Single-period Models Research Articles

Probabilistic Inventory Models and Productivity of Selected Manufacturing Firms in Port Harcourt

This study examines the relationship between probabilistic inventory models and productivity of selected manufacturing firms in port Harcourt. Correlational survey research design was adopted for this study as this study seek to determine the relationship between the two variables. The population of this study is thirty-two (32) manufacturing companies in Rivers State which are registered with the Rivers State branch of Manufacturers Association of Nigeria (MAN). This gave us a total of ninety-two (92) for the study. Structured questionnaire instrument title” Probabilistic inventory models and productivity of selected manufacturing firms in Port Harcourt. questionnaire was developed on five- point likert scale. The result of the Cronbach's Alpha reliability test indicates .800 which is above .70 which implies that the items are reliable. Pearson product moment correlation was used to test the hypotheses using SPSS (statistical package social sciences). The study revealed that there is a significant relationship between Continuous Review Models and Productivity of manufacturing firms in Port Harcourt, Rivers State. There is a significant relationship between Periodic Review Models and Productivity of manufacturing firms in Port Harcourt, Rivers State. There is a significant relationship between Single-Period Models and Productivity of manufacturing firms in Port Harcourt, Rivers State. The study concluded that Probabilistic inventory models play a crucial role in optimizing inventory management for manufacturing firms. The study recommended that Manufacturing firms in Port Harcourt should consider implementing probabilistic inventory models such as continuous review, periodic review, and single-period models to optimize their inventory management processes.

Winter Wheat Yield Estimation Based on Multi-Temporal and Multi-Sensor Remote Sensing Data Fusion

Accurate yield estimation before the wheat harvest is very important for precision management, maintaining grain market stability, and ensuring national food security. In this study, to further improve the accuracy of winter wheat yield estimation, machine learning models, including GPR, SVR, and DT, were employed to construct yield estimation models based on the single and multiple growth periods, incorporating the color and multispectral vegetation indexes. The results showed the following: (1) Overall, the performance and accuracy of the yield estimation models based on machine learning were ranked as follows: GPR, SVR, DT. (2) The combination of color indexes and multispectral vegetation indexes effectively improved the yield estimation accuracy of winter wheat compared with the multispectral vegetation indexes and color indexes alone. The accuracy of the yield estimation models based on the multiple growth periods was also higher than that of the single growth period models. The model with multiple growth periods and multiple characteristics had the highest accuracy, with an R2 of 0.83, an RMSE of 297.70 kg/hm2, and an rRMSE of 4.69%. (3) For the single growth period, the accuracy of the yield estimation models based on the color indexes was lower than that of the yield estimation models based on the multispectral vegetation indexes. For the multiple growth periods, the accuracy of the models constructed by the two types of indexes was very close, with R2 of 0.80 and 0.80, RMSE of 330.37 kg/hm2 and 328.95 kg/hm2, and rRMSE of 5.21% and 5.19%, respectively. This indicates that the low-cost RGB camera has good potential for crop yield estimation. Multi-temporal and multi-sensor remote sensing data fusion can further improve the accuracy of winter wheat yield estimation and provide methods and references for winter wheat yield estimation.

Risk-Taking of Hedge Funds: Empirical Evidence vs. Theoretical Modeling

When an investor delegates portfolio management to a hedge fund manager, whose risk-taking preference governs? Single-period models with option-like incentives suggest stark variation in risk-taking across fund value and time as fund managers maximize their own well-being. Empirical validation is hard to come by, as each hedge fund traces out only a few points on that risk-taking surface. Cross-sectional pooling of normalized returns allows precise estimation of the normalized risk-taking surface. In fact, it is almost flat with some increased risk-taking at very low fund values. A multi-year model is consistent with these findings.

