Stochastic optimization models in forest planning: a progressive hedging solution approach

Annals of Operations Research - We consider the important problem of medium term forest planning with an integrated approach considering both harvesting and road construction decisions in the...     

Stochastic optimization models for a single-sink transportation problem

In this paper, we study a single-sink transportation problem in which the production capacity of the suppliers and the demand of the single customer are stochastic. Shipments are performed by capacitated vehicles, which have to be booked in advance, before the realization of the production capacity and the demand. Once the production capacity and the demand are revealed, there is an option to cancel some of the booked vehicles against a cancellation fee; if the quantity shipped from the suppliers using the booked vehicles is not enough to satisfy the demand, the residual quantity is purchased from an external company. The problem is to determine the number of vehicles to book in order to minimize the total cost. We formulate a two-stage and a multistage stochastic mixed integer linear programming models to solve this problem and test them on a real case provided by Italcementi, the primary Italian cement producer and the fifth largest cement producer in the world. We test the influence of different scenario-tree structures on the solutions of the problem, as well as sensitivity of the results with respect to the cancellation fee.     

Facility location models for planning a transatlantic communications network

This paper presents two facility location models for the problem of determining how to optimally serve the requirements for communication circuits between the United States and various European and Middle Eastern countries. Given a projection of future requirements, the problem is to plan for the economic growth of a communications network to satisfy these requirements. Both satellite and submarine cable facilities may be used. The objective is to find an optimal placement of cables (type, location, and timing) and the routing of individual circuits between demand points (over both satellites and cables) such that the total discounted cost over a T-period horizon is minimized. This problem is cast as a multiperiod, capacitated facility location problem. Two mathematical models differing in their provisions for network reliability are presented. Solution approaches are outlined and compared by means of computational experience. Use of the models both in planning the growth of the network and in the economic evaluation of different cable technologies is also discussed.     

Stochastic and minimum regret formulations for transmission network expansion planning under uncertainties

After deregulation of the Power sector, uncertainty has increased considerably. Vertically integrated utilities were unbundled into independent generation, transmission and distribution companies. Transmission network expansion planning (TNEP) is now performed independent from generation planning. In this environment TNEP must include uncertainties of the generation sector as well as its own. Uncertainty in generation costs affecting optimal dispatch and uncertainty in demand loads are captured through composite scenarios. Probabilities are assigned to different scenarios. The effects of these uncertainties are transferred to the objective function in terms of total costs, which include: generation (dispatch), transmission expansion and load curtailment costs. Two formulations are presented: stochastic and minimum regret. The stochastic formulation seeks a design with minimum expected cost. The minimum regret formulation seeks a design with robust performance in terms of variance of the operational costs. Results for a test problem and a potential application to a real system are presented.     

“走出去”的最优税筹——境外所得税抵免制度对中国企业境外投资架构的影响及对策

从国际税收筹划角度,就125号文对中国企业境外控股架构的影响进行解析,可以帮助企业对境外投资进行更有效的筹划和安排。     

Stochastic optimization using a trust-region method and random models

Mathematical Programming - In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random...     

Stochastic dominance and mean–variance measures of profit and loss for business planning and investment

In this paper, we first extend the stochastic dominance (SD) theory by introducing the first three orders of both ascending SD (ASD) and descending SD (DSD) to decisions in business planning and investment to risk-averse and risk-loving decision makers so that they can compare both return and loss. We provide investors with more tools for empirical analysis, with which they can identify the first-order ASD and DSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors and business planners to identify the third order ASD and DSD prospects and make better choices.     

Trajectory planning for unmanned aerial vehicles: a network optimization approach

This paper presents a new approach for trajectory planning of air vehicles. It considers scenarios with risk areas and forbidden zones and takes into account the maneuverability of the air vehicle. It is flexible as to allow different kinds of objective functions such as minimizing risk, flight path length or flight time, and allows to implement constraints on fuel consumption or other resources. Additionally, it can incorporate waypoints to be passed by the air vehicle with or without specified overflight directions. The method includes planning of one-way and return trips. The underlying model is based on a discretization of the airspace into a non-regular network. Every path in the network corresponds to a flyable trajectory which means that the trajectory is within the performance limits of the air vehicle. The generation of the network is done non-deterministically. One of the main benefits of the model is that one can make use of standard network optimization techniques.     

