A portfolio of purchase contracts--an example of solving large-scale dynamic programming on parallel computers

The curse of dimensionality means that, though many stochasticsequential decision problems can be modelled as dynamic-programmingproblems, their memory requirements and large solution timesmake them impracticable to solve on most serial computers. Thispaper looks at an example of such a problem—the optimalportfolio of purchase contracts—whichwas solved usinga parallel computer and a LAN of workstations. It concentrateson two questions related to the solution of this problem.     

A dynamic model of supplier switching

While a broad branch of literature deals with the development of buyer–supplier relationships, limited research exists under which circumstances a buyer should terminate such a relationship and switch to a new supplier. Recently, Wagner and Friedl (2007) have developed a framework to analyze a static one-shot supplier switching decision when the buyer has asymmetric information about the supplier’s production costs. We extend their basic framework to a dynamic one, assuming that the supplier learns the production costs over time when he sets up the production process. Since the supplier’s cost information at the individual stages crucially determines the setup and the switching decision, it becomes essential for supply chain management to provide proper incentives so that the supplier reveals his cost information truthfully over time. We characterize the optimal setup and switching strategy as well as the optimal supply chain contract. We also compare our findings with those of the static setting to provide further insights.     

A multiattractor model for the dynamic control of companies

The dynamic behaviour of complex human organisations in dynamic environments results from the interplay of multiple agents. In the particular case of a commercial or industrial companies, the agents are for example the shareholders, the customers/consumers, the subcontractors/competitors, the workers/employees etc. The role of the managers is to find and to maintain the adequate balance of resources between various management levels to respond to the conflicting interests of these agents without endangering the viability of the company. A distinction is made between operational, strategic and normative levels. Kolm's triangle is introduced as a convenient representation for making visible the relative strength of the three management levels. In the triangle a stability polygon representing a viability zone is identified and monitored by observing the company's indicators. Failure paths are followed whenever the current representative point in Kolm's triangle shifts towards the boundaries of the stability polygon. Herewith a diagnostic tool is provided to the managers in charge to design control policies preventing such adverse evolution.     

A duopolistic model of dynamic competitive advertising

This paper proposes a differential game model of competitive advertising decisions for non-durable products by extending the Lanchester model and the Deal model of competitive advertising in the literature. The proposed model is compared empirically with the Lanchester model for model fitting and forecast accuracy. It is shown that the model is suitable for an actual market and out-performs the Lanchester model in forecast accuracy. The model provides a sensible modeling alternative to the Lanchester model for the study of dynamic competitive advertising decisions. Necessary and sufficient conditions for open-loop and closed-loop Nash equilibrium solutions to the model are discussed. A numerical algorithm for open-loop and closed-loop Nash strategies to the model is developed.     

A dynamic competition model of regime change

A dynamic competition model for an oppressive government opposed by rebels is proposed, based on coupled differential equations with constant coefficients. Depending on their values, the model allows scenarios representing a stable, oppressive government and violent regime change. With constant coefficients, there can be no limit cycles. However, cycles emerge if rebels and governments switch characteristics after a revolution, if resources change hands and rebel motivations switch from grievance to greed. This mechanism is proposed as an explanation for the establishment of a new repressive regime after the overthrow of a similar regime.     

A dynamic systems model of dyadic interaction

We develop a differential equation model of dyadic interaction that embodies the basic assumption that members of intimate couples form an interactive system in which the behavior of each member of a couple is influenced by the other's behavior and by goals that each person has for herself or himself. The dynamic solutions of this system suggest that when each person in the dyad is “cooperative”, then an equilibrium can be approached. The equilibrium represents a compromise position between the individuals’ own ideals and those of the partner. On the other hand, if one individual, or both, is uncooperative, then this system often, but not always, becomes unstable. One paradoxical deduction from the model is that, through mutual cooperation, couples can experience periods of stability, but such stable situations are not necessarily satisfying.     

A dynamic process interpretation of the sparse ERGM reference model

Exponential family random graph models (ERGMs) can be understood in terms of a set of structural biases that act on an underlying reference distribution. This distribution determines many aspects of the behavior and interpretation of the ERGM families incorporating it. One important innovation in this area has been the development of an ERGM reference model that produces realistic behavior when generalized to sparse networks of varying sizes. Here, we show that this model can be derived from a latent dynamic process in which tie formation takes place within small local settings between which individuals move. This derivation provides one possible micro-process interpretation of the sparse ERGM reference model and sheds light on the conditions under which constant mean degree scaling can emerge.     

A dynamic input-output model with renewable resources

The paper studies a generalisation of the dynamic Leontief input-output model. The standard dynamic Leontief model will be extended with the balance equation of renewable resources. The renewable stocks will increase regenerating and decrease exploiting primary natural resources. In this study the controllability of this extended model is examined by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate the exhaustion of renewable resources in dependence on the balanced growth rate and on the rate of natural regeneration. In doing so, classic results from control theory and on eigenvalue problems in linear algebra are applied.     