A novel data envelopment analysis for location of renewable energy site with respect to sustainability

The feasibility of a photovoltaic project depends on strategic decisions such as the location of the power plant. This article contributes to the literature by proposing a novel algorithm employing non-radial data envelopment analysis and a clustering method, including single-period and multi-period models, to select appropriate locations to establish photovoltaic sites. This algorithm evaluates the candidate locations’ efficiency to establish photovoltaic power plant considering defined sustainability criteria. Due to different results obtained from the presented models, the clustering method identifies the best locations. Iran is used to assess the performance of the proposed algorithm. The results show that six provinces are suitable locations to launch photovoltaic sites and the obtained locations are in good agreement with the photovoltaic potential for Iran. Furthermore, the results reveal that Iran has a high potential to generate photovoltaic energy. Besides, the locations identified for the establishment of photovoltaic sites are close to high electricity consumption provinces.

無套利市場、完全市場與風險中立機率的唯一存在 (An Arbitrage-Free and Complete Market and the Unique Existence of Risk-Neutral Probabilities)

Chinese Abstract: 衍生性金融商品的基本訂價理論，是根植於不存在套利機會與完全市場假設，它的對等命題是存在唯一的風險中立測度。闡述以上定理的直覺、精簡模型是單期、二資產且二狀態的二項樹模型；因此，原文的衍生性金融商品教科書，都將二項樹模型安排在布雷克修斯連續時間模型之前。然而，大部分的中文教科書卻將二項樹模型安排在連續模型之後，而且普遍忽略風險中立訂價的必要條件：無套利機會假設，以及忽略風險中立機率唯一存在的必要條件：完全市場。本文利用單期、三狀態與三獨立基礎資產假設，呈現三維度報酬率的圖形表達、闡述不存在套利機會市場、完全市場與平賭測度機率的直覺意涵。最後，本文列表比較十數冊教科書對於本文討論議題的表達方式，並且提出評論。本文作者相信，也試圖為期貨與選擇權教科書貢獻清楚、嚴謹的學理意涵，也啟發對無套利市場、完全市場與平賭測度的解讀。 English Abstract: The fundamental pricing theory of derivatives is based on the assumptions of arbitrage-free and complete markets, which is equivalent to the unique existence of a risk-neutral measure. A single-period binomial-tree model with two assets and two states provides an intuitive and concise way to interpret this theory. As a result, English textbooks on derivatives present binomial-tree models before the Black-Scholes continuous-time model. However, most Chinese textbooks on derivatives present them in reverse order. In particular, they tend to neglect that the assumption of arbitrage-free markets is a necessary condition for the legitimacy of risk-neutral pricing, and that a condition of complete markets is for the uniqueness of a risk-neutral measure. The objective of this paper is to provide an intuitive interpretation of arbitrage-free and complete markets, as well as martingale measures, in three-dimensional figures. It is done by presenting discrete single-period models with three states, accompanied by three underlying assets. Finally, this paper compares and critiques the contents of more than ten textbooks. This paper intends to contribute to a clearer theoretical illustration of arbitrage-free, complete markets, and martingale measures.

Process Flexibility for Multiperiod Production Systems

The classical process flexibility literature has mostly focused on single-period models as finding the optimal multiperiod policy is difficult because of the curse of dimensionality. In “Process Flexibility for Multiperiod Production Systems,” Cong Shi, Yehua Wei, and Yuan Zhong study the design of sparse flexibility in dynamic make-to-order environments. Leveraging theories from applied probability, they propose a notion of “generalized chaining,” which allows one to design effective sparse flexibility structures in regimes in which capacity slacks are low. They then construct a structure that performs asymptotically close to full flexibility with only m + n arcs, where m and n represent the number of plants and product types, while also demonstrating that m + n is tight, that is, constructing systems in which even the best flexibility structure with m + n − 1 arcs cannot achieve the same asymptotic performance. These results provide insights into how design principles for process flexibility extend beyond the classical single-period model.

An Effective League Championship Algorithm for the Stochastic Multi-Period Portfolio Optimization Problem

The multi-period portfolio optimization models were introduced to overcome the weaknesses of the single-period models via considering a dynamic optimization system. However, due to the nonlinear nature of the problem and rapid growth of the size complexity with increasing the number of periods and scenarios, this study is devoted to developing a novel league championship algorithm (LCA) to maximize the portfolio’s mean-variance function subject to different constraints. A Vector Auto Regression model is also developed to estimate the return on risky assets in different time periods and to simulate different scenarios of the rate of return accordingly. Besides, we proved a valid upper bound of the objective function based on the idea of using surrogate relaxation of constraints. Our computational results based on sample data collected from S&P 500 and 10-year T. Bond indices indicate that the quality of portfolios, in terms of the mean-variance measure, obtained by LCA is 10 to 20 percent better than those of the commercial software. This sounds promising that our method can be a suitable tool for solving a variety of portfolio optimization problems.

