Understanding supply chain dynamics: A chaos perspective

Variability in orders or inventories in supply chain systems is generally thought to be caused by exogenous random factors such as uncertainties in customer demand or lead time. Studies have shown, however, that orders or inventories may exhibit significant variability even if customer demand and lead time are deterministic. In this paper, we investigate how this class of variability, chaos, may occur in a multi-level supply chain and offer insights into how to manage relevant supply chain factors to eliminate or reduce system chaos. The supply chain is characterized by the classical beer distribution model with some modifications. We observe the supply chain dynamics under the influence of various factors: demand pattern, ordering policy, demand-information sharing, and lead time. Through proper decision-region formation, the effect of various factors on system chaos is investigated using a factorial design. The degree of system chaos is quantified using the Lyapunov exponent across all levels of the supply chain. This study shows that, to reduce the degree of chaos in the supply chain system, the adjustment parameters for both inventory and supply line discrepancies should be more comparable in magnitude. Counter-intuitively, in certain decision regions, sharing demand information can do more harm than good. Similar to the bullwhip effect observed previously in demand, we discover the phenomenon of “chaos-amplification” in inventory across supply chain levels.     

An extremum problem in production economics

We consider a linear investment model with cost minimization. The lagged effect of investment on production is allowed for by using a distributed (instead of concentrated) control: the right-hand side of the controlled equation contains an integral of the product of control by a variable coefficient. Constructive optimality conditions are derived, the properties of optimal controls are described, and a method is proposed for approximate computation of the sought optimal control. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 225–236, 2003.     

Multicriteria decision analysis and environmental economics: An approximation

A multicriteria approach to address basic problems in environmental economics is proposed in this paper. The methodology is underpinned by the wellknown multicriteria method called Compromise Programming together with some recent results relating the compromise sets with the traditional optimisation of the utility functions. To illustrate the proposed methodology the following two cases are suggested: (1) The reconciliation between economic, environmental as well as recreational objectives inherent to the management of an environmental asset such as forestry system, and (2) Its application to the appraisal of environmental improvements or damages when nonmonetary objectives are involved.     

Extreme shock models: An alternative perspective

Extreme shock models have been introduced in Gut and Hüsler (1999) to study systems that at random times are subject to a shock of random magnitude. These systems break down when the shock overcomes a given resistance level.In this paper we propose an alternative approach to extreme shock models using reinforced urn processes. As a consequence of this we are able to look at the same problem under a Bayesian nonparametric perspective, providing the predictive distribution of systems’ defaults.     

An application of time scales to economics

Economics is a discipline in which there appears to be many opportunities for applications of time scales. The time scales approach will not only unify the standard discrete and continuous models in economics, but also, for example, allows for payments which arrive at unequally spaced points in time. We present a dynamic optimization problem from economics, construct a time scales model, and apply calculus of variations to derive a solution. Time scale calculus would allow exploration of a variety of situations in economics.     

Modelling variations in hospital service delivery based on real time locating information

Variations in service delivery have been identified as a major challenge to the success of process improvement studies in service departments of hospital such as radiology. Largely, these variations are due to inherent system level factors, i.e., system variations such as unavailability of resources (nurse, bed, doctors, and equipment). These system variations are largely unnecessary/unwarranted and mostly lead to longer waiting times, delays, and lowered productivity of the service units. There is limited research on identifying system variations and modelling them for service improvements within hospital. Therefore, this paper proposes a modelling methodology to model system variations in radiology based on real time locating system (RTLS) tracking data. The methodology employs concepts from graph theory to identify and represent system variations. In particular, edge coloured directed multi-graphs (ECDMs) are used to model system variations which are reflected in paths adopted by staff, i.e., sequence of rooms/areas traversed while delivering services. The main steps of the methodology are: (i) identifying the most standard path followed by staff for service delivery; (ii) filtering the redundant events in RTLS tracking database for analysis; (iii) identifying rooms/areas of hospital site involved in the service delivery; (iv) determining patterns of paths adopted by staff from filtered tracking database; and, (v) representation of patterns in graph based model called as edge coloured directed multigraphs (ECDMs) of a role. A case study of MR scanning process is utilized to illustrate the implementation of the proposed methodology for modelling system variations reflected in the paths adopted by staff.     