A three-dimensional dynamic model for train-track interactions

This paper develops a novel three-dimensional (3-D) train-track interaction model, where the train is modelled as a group of multi-rigid-body vehicles connected by coupler and gear draft systems, and the tracks are modelled as ballastless tracks using finite element method, and finally the train and the tracks are integrated into an entire system by train-rail coupling matrices. In this model, the time-dependent coupling matrices are developed to characterize the train-track interaction in 3-D space. Mostly important the difficulties in establishing dynamic equations of motion for train-track systems by matrix representations of wheel-rail separation and infinite length computation are properly solved. The numerical results show that this model has high efficiency, stability and accuracy in the calculation of train-track interactions. Besides this model can further provide insights into a number of railway dynamics related subjects, such as train-track dynamic assessment and train derailment.     

A two-compartment model interacting with dynamic drugs

By combining the total cell evolution curve and a two-compartment model interacting with dynamic anti-cancer agents, the evolution of subpopulations has been analytically obtained and investigated in this work.     

A capacity constrained single-facility dynamic lot-size model

A computationally efficient algorithm for a multi-period single commodity production planning problem with capacity constraints is developed. The model differs from earlier well-known studies involving concave cost functions in the introduction of production capacity constraints which need not be equal in every period. The objective is to find an optimal production schedule that minimizes the total production and inventory costs. Backlogging is not allowed. The structure of the optimal solution is characterized and then used in an efficient algorithm.     

A new dynamic programming algorithm for the single item capacitated dynamic lot size model

We develop a new dynamic programming method for the single item capacitated dynamic lot size model with non-negative demands and no backlogging. This approach builds the Optimal value function in piecewise linear segments. It works very well on the test problems, requiring less than 0.3 seconds to solve problems with 48 periods on a VAX 8600. Problems with the time horizon up to 768 periods are solved. Empirically, the computing effort increases only at a quadratic rate relative to the number of periods in the time horizon.This research was supported in part by NSF grants DDM-8814075 and DMC-8504786.     

A dynamic model and simulation of system generation

Translated from Issledovaniya po Prikladnoi Matematike, No. 5, pp. 18–24, 1976.     

A dynamic model for a study of diabetes

In this paper a dynamic model for diabetes prevalence in a country is analyzed. The goal of this study is to estimate the prevalence of diabetes in a hypothetical community. The model is formulated using a difference-algebraic equation and then singular system theory is used to obtain the solution.     

A model for speculation in a dynamic economy

The paper deals with speculation strategies in a dynamic economy, where “speculation” means participating in a market with the intention to gain a reward by first buying an item and thereafter selling it at a possibly higher price. By assuming that the states of the economy form a Markov chain the problem is modeled as a discrete time Markov decision process. The optimal strategies (which are pairs of stopping times) are identified. Under quite general conditions the optimal rule for the selling process turns out to be a control limit policy in both state of economy and time. Techniques for the computation of optimal strategies are presented; some numerical examples are also discussed. For a static economy closed-form solutions are given     

A dynamic Stackelberg duopoly model with different strategies

In this paper, a duopoly Stackelberg model of competition on output is formulated. The firms announce plan products sequentially in planning phase and act simultaneously in production phase. For the duopoly Stackelberg model, a nonlinear dynamical system which describes the time evolution with different strategies is analyzed. We present results on existence, stability and local bifurcations of the equilibrium points. Numerical simulations demonstrate that the system with varying model parameters may drive to chaos and the loss of stability may be caused by period doubling bifurcations. It is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos.     

A dynamic model for road protection against flooding

This paper focuses on the problem of identifying optimal protection strategies to reduce the impact of flooding on a road network. We propose a dynamic mixed-integer programming model that extends the classic concept of road network protection by shifting away from single-arc fortifications to a more general and realistic approach involving protection plans that cover multiple components. We also consider multiple disruption scenarios of varying magnitude. To efficiently solve large problem instances, we introduce a customised GRASP heuristic. Finally, we provide some analysis and insights from a case study of the Hertfordshire road network in the East of England. Results show that optimal protection strategies mainly involve safeguarding against flooding events that are small and likely to occur, whereas implementing higher protection standards are not considered cost-effective.     

A novel dynamic model of pseudo random number generator

An interesting hierarchy of random number generators is introduced in this paper based on the review of random numbers characteristics and chaotic functions theory. The main objective of this paper is to produce an ergodic dynamical system which can be implemented in random number generators. In order to check the efficacy of pseudo random number generators based on this map, we have carried out certain statistical tests on a series of numbers obtained from the introduced hierarchy. The results of the tests were promising, as the hierarchy passed the tests satisfactorily, and offers a great capability to be employed in a pseudo random number generator.