Multi-period portfolio optimisation with alpha decay

The traditional Markowitz MVO approach is based on a single-period model. Single period models do not utilise any data or decisions beyond the rebalancing time horizon with the result that their policies are myopic in nature. For long-term investors, multi-period optimisation offers the opportunity to make wait-and-see policy decisions by including approximate forecasts and long-term policy decisions beyond the rebalancing time horizon. We consider portfolio optimisation with a composite alpha signal that is composed of a short-term and a long-term alpha signal. The short-term alpha better predicts returns at the end of the rebalancing period but it decays quickly, i.e., it has less memory of its previous values. On the other hand, the long-term alpha has less predictive power than the short-term alpha but it decays slowly. We develop a simple two stage multi-period model that incorporates this alpha model to construct the optimal portfolio at the end of the rebalancing period. We compare this model with the traditional single-period MVO model on a simulated example from Israelov and Katz (2011) and also a large strategy with realistic constraints and show that the multi-period model tends to generate portfolios that are likely to have a better realised performance.

Optimal self-protection in two periods: On the role of endogenous saving

Self-protection is a costly investment to reduce the probability of loss. This paper studies optimal self-protection in a two-period model with endogenous saving. In a setting with a binary loss we show that prudence is negatively associated with the optimal level of self-protection, consistent with results obtained in single-period models. We provide intuition for this finding with the help of a recent approach based on stochastic dominance. Furthermore, we determine the effect of interest rate risk on optimal self-protection and study a model in which a decision-maker engages in advance effort to increase the probability of facing a better risky situation. All our results suggest that the understanding of advance self-protection crucially hinges on whether the decision-maker also uses saving to optimize intertemporal consumption utility. If so, the fact that self-protection expenditures are upfront turns out to be irrelevant.

An Analysis of Theories on Stock Returns

Objective in writing this article is to provide an overview of the theories that has been developed for stock returns which is an important area of financial markets’ researches. Since the researches in this field are very active for the past quarter, it is not possible to describe all works that has been done in this area. Most important researches will be discussed without going deeper in mathematical tools and theories.Empirical works have been showing that stock returns are predictable cross-sectional and by time. The discussions about prediction of stock price behavior started with Markowitz with his article –Portfolio Selection-. Markowitz won Nobel Prize in 1990 for his research about portfolio theory. However he criticized by many economists since implementation of the theory requires lots of effort to evaluate data and since it uses historical data the prediction will not be accurate. In addition the assumption that stock returns are normally distributed is not true in reality. Sharpe, Lintner, and Mossin independently developed a model which has come to be known CAPM (capital asset pricing model) in 1964, 1965, and 1966 respectively. Beta coefficient is a key parameter in CAPM world. Beta measures risk of an asset in relation to the market such as S&P500 or an alternative factor. Actually the CAPM is a simple model which is based on sound reasoning and some of the assumptions -all investors have the same information, information is costless, and there are no taxes transactions costs- are unrealistic in market. APT (arbitrage pricing theory) presented for a better estimation for stock returns than CAPM. CAPM is a modified theory while APT is a completely different model. APT’s multiple factors provide a better indication of asset risk and a better estimate of expected return. There are n-factors effecting stock returns in APT but the number of factors are unknown. Furthermore CAPM and APT are single-period models. To get multi-period aspects of market ICAPM was developed. After that CCAPM (consumption-oriented capital asset pricing model) was introduced. It tried to explain behavior of stock returns by a logical extension of APT. A long literature exist on prediction of stock market returns but especially after the latest financial crisis these theories must be analyzed and suggested new ideas for forecasting behavior of stock returns. Keywords: Stock Returns, Markowitz, CAPM, APT, ICAPM, CCAPM, Fama-French 3-factor model.

