Forecast and decision horizons in a commodity trading model

Forecasts of demands or prices become increasingly unreliable as the future becomes more distant. It is, therefore, beneficial to show that optimal decisions during an initial time interval are either partially or wholly independent of the forecasted data from some future time onwards. Using a commodity trading model as an example, we obtain conditions that allow us to make optimal buying and selling decisions for a commodity in some initial time interval without knowing its price forecast beyond some future time. Such an initial time interval is called a decision horizon and the time up to which the forecasted data is required to make the optimal decisions during the decision horizon is called a forecast horizon. We use the maximum principle to solve the example and show that the decision and forecast horizons in the problem arise from lower and upper bounds imposed on the on-hand inventory of the commodity

Feedback Stackelberg-Nash equilibria in mixed leadership games with an application to cooperative advertising

In this paper we characterize the feedback equilibrium of a general infinite-horizon Stackelberg-Nash differential game where the roles of the players are mixed. By mixed we mean that one player is a leader on some decisions and a follower on other decisions. We prove a verification theorem that reduces the task of finding equilibrium strategies in functional spaces to two simple steps: First solving two static Nash games at the Hamiltonian level in a nested version and then solving the associated system of Hamilton-Jacobi-Bellman equations. As an application, we study a novel manufacturer-retailer cooperative advertising game where, in addition to the traditional setup into which the manufacturer subsidizes the retailer's advertising effort, we also allow the reverse support from the retailer to the manufacturer. We find an equilibrium that can be expressed by a solution of a set of quartic algebraic equations. We then conduct an extensive numerical study to assess the impact of model parameters on the equilibrium

The Genuine Saving Criterion and the Value of Population in an Economy with Endogenous Population Changes

We study an economy in which the rate of change of population depends on population policy decisions. This requires population as well as capital as state variables. By showing the algebraic relationship between the shadow price of the population and the shadow price of the per capita capital stock, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. Moreover, we derive explicitly the expression of genuine savings in our model to evaluate the sustainability of the system

The Genuine Saving Criterion and the Value of Population in an Economy with Endogenous Population Changes

We study an economy in which the rate of change of population depends on population policy decisions. This requires population as well as capital as state variables. By showing the algebraic relationship between the shadow price of the population and the shadow price of the per capita capital stock, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. Moreover, we derive explicitly the expression of genuine savings in our model to evaluate the sustainability of the system

A note on M(atrix) theory in seven dimensions with eight supercharges

We consider M(atrix) theory compactifications to seven dimensions with eight unbroken supersymmetries. We conjecture that both M(atrix) theory on K3 and Heterotic M(atrix) theory on T^3 are described by the same 5+1 dimensional theory with N=2 supersymmetry which is broken to N=1 by the base space. The emergence of the extra dimension follows from a recent result of Rozali[hep-th/9702136]. We show that the seven dimensional duality between M-theory on K3 and Heterotic string theory on T^3 is realised in M(atrix) theory as the exchange of one of the dimensions with this new dimension.Comment: RevTeX, 8 pages, version to appear in journa

Performance evaluation of flexible manufacturing systems under uncertain and dynamic situations

The present era demands the efficient modelling of any manufacturing system to enable it to cope with unforeseen situations on the shop floor. One of the complex issues affecting the performance of manufacturing systems is the scheduling of part types. In this paper, the authors have attempted to overcome the impact of uncertainties such as machine breakdowns, deadlocks, etc., by inserting slack that can absorb these disruptions without affecting the other scheduled activities. The impact of the flexibilities in this scenario is also investigated. The objective functions have been formulated in such a manner that a better trade-off between the uncertainties and flexibilities can be established. Consideration of automated guided vehicles (AGVs) in this scenario helps in the loading or unloading of part types in a better manner. In the recent past, a comprehensive literature survey revealed the supremacy of random search algorithms in evaluating the performance of these types of dynamic manufacturing system. The authors have used a metaheuristic known as the quick convergence simulated annealing (QCSA) algorithm, and employed it to resolve the dynamic manufacturing scenario. The metaheuristic encompasses a Cauchy distribution function as a probability function that helps in escaping the local minima in a better manner. Various machine breakdown scenarios are generated. A ‘heuristic gap’ is measured, and it indicates the effectiveness of the performance of the proposed methodology with the varying problem complexities. Statistical validation is also carried out, which helps in authenticating the effectiveness of the proposed approach. The efficacy of the proposed approach is also compared with deterministic priority rules

Reducing greenhouse gas emissions of Amazon hydropower with strategic dam planning

Hundreds of dams have been proposed throughout the Amazon basin, one of the world’s largest untapped hydropower frontiers. While hydropower is a potentially clean source of renewable energy, some projects produce high greenhouse gas (GHG) emissions per unit electricity generated (carbon intensity). Here we show how carbon intensities of proposed Amazon upland dams (median = 39 kg CO2eq MWh−1, 100-year horizon) are often comparable with solar and wind energy, whereas some lowland dams (median = 133 kg CO2eq MWh−1) may exceed carbon intensities of fossil-fuel power plants. Based on 158 existing and 351 proposed dams, we present a multi-objective optimization framework showing that low-carbon expansion of Amazon hydropower relies on strategic planning, which is generally linked to placing dams in higher elevations and smaller streams. Ultimately, basin-scale dam planning that considers GHG emissions along with social and ecological externalities will be decisive for sustainable energy development where new hydropower is contemplated. © 2019, The Author(s)