Stochastic models for air cargo terminal manpower supply planning in long‐term operations

In this research, based on two deterministic‐demand planning models, we established two long‐term stochastic‐demand planning models by incorporating the stochastic disturbances of manpower demands that occur in actual operations. The models are formulated as mixed integer linear programs that are solved using a mathematical programming solver. To compare the performance of the two stochastic‐demand and two deterministic‐demand planning models under the stochastic demands that occur in actual operations, we further develop a simulation‐based evaluation method. Finally, we perform numerical tests using real operating data from a Taiwan air cargo terminal. The preliminary results show that the stochastic models could be useful for planning air cargo terminal manpower supply. Copyright © 2008 John Wiley & Sons, Ltd.     

Stochastic models for life contingencies

This review gives a survey of the traditional field of individual risk theory in relation to the more recent stochastic models for life contingencies. The stochastic approach on the basis of loss functions is extended to the Markov model, of which multiple decrement theory is a special case.     

A survey of optimization models on cancer chemotherapy treatment planning

While chemotherapy is an effective method for treating cancers such as colorectal cancer, its effectiveness may be dampened by the drug resistance and it may have significant side effects due to the destruction of normal cells during the treatment. As a result, there is a need for research on choosing an optimal chemotherapy treatment plan that minimizes the number of cancerous cells while ensuring that the total toxicity is below an allowable limit. In this paper, we summarize the mathematical models applied to the optimal design of the cancer chemotherapy. We first elaborate on a typical optimization model and classify relevant literature with respect to modeling methods: Optimal control model (OCM) and others. We further classify the OCM models with respect to the solution method used. We discuss the limitations of the existing research and provide several directions for further research in optimizing chemotherapy treatment planning.     

Estimation of resource requirements in optimization problems of network planning

It is well known that optimization problems of network planning concerned with non-depositable resources are as a rule non-convex. The extreme difficulties of solving non-convex optimization problems make any pre-solution analysis of such problems highly welcome. This paper is devoted to an important tool for such analysis of our class of problems. The main ideas of the paper are as follows.Jointly with a given non-convex problem Ξ we consider an adjoint convex problem Θ, which is obtained from Ξ by lifting all resource constraints. Feasible schedules of the problem Θ are called Θ-feasible for the problem Ξ. By estimation of resource requirements we understand construction of such estimates which are valied for every Θ-feasible schedule. Two kinds of estimates are considered: pointwise (i.e. for single time units) and interval (for longer time spans) ones.Much attention is paid to numerical aspects of estimation. That is why a hierarchy of upper estimates is built ranging from a rough but easily computed one to the best estimate, requiring much more sophisticated computations. Amazingly enough such hierarchy does not exist for lower estimates, the simplest of them, next in roughness to the total zero only, being the best.     

A general rapid network design,line planning and fleet investment integrated model

We study four proofs that the Gittins index priority rule is optimal for alternative bandit processes. These include Gittins’ original exchange argument, Weber’s prevailing charge argument, Whittle’s Lagrangian dual approach, and Bertsimas and Niño-Mora’s proof based on the achievable region approach and generalized conservation laws. We extend the achievable region proof to infinite countable state spaces, by using infinite dimensional linear programming theory.     

Stochastic optimization for the ruin probability

The Cramér‐Lundberg insurance model is studied where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is the ruin probability. The problem can be imbedded in the framework of discrete‐time stochastic dynamic programming. Basic tools are the Howard improvement and the verification theorem. Explicit conditions are obtained for the optimality of employing no reinsurance and of not investing in the market.     

A structural framework for the design of integrated environmental and land-use planning optimization models

This study presents a structural framework for analyzing land-use/environmental interactions and formulating planning models accounting for these interactions. A general conceptual planning model is first developed. Its applicability is illustrated through a review of major environmental pollution transfer models, and through the development of a prototypical model that is progressively expanded to account for centralized treatments, transfer modifications, short-term and long-term dynamics, and the stochasticity of the environment.     

Stochastic modelling of long-term investment risks

There are many risks that individuals, firms, and societieshave to face, and among them are the uncertainties of futureinvestment variables, which include inflation (both of pricesand earnings), interest rates,exchange rates, and returns onordinary shares (including both dividend income and changesin capital values).These investment risks affect inviduals intheir own financial planning; affect companies in planning investmentprojects and in arrangements for raising capital;affect governmentsand government institutions that have to borrow in the capitalmarkets; and especially affect investment institutions and intermediarieswho take on borrowings, deposits, insurance contracts, or pensionfund liabilities on the one hand and invest assets in loans,ordinary shares, property, or other investments on the other. A great deal of work done by financial economists in recentdecades has established reasonable models for describing movementsof many investment variables in the short run. Typically thesemodels are based on a 'random walk' or Gauss-Wiener continuousdiffusion process. This sort of model has been particularlyvaluable to market-makers and other investment participantswhose time horizon is short. But these short-term models oftendo not provide a satisfactory structure for the long term. Thispresentation will describe some of the author's work in thestatistical analysis of long-term investment series, both inthe United Kingdom and in other countries, based on statisticaltime-series analysis of historical data. Although many of the series could be valued using multivariatemethods, such as vector autoregressive (VAR) models, preliminaryinvestigation showed that many of the series could be investigatedin a 'cascade' fashion, with price inflation being put as theinitial 'driver'. A very long historic series shows long periodswhen changes in prices in successive years could be taken asrandom, with zero drift, and other periods (including most ofthis century) when inflation rates in successive years werecorrelated. A similar pattern has applied in recent years inmany other countries. It is postulated that the prices of ordinary shares in aggregateare closely related to the dividends paid on them, so that theratio between dividend and price, i.e. the dividend yield, isstationary—fluctuating around a constant mean. The dividend-yieldseries can be described by means of a first-order autoregressivetime-series model,while the dividend series can be describedby a model that depends on inflation in the current and precedingyears, with an appropriate time lag. Interest rates, both long-term and short-term, are first decomposedinto an allowance for prospective future inflation and a 'real'rate of interest, comparable to the yield on index-linked stocks.The real rate of interest can also be modelled as a mean-revertingautoregressive model. The allowance for future inflationcanbe derived as a moving average of past inflation rates.In orderto link models for different countries, it is necessary to havea model for currency exchange rates. This can be done by postulatinga hypothetical 'purchasingpower parity' exchange rate, whichexactly allows for changes in inflation, and then by modellingthe deviation of the actual rate from the hypothetical rateby means of yet another autoregressive model. It is necessaryalso to keep an appropriate structure for cross rates betweenany pair of currencies. This series of stochastic models is particularly useful forestimating future scenarios of all the variables in a consistentmanner, and for estimating their likely variability. In some cases this can be done analytically, but in generalit requires ’Monte Carlo‘ simulations. Various possibleapplications of the model in different fields will be described.     

Stochastic bargaining models

Two stochastic models of labor-management negotiations are proposed and solved explicity. The cost function considered is such that either a penalty is incurred as long as negotiations take place, or an infinite penalty is incurred if a settlement is not reached before a fixed time. Furthermore, the cost function takes the risk sensitivity of the optimizers into account.This research was supported by the Natural Sciences and Engineering Research Council of Canada and by the fund FCAR of Québec.     

Long-term real dynamic investment planning

When long-term savers plan for retirement they need to know their investment prospects in terms of real income (Merton, 2014). While inflation has traditionally been considered as a complication in financial analysis and financial practise, we obtain enhanced predictability and model fit if the real returns are targeted in conjunction with earnings-by-price minus inflation as predictor. For this latter case, we propose an investment strategy of updating the simple classical Merton proportion as we go along. This simple strategy is very close to the complicated theoretically optimal solution but has comparably much lower parameter uncertainty.     

Automatic identification of embedded network rows in large-scale optimization models

The solution of a large-scale linear, integer, or mixed integer programming problem is often facilitated by the exploitation of special structure in the model. This paper presents heuristic algorithms for identifying embedded network rows within the coefficient matrix of such models. The problem of identifying a maximum-size embedded pure network is shown to be among the class of NP-hard problems. The polynomially-bounded, efficient algorithms presented here do not guarantee network sets of maximum size. However, upper bounds on the size of the maximum network set are developed and used to show that our algorithms identify embedded networks of close to maximum size. Computational tests with large-scale, real-world models are presented.