Multi-Period Factor Model of a Loan Portfolio

We construct a general dynamic model of losses of a large loan portfolio, secured by collaterals. In the model, the wealth of a debtor and the price of the corresponding collateral depend each two factors: a common one, having a general distribution, and an individual one, following an AR(1) process. The default of a loan happens if the wealth stops to be sufficient for repaying the loan; the loss given default (LGD) equals to the part of the principal exceeding the collateral price.We show that the mapping transforming the common factors into the probability of default (PD) and the average LGD has some desirable properties; namely, it is is one-to-one twice continuously differentiable. As the transformation is not analytically tractable, we propose a numerical technique for its computation and demonstrate its accuracy by a numerical study. We demonstrate that the results given our model may differ significantly from those resulting from single-period models. We also show that our model is able to replicate implicitly the empirically observed decrease of PDs within a portfolio in time.Finally, we give a formula for the overall loss associated with the portfolio and, as an example of its application, we formulate a simple optimal scoring decision problem and discuss its solution.

Optimization of Multi-period Bilevel Supply Chains under Demand Uncertainty

Due to advance of global manufacturing, the decentralized optimization of multi-tier supply chains for multiple retailers and manufacturers becomes more and more important. Conventional works on game theoretical model for supply chain planning problems concentrates on single period models. However, the situations for decision making in decentralized supply chains are subject to change with respect to time periods. In this paper, we address the optimization of multi-period bilevel supply chains under demand uncertainty. The decentralized supply chain planning problem is modelled as a multi-period non-cooperative game. The problem is formulated as a stochastic multi-period bilevel optimization problem under demand uncertainty. The optimization algorithm to derive a Stackelberg equilibrium for multi-period bilevel supply chain planning problem is developed. The effectiveness of the proposed method is validated by comparing it with the single period models.

Shock Diffusion: Does Inter-Sectoral Network Structure Matter?

This paper introduces the concept of diffusion of shocks in a macroeconomic network consisting of inter-sectoral production linkages. I show that if sectors have different reaction horizons it would lead to diffusion of shocks through the network over time which prevents the inter-sectoral linkages to form the feedback loop structure essential to generate aggregate volatility. This result is different from other recent papers which have single period model with contemporaneous production linkages between different sectors thus generating sectoral shock amplification as one sector reacts to another contemporaneously resulting in bigger aggregate fluctuations. In contrast if sectors have different production horizons due to varying complexity of their production process or supply chain, it would break down the feedback architecture present in single period models. I further show that if the diffusion rate is varied for different sectors, the contribution of network structure to aggregate volatility can be insignificant. Also, it is no longer sufficient to characterize this contribution of inter-sectoral production network to aggregate volatility by just looking at input-output matrix or its summary statistics like degree distribution. The paper thus highlights the stark difference between the study of financial and inter-sectoral production networks because of the possibility of contemporaneous amplification and hence cascades in the case of financial networks. In the end, I propose lead time indicator as a possible proxy for measuring differential sectoral diffusion rates.

A distribution-free newsvendor model with balking penalty and random yield

Purpose: The purpose of this paper is to extend the analysis of the distribution-free newsvendor problem in an environment of customer balking, which occurs when customers are reluctant to buy a product if its available inventory falls below a threshold level. Design/methodology/approach: We provide a new tradeoff tool as a replacement of the traditional one to weigh the holding cost and the goodwill costs segment: in addition to the shortage penalty, we also introduce the balking penalty. Furthermore, we extend our model to the case of random yield. Findings: A model is presented for determining both an optimal order quantity and a lower bound on the profit under the worst possible distribution of the demand. We also study the effects of shortage penalty and the balking penalty on the optimal order quantity, which have been largely bypassed in the existing distribution free single period models with balking. Numerical examples are presented to illustrate the result . Originality/value: The incorporation of balking penalty and random yield represents an important improvement in inventory policy performance for distribution-free newsvendor problem when customer balking occurs and the distributional form of demand is unknown.