An existence theorem in the calculus of variations

In this paper, a nonparametric variational problem is considered in the setting of the theory of generalized curves. It is assumed that the integrand of the problem does not grow at infinity faster than the norm of the variable , for all values of the other variablest andx (which take their values in a compact product set). It is shown that a generalized curve exists such that the minimum of the functional over an appropriate set is achieved. This generalized curve does not in general have compact support.     

Incentives and the needham paradox: An agent-based perspective

This article discusses how restructured incentives could have inhibited innovation in ancient China and explain the Needham paradox. Agents in a genetic algorithmic game maximize their payoffs by choosing between innovating and studying the Classics. By restructuring incentives toward studying the Classics, initial spurts of innovation are smothered, resulting in a population with all agents studying the Classics. The incentive structure has a statistically and quantitatively significant impact on the expected average payoffs and the strategy profile of the population: the average payoffs for a regime which rewards innovation fluctuate more but are always higher and the strategy profile is varied. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Productive efficiency and energy use: An historical perspective

The paper discusses long-term trends in relationships between energy use and the overall productive efficiency of the American economy. While total energy consumption grew strongly during the twentieth century, the intensity of energy use (i.e. the energy/GNP ratio) fell persistently much of the time. Thus, there were simultaneous long-term improvements in labor productivity, total factor productivity,and energy productivity. The historical record appears to be at odds with conventional beliefs that gains in productive efficiency depend upon the rising intensity of energy use in production processes. A key role in bringing about these counter-intuitive results is assigned to what is referred to as the energy-technology-productivity nexus, in which the quality of particular energy forms such as electricity and liquid fuels (along with closely linked changes in energy-using technologies) played a critical part in leveraging the overall efficiency of production. As a result of these energy form-dependent improvements in productive efficiency, outputs grew more rapidly than all inputs, including the inputs of energy. The more recent past stands in sharp contrast to the long-term record. While energy efficiency (as measured by energy/GNP) showed strong gains during the late 1970's and early 1980's, the growth in overall productive efficiency was severely retarded. Implications for the future of suggested linkages between the quality of particular energy forms and technological progress are considered.     

Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters

Despite the simplicity and practicality of (deterministic) fundamental diagram models in highway traffic flow theory, the wide scattering effect observed in empirical data remains highly controversial, particularly for explaining traffic state variations. Owing to the analytical properties of the fundamental diagram modeling approach, in this study, we proposed an analytical and quantitative method for analyzing traffic state variations. We investigated the scattering effect in the fundamental diagram and proposed two stochastic fundamental diagram (SFD) models with lognormal and skew-normal distributions to explain the variations in traffic states. The first SFD model assumes that the scattering effect results from stochasticity in both the free-flow speed and the speed at critical density. Both random variables were assumed to follow the lognormal distribution. In the second SFD model, an integrated error term that was assumed to follow the skew-normal distribution over different density ranges was appended to the deterministic fundamental diagram. The properties of these two SFD models were analyzed and compared, and the parameters in these SFD models were calibrated using real-world loop detector data. The observed scatters from the empirical data were reproduced well by the simulated fundamental diagram model, indicating the validity of the proposed SFD models for explaining traffic state variations. Using these two analytical SFD models, we can analyze the stochastic capacity of freeways with closed forms. More importantly, the sources of stochasticity in freeway capacity can be traced in terms of randomly distributed parameters in fundamental diagram models.     

Simple formulas for the expected costs in the newsboy problem: An educational note

This educational note presents closed-form (or near closed-form) formulas for computing the expected cost and the optimal expected cost of the newsboy problem. The formulas are sufficiently easy to be used in undergraduate OR and MBA operations-management courses.