − 1)

(7) P (n, 3) = n(n − 1)(n − 2)


When order matters and an object can be chosen more than once then thenumber of permutations is nr (where n is the number of objects from which youcan choose and r is the number to be chosen). When order matters and eachobject can be chosen only once, then the number of permutations is:

(8) P (n, r) =n!

r!(n − r)!

where n is the number of objects from which we can choose and ’ !’ is thestandard symbol meaning factorial.

Combinatorics are useful in the mathematical sets, which offer reliableguides for the choice of an order of preferences, or a value function which cor-responds with sufficient accuracy to objectives. More specifically, the mathe-matical sets theory assists the conversion of objectives into criteria of choice.This has great importance in decision making, since the criteria of choice is thetrickiest problem in the rational preparation of action, according to economistsand psychologists. The arguments used offer reliable guides for the choice ofan order of preferences, or a value function which corresponds with sufficientaccuracy to objectives. The notion of a graph, in the sense of the theory of sets,can avoid using mathematical formulae, which would be difficult for some. Thefirst difficulty to overcome concerning no measurable intentions and ideas comesfrom rediscovering the considerations of Descartes which later economists - inparticular Pareto (1927) - demonstrated that if there is a pre-order relationship,it permits to obtain an order with a specific procedure (Kaufmann 1968).

In particular, objectives constitute a set only when well defined and dis-tinct. The combinations of the elements representing the product of a set canbe broken down in two parts, one having certain properties (called graph) andthe other not having them. Identifying the properties of a graph, it is possibleto convert it into a preference criterion.

The general properties of a graph, essential to the notion of preference,are: transitivity, reflexibility, symmetry, pre-order and equivalence relationships.As a simple example, suppose a set as a collection of four objects:

(9) A = (x, y, z, u)

There combinations of elements can be broken down into two parts, one graphhaving certain property and another not having that property. Suppose that anorder exists between two elements x and y of the set in the sense that x precedesy indicated by the symbol ’≺’, then we write:

(10) x ≺ y

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In so far as, y precedes a third element z, then we can expect:

(11) x ≺ y ≺ z

More generally, the ordered relationship (11) implies that there is a combinatione, which precedes all x up to u:

(12) e ≺ x ≺ y ≺ z ≺ u

If x and y are a matter of indifference, we can say that the pairs (x, y) and (y, x)belong to the built-up graph. If y is preferred to x, we shall say that the pair(x, y) belongs to the graph which represents the set of judgements. Supposefurther that:

(13) e ≺ y

(14) z ≺ e

and

(15) y ≺ z

The relation (15) though incompatible with the transitivity property, whichwould imply that zpy, according to (13) and (14), may be conceivable even if itis not logical. It simply implies that free preferences require not pure logic, ineffect marking the human civilization.

The study of individual choices was first conceived as one of calcula-tion of utilities or satisfactions considered to be measurable by certain classicaleconomists: Devons, Walras, Edgeworth and Marshall. By preordering classesof equivalence the assortments belonging to the same curves called ’indifferencecurves’ are identified, which evidently cannot be intersected forming a total or-der between classes of equivalence. The convexity of the ’indifference curves’ isbased on the psychological analysis of a consumer. Similar though in oppositecurvature prevail for ’iso-production curves’, etc.

The set structures are associated with preference functions. A set struc-ture is a set objectives partially ordered. If x1, x2 are perfectly divisible, there isa ’marginal rate of substitution’, given by the variation of x2 as a function of x1

in infinitely small intervals giving the slope of an ’indifference curve’. Similarly,equivalent surfaces are formed with more than two elements in combination, as-sisting building up a rational theory of consumer behaviour. To choose among


combinations of preference order of all elements we need a preference criterionof choice among a set of objectives:

(16) V = (x1, x2, x3, ..., xn)

corresponding to different values. The notion of a ’preference function’ or a’value function’ helps to determine completely ordered classes of equivalences(with the mathematical sense of the term ’function’). Correspondence of el-ements one by one in any two sets gives the sense of a ’function’ commonlyexpressed as:

(17) y = f(x)

To face the trickiest problem of associating a set of objectives and a preferencefunction, useful is the introduction of a ’measure’ of the set of objectives. Iden-tifying a preference function for a set of objectives becomes the ’criterion ofdecision making’.

Building-up a preference function requires a thorough investigation of theproblem and an analysis of a man or the group having the power of decision.Mathematicians use the ’Hasse diagram’ to specify the preferable one from a setof ordered objectives. In finite sets of objectives, there is always an objectivewhich is preferable to all others, or all others are preferable to it, with use ofsome measurement system. The first is called ’maximum’ and the second iscalled ’minimum’ or vice versa. Infinite sets of objectives do not necessarilyposses a ’maximum’ and/or a ’minimum’. In particular, insofar as the soleobjective of a company is the profits maximization, with profits (N) defined asthe difference between total receipts (E) and total cost (C) then:

(18) N = E − C = Maximum

Hence, we have:

(19) N ′ = ∂N/∂Q, E′ = ∂E/∂Q, C ′ = ∂C/∂Q

and

(20) N ′′ = ∂N ′/∂Q, E′′ = ∂E′/∂Q, C ′′ = ∂C ′/∂Q

The conditions of maximization are the first derivative equals to zero and thesecond one is negative, namely:

(21) N ′ = E′ = C ′ = 0

270 G. Malindretos

and

(22) N ′′ = E′′− C ′′

≤ 0

From these relations it derives that:

(23) E′ = C ′

and

(24) ∂E′′/∂Q ≤ ∂C ′′/∂Q

The last two relations simply imply that profits maximization occurswhen ’marginal cost’ equals ’marginal revenue’ (23) and the slope of the ’mar-ginal revenue’ curve is smaller than that of the ’marginal cost’ curve (24), whichmeans intersection from below of the ’marginal revenue’ curve.

Ordered sequences of elements and sets of objectives, called vectors, areformed by real or binary numbers known as ’vector spaces’ or ’modules’ if builton integer numbers. If a vector space is such that the multiplication of theobjectives by a real number or adding two vectors, new objectives derive whichare part of the same set of objectives (Kaufmann 1968). In such case it is saidthat there is a ’linear vector space’:

(25) λ(α1, α2, α3, ..., αn) = (λα1, λα2, λα3, ..., λαn)

(26) (α1, α2, α3, ..., αn) + (b1, b2, b3, ..., bn) =

(α1 + b1, α2 + b2, α3 + b3, ..., αn + bn)

Multiple criteria can be forwarded, by trying to make comparisons with keepingone the same or others except one, e.g. with certain production to maximize theprofit rate. More broadly, let there be five objectives and two preference func-tions V1(X) and V2(X) constituting two criteria. Suppose that the preferencefunction V1(X) includes five objectives A, B, C, D, E:

(27) V1(B) ≤ V1(A) ≤ V1(C) ≤ V1(D) ≤ V1(E)

And that there is another preference function V2(X) with the same objectives:

(28) V1(C) ≥ V1(A) ≥ V1(D) ≥ V1(B) ≥ V1(E)

Seeking a ’minimum’, with V1(X) the optimal objective is B, while with theV2(X) the optimal objective is C, so that there is not concordance between the


results given by the two preference functions V1(X) and V2(X). The attitudescan be modified by new information, technology change, etc. Within continuoustechnological progress and a flexible environment, objectives can be changing inthe short, medium and long term. The process of changes in objectives is notuniversal at individual and group level.

Mathematical system conditions

Understanding the mathematical sets theory helps significantly the useof programming and econometrics. Because, the sets theory has been devel-oped in terms of mathematical constraints (Goldratt 1990; Balakrishnan 1999)and a preference or objective function (Pareto 1927; Hicks 1956; Dehem 1958;Kaufmann 1968). Because of the critical importance of the choice of researchmethod by use of quantitative techniques for improving decision making (e.g.Anderson et al. 1992; Render and Stair 2000; Vohra 1990), it is useful to erasesome misunderstanding concerning the use of Maths in Logistics for the cor-poration adjustment planning and management. The objective function andthe constraints are useful to apply mathematical linear programming for se-lecting the best from a set of feasible alternatives. The ’linear programming’has to be distinguished from the ’computer programming’, which however hasplayed important role in the advancement and use of ’linear programming’ and’econometrics’ (Walters 1968), thus helping Logistics and SCM (Shapiro 2001).The assumptions underlying ’linear programming’ (proportionality, additivity,continuity, certainty finite, choices), are extended by linear approximations to’non-linear programming’ and to ’goal programming’, which involves multiplegoals and serves the ’satisfaction criterion’ in place of optimisation.

The ’linear programming’ has great advantages that contributed to inte-grating many areas of thought by incorporating restrictions, in simple operationswhich can be handled by digital computer. It has been especially useful in pro-ducing important ’synergy effects’ by using modelling systems (Shapiro 2001;Robinson and Dilts 1999). Non-convexities, change in constraints, in factorsavailability, as well as shifts in parameters, have induced modifications to ’para-metric programming’, post optimality analysis, sensitivity analysis, ’dynamicprogramming’, ’integer programming’, etc. The ’lean production’ (Womack etal. 1990), ’agile methodologies’ (Goldman and Preish 1991), ’heuristics’, etc.,facilitate the measurement of changes in objective function coefficient, in tech-nological coefficients, resource changes, etc.

Without undervaluing the usefulness of the ’linear programming’, men-tion is made on the structural analysis and the interdependence among eco-nomic variables which are the essence of much economics (Walters 1968), and

272 G. Malindretos

central issue of Logistics (Attorney 1990). Mathematical systems comprise re-lationships, expressed in equations and inequalities, so that they help greatlyin depicting all the relations underneath. The relationships contain variables inmeasurable quantities that may vary and parameters which remain relativelyconstant. The decision variables are controllable by the decision-maker. Theresult variables express the outcome and are also termed dependent variables.In systems analysis the ’old nomenclature of dependent/independent variablesis not very useful’ and the new term for variables which are predicted by themodel is ’endogenous variables’ (Walters 1968). The uncontrollable variablesinfluence the result variables but are beyond the control of the decision-maker(exogenous variables). Because of the interrelation among variables, they areoften termed altogether ’explanatory variables’. The rule in model-building isto have as many equations as endogenous variables if one wish to predict all ofthem. Models that describe the structure of a system contain ’structural equa-tions’ and exogenous or ’autonomous’ variables which are determined by causesoutside the model and express theoretical casualties to be tested against data(Garver 1999). There is not upper limit to the number of exogenous variablesexcept for the statistical limit imposed by the number of observations, providedsufficient number of degrees of freedom.

A system of relationships is solved conveniently with use of ’matrix al-gebra’ and ’differential calculus’. Measurement problems indicatively includeestimation errors, sampling, reduced form equations, multiple regression analy-sis, the identification problem, the behaviour of the residuals, multicolinearity,etc. (Walters 1968; Fox 1968). A sub-system incorporates a complex of interre-lations of component processes and a number of constraints for exogenous cor-porate and technological environment, which represent irreversible conditions.The main emphasis in Logistics model-building is not so much the constructionof ’optimising models’ - that is, models which will generate a unique solutionthat cannot be further improved. Because optima, in the complex real-world, ifreally exist, are the ’best currently available’ or the ’best yet identified’. Theymay not exist at all, or may not be attainable. More realistic is to seek for theidentification of outcomes by simulation, as an approach to help evaluating al-ternative options using models of the system under consideration. A big numberof widely and flexible computer software packages are available now, enabling anorganization’s Logistics System to be adequately represented (Christopher 1990,2000). Installation of databases and gradual accumulation of actual data enablessimulation retrials, to ascertain actual outcomes, such as customer service level,etc. This validation procedure will confirm the accuracy of the system represen-tation, after which the company management can use the model as a ’decision


Chart 1: Combination of time-cost-quality

support system’ (DSS). In other words, the adjustability of such packages in par-ticular cases, based on the feedback ’running-tests’ process (pilot application),is a key for approaching the real decision-making problems effectively.

Holistic corporation restructuring

It has been observed that planned combination of men/machines hasproved to produce unforeseeable benefits in creating comparative advantage andimproving competitive position in today’s internationalised markets. Coordi-nated cooperation includes turning of attention to outside looking and morespecifically to ’a new boss’, the customer and more generally the consumersas final users of public goods and services. Because, this is value adding andderives benefits to all partners. It drives the corporation to holistic restruc-turing in processes for maximizing customers’ satisfaction, in place of the con-ventional vertical functional organization and structuring. Orders, complains,or adjusting to new customer preferences, pass through a number of depart-ments and involve cumbersome, delayed, bureaucratic, possibly not sufficientlycoordinated activities and decisions, overlooking and underrating the customersand the consumers. In more complicated contemporary market conditions, thecorporation uses time-cost-services quality criteria in combination, for creatingvalue to customers and assisting performance (chart 1).

This move of corporate attention has been based on the observation thatthe cost of gaining a new customer is many times the cost of keeping an existingone and even more is the cost of regaining an unsatisfied customer. In addition,

274 G. Malindretos

Chart 2: Corporate Re-organization in Processes

it has been observed that software construction is relatively cheap and effortmoves in design, requiring creativity and talent.

Creative, innovative processes are not easily planned, and so we shouldbe wary of the traditional engineering metaphor in building software. Logisticsmanagers should be trained how to use advanced up-to-date computer-basedtools in order to test radical ideas and improve decisions.

The effective ’time-cost-quality’combination requires a totally new cor-porate structure and its relations with the suppliers, the transformation withinthe corporation and the value creation to the customer, in a feedback process.The main corporate objective has become the customer’s satisfaction, throughtotal corporation restructuring in processes throughout the supply chain (chart2).

The corporate processes are rightly treated as sub-systems in mathemat-ical sense; they comprise sets of activities that are closely interrelated. Theyare classified in core processes and non-core processes; the last may be assignedto third parties (known as 3PL), aiming at benefits derived from specialization,’scale economies’, cost, quality and time (though 3PL is also subject to follow-up). More generally, partnerships with other companies in specific processesmust be examined, for gaining mutual benefits.

The new framework of corporation organization set-up is a constituentpart of the advance of Logistics to SCM.


Chart 3: Integrated Corporate Adjustment

Corporation re-engineering

Special attention in the choice of Logistics research method is attributedto the requirements of systems analysis and integrated approach, since Logisticsprocesses, such as transportation, inventory control, handling, and sorting, mustbe carefully coordinated if cost-effectiveness is to be achieved. Yet, both intheory and practice, processes and activities are often examined separately. Asa consequence, decisions in the best interests of the firm are difficult to make,particularly in cases when the responsibilities for different Logistics activitiesare allocated to different managers or when firms become compartmentalized(Ruston & Oxley 1989; Gattorna 1990).

Moving attention to the integrated Logistics approach for identificationand problem solving does not imply rejection of any specialization whatsoever.Quite the contrary, efficiency is served by co-ordination of all specialties engagedwith different corporation processes, such as procurement, transportation, ware-housing, transformation and distribution, in collaboration. Thus, the corpora-tion reorganization is founded upon all available know-how infrastructure, byintegrated approach, going back to the ordinary scientific management functions(e.g. Koontz & Weihrich, 1990), giving room for creation of a dynamic feedbackprocess of adjustment (chart 3).

Logistics, traditionally a boundary-spanning discipline, is uniquely po-sitioned to contribute to the vision of integrating supply chain components.Researchers responding to increasing emphasis in integration requirements havefocused on understanding Logistics competencies and skills needed to enhancecustomer value (Ellinger, Daugherty, and Keller 2000; Lynch, Keller, and Oz-ment 2000; Morash, Droge, and Vickery 1996; Stalk 1998; Wisner 2003; Ro-drigues et al. 2004).

The corporation system re-organization is part of the designing the ad-justment to the new technological and business environment. In particular, thereare situations where corporate adjustment requires putting everything under sci-entific doubt, not excluding the management itself (Hammer & Champy 1993;

276 G. Malindretos

Chart 4: Integrated Re-engineering

Davenport 1993; Manganelli and Klein 1996). The re-engineering of the corpo-ration supply chain has advanced rapidly, deepened from various respects anddiffused in the form the so called BPR and more recently SCR (Malindretos2001, 2002).

BPR has been recognized as a ’revolution’ in corporate decision making.Revolutions by definition contain radical ’brainstorming rethinking’ and are his-torically tested at application level, through learning by experience and diffusionof benefits. It encompasses re-organization, strategic and operational planningfrom scratch, based on all available resources, aiming at process re-engineering(chart 4).

The integrated system approach has overcome the question whether itis a matter of strategy, management competence, etc. Without looking for auniversal method, it is a streamlining of business processes, re-inventing newselected ’core processes’ and ’value-adding activities’, by proper use of Logisticsand continuous follow-up and modifications, looking for new deals and partner-ships.

The corporation re-engineering is seeking for a set of flexible rules, ad-justable to particular corporate circumstances, since perfect methods to be usedas panacea, simply do not exist. An approach to the supply chain design,planning and operational management focuses on a cycle view of supply chainprocesses (e.g. Chopra and Meindl 2001). Integrated planning is concerned


with functional, spatial and intertemporal integration over strategic, tacticaland operational planning horizons (Shapiro 2001).

Managers impelled to alleviate tensions, by allowing variation and per-sonnel motivation can improve financial and operating performance (Bennetand Heblund 2001), and overcome the ’downsizing’ as a not inevitable ’myth’(Tenner and DeToro 1997).

The corporation restructuring for the formation of a dynamic feedbackprocess towards continuous improvement, is founded on and seeking for per-forming strategies, within SCM. The dual objective is maximization of expectedreturn (rm) along with minimization of total risk of a portfolio (s). The meanof the expected return is estimated by statistical method of forecasting withconfiguration of any available data and information (from balance sheet, incomeaccount, etc) and is given as (Malindretou 2000):

(29) rm =∑

(r/n)

A measure of risk in the formation of a portfolio, given the investor’s objectiveschoice is given by:

(30) σ =√

∑

(r − rm)2/(n − 1)

According to the ’diversification principle’, the minimization of total risk ofa portfolio, between two alternative investments, is estimated as a weightedaverage of the variances of them σ2

1and σ2

2:

(31) σ2 =∑

(α1σ1 + α2σ2)2 = α2

1σ2

1+ α2

2σ2

2+ 2α1α2σ1σ2ρ12

where α for the percentage participation of the investments 1 and 2, given theinterrelation of their variances with a correlation coefficient ρ12 taking valuesbetween :

(32) −1 < ρ12 < +1

With negative values of ρ12, it is obvious that the σ2 of a portfolio is less thanthe sum of σ2

1+ σ2

2. It is noted in addition that in case of a ’normal distribution’

in the range of about ±2σ and more specifically +1, 96s it is covered about the95% of the cases of the sample as a representation of the population (level ofsignificance 0,05: chart 5). In the range of ±3σ almost all cases are covered(known as ’six-sigma’ analysis of customers’ satisfaction: George 2003).

278 G. Malindretos

Chart 5: Six-sigma analysis

Dynamic Processing

Because of ’leads and lags’ in the response of the corporation system tochanges in an input, the interrelationships may not be stable. E.g. an increasein the forecasted consumer demand of a manufacturing company which sellsoutput to wholesalers, requires knowledge of time-lags of readjustment of ware-housing and the factory, etc. (known as ’acceleration effect’). Within complexcompany systems, Forrester has developed the notion of ’Industrial Dynamics’(Forrester 1961). Subsequently, Senge (1990), Richmort (1997), etc. proceededin social dynamics and the notion of Systems Thinking (ST), as the art and sci-ence of understanding how the organization structure determines performance,so that to change structure for improving performance. The ST is an exten-sion of the Systems Dynamics that belong to the Social Dynamics and has beenextensively applied to industrial, urban and world systems. The process ofintroducing ST within the framework of organizational change has used two dis-


tinct approaches: modelling and conventional mapping (Soderquist 1999). TheST provides a helpful framework for integrating the functional areas of man-agement - marketing, production, accounting, research and development andcapital investment - by treating interactions between the flows of information,orders, materials, money, personnel and capital equipment, in a company, anindustry or a national economy. It is useful at first, to simplify essential notionsconcerning organization’s goals fixed by supposently independent management,the strategic decision variables (taken as ’intermediate targets’ to achieve goals)and the uncontrolled ’explanatory variables’, which exert influence upon deci-sion variables for succeeding the goals. In view of data inadequacy at least inthe beginning of the Logistics planning, using simulation can help to explain thereasons for fluctuations in a system as well as providing a guide to managementaction to overcome these effects (Coyle 1977).

A modelling approach is founded through a ’Strategic Forum’ formedby external consultants, management staff-members and company officers, todevelop a dynamic model of the organization. Working with a specific process(chart 6) of listing goals as critical success factors, and specifying a strategyfor achieving them, it goes on to a detailed simulable model which inhibits thesystem that the model is trying to explain. The quantitative analysts and con-sultants can help organizations to develop a clear ’self-understanding’ throughST. It improves the ability of providing insight into the company’s goals and itsstrategy for achieving them.

In effect, the corporation adjustment is treated as a process of spec-ifying and identifying the problem, as a difference between some actual andsome desired state of affairs, and then searching, with the available science andmodelling equipment, how to resolve the difference (Tenner & DeToro 1997;Walker 2000; Shapiro 2001; Klose et al. editors 2002; Tayur et al. editors 2003;Malindretos 2003, 2005). In such sense, the supply chain is approached as amulti-echelon process involving interactions associated with issues that can bebroadly abstracted in three stages: procurement, manufacturing and distribu-tion (Ganapathy et al., 2003, chart 7).

A fair knowledge of each of the three stages is helpful to integrate thedifferent levels of the supply chain system. This knowledge has to be transformedin a modelling process, which is crucial for the specification, identification andperforming problem solving (Anderson et al.1992). Otherwise, poor planningmay lead to supply chain system instability and seriously impair its ability tosatisfy customers.

280 G. Malindretos

Chart 6: Simple strategic planning and implementation

The problem definition phase leads to a set of objectives (e.g. short-termprofit maximization, cost minimization, company’s competitiveness, etc.). Italso gives a set of restrictions or constraints (such as production capacity, orders’fulfilment capacity, high quality specialties, external finance limits, etc.). Thesteps of the problem solving process are summarized as follows:

a) Define the problem (recording of the actual situation and the desired one).

b) Identify a set of alternative solutions.

c) Determine the criteria of evaluation of alternatives.

d) Evaluate the alternatives.


Chart 7: Supply Chain process

e) Choose an alternative.

f) Implement the selected alternative.

g) Evaluate the results.

Inter-disciplinary team approach is required for mathematical models’building-up and application, since not any individual can have a thoroughknowledge to handle adequately the various aspects of complex today real prob-lems (economic, physical, psychological, biological, sociological, and engineering,etc.).

Partnerships and Simple Techniques

Based on awareness of the challenge of adjustment to the new corporationenvironment, and the usefulness of modern Maths and Logistics, there can besignificant support to the introduction of Logistics in conditions of not equalchances, namely where the SMEs represent the dominant form of the corporationstructure and there are institutional rigidities (Daganzo 2002). Two sets ofactions are mentioned here:

– Encouraging allying among corporations (co-operative partnerships pro-motion).

282 G. Malindretos

Chart 8: Processes collaboration between SMEs and SMEs with providers

– Applying simple techniques to help understanding the hidden expectedbenefits from R&D and more particularly the introduction of Logisticsand SCM.

More specifically :

Partnerships promotion:

Experience has shown that collaboration among SMEs of the same or sim-ilar sector as well as between SMEs and 3PL (Third Party Logistics) services’providers companies, contribute to significant benefits in terms of cost, quality,flexibility, etc parameters that enhance corporations’ performance (chart 8). Inthe first instance, benefits derive from achieving ’economies of scale’ in processeswhich do not impair the independence of company management, such as pro-curement, warehousing, transport, etc., whereas in the second case from theoutsourcing concept, namely the assignment of certain processes in specializedcompanies, such as 3PL for the Logistics processes.

Simplified techniques:A series of simplified techniques which can help to making decisions are

available, where many factors are claiming management’s attention. These canbe included in the broader notion of decision support techniques and help tomake the best decisions possible with the available information. These toolshelp map out the likely consequences of decisions, work out the importanceof individual factors and choose the course of action to take, since they areharmonized with more powerful techniques. Worth mentioning is that thesetools ’fit together’ and can be used in different combinations, needing moreanalysis.


Concluding Remarks

1. This paper focused on erasing a series of misconceptions that arise inLogistics modelling and application at corporate level, as it happens intransitional phases of major structural transformations.

2. There has been formed a MSM framework suited to the new corporationand technology environment.

3. It has been clarified that the rapid advance of Logistics to SCM and toSCR has been based on Maths and information technology ’revolution’,particularly NIT.

4. Particular attention attributed to the mathematical sets theory and thecombinatorics approach, for support of decision making in introducingLogistics.

5. Integrated Logistics planning and design suits to the requirements of cor-poration adjustment challenge, in terms

6. The total corporation restructuring in processes was treated as criticalfor enabling the corporation adjustment and foundation of a sustainablefeedback process.

7. It was pointed out that the development of human resources is vital for in-troducing Logistics towards effective use of the high-tech and mobilizationof all available resources.

8. It was substantiated that there are possibilities of introducing Logisticseven with the use of minimum available information, in conditions of dom-inance of SMEs and extreme institutional frictions.

284 G. Malindretos

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