A comparison of dynamic hazard models and static models for predicting the special treatment of stocks in China with comprehensive variables

The stock exchanges in China give a stock special treatment in order to indicate its risk warning if the corresponding listed company cannot meet some requirements on financial performance. To correctly predict the special treatment of stocks is very important for the investors. The performance of the prediction models is mainly affected by the selection of explanatory variables and modelling methods. This paper makes a comparison between the multi-period hazard models and five widely used single-period static models by investigating a comprehensive category of variables including accounting variables, market variables, characteristic variables and macroeconomic variables. The empirical result shows that the performance of the models is sensitive to the choice of explanatory variables but the performance between the multi-period hazard models and the single-period static models has no significant difference.

Optimising a Plant Economic and Environmental Performance Over a Full Lifetime

A significant reduction in energy consumption can be achieved by applying Process Integration methodology. More sustainable process solutions can be achieved both environmentally friendlier (reducing the emissions and pollution) and economically more attractive (reducing utility cost). An improved process design can be achieved by an appropriate trade-off between investment and operating cost. However, the trade-off can only be established correctly if it reflects the future variability, and even unpredictability, of prices for utilities, raw material and products. The objective of this work was to optimise process design for full process lifetime by considering some provisions for future price fluctuations. Most process synthesis models are single-period models that only consider only fixed cost coefficients. However, prices are fluctuating rather quickly and an optimal process design obtained for one year can be different for another. This work focused on the separation processes as they consume a significant amount of energy. The synthesis of a distillation column sequence integrated with its heat exchanger network was used as a case study for the separation of a multi-component stream into pure component products. In order to consider future price fluctuations, a multi-period mixed-integer nonlinear (MINLP) model was developed. Different projections regarding utility prices based on past prices were derived at due to the uncertainties of forecasting. Maximisation of Net Present Value was chosen as an optimisation criterion, in order to account for future price fluctuations and the time-value of money over a full lifetime. Trade-off between investment and operating cost, and their distribution between the heat exchanger network (HEN) and the distillation columns were evaluated in the following step. Significant utility savings and a reduction in operational cost can be achieved in this way when compared to those cases where empirical actual-to-minimal ratios within the range of 1.2 - 1.5 is used, especially when future utility prices are considered. The solution obtained by this novel optimisation methodology seems to be more robust compared to the conventional single–period optimisation as it reflects any forecasted future price fluctuations. Consequently, the probability of meeting the optimal design for each year over a full lifetime of the separation process is thus higher.

A Profit-Maximizing Approach to Disposition Decisions for Product Returns*

Motivated by the asset recovery process at IBM, we analyze the optimal disposition decision for product returns in electronic products industries. Returns may be either remanufactured for reselling or dismantled for spare parts. Reselling a remanufactured unit typically yields higher unit margins. However, demand is uncertain. A common policy in many firms is to rank disposition alternatives by unit margins. We propose a profit-maximization approach that considers demand uncertainty. We develop single period and multiperiod stochastic optimization models for the disposition problem. Analyzing these models, we show that the optimal allocation balances expected marginal profits across the disposition alternatives. A detailed numerical study reveals that our approach to the disposition problem outperforms the current practice of focusing exclusively on high-margin options, and we identify conditions under which this improvement is the highest. In addition, we show that a simple myopic heuristic in the multiperiod problem performs well.

Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model

Investment and risk control are becoming increasingly important for financial institutions. Asset allocation provides a fundamental investing principle to manage the risk and return trade-off in financial markets. This article proposes a general formulation of a first approximation of multiperiod asset allocation modeling for institutions that invest to meet the target payment structures of a long-term liability. By addressing the shortcomings of both single-period models and the single-point forecast of the mean variance approach, this article derives explicit formulae for optimal asset allocations, taking into account possible future realizations in a multiperiod discrete time model.

The Value of Component Commonality in a Dynamic Inventory System with Lead Times

Component commonality has been widely recognized as a key factor in achieving product variety at low cost. Yet the theory on the value of component commonality is rather limited in the inventory literature. The existing results were built primarily on single-period models or periodic-review models with zero lead times. In this paper, we consider a continuous-review system with positive lead times. We find that although component commonality is in general beneficial, its value depends strongly on component costs, lead times, and dynamic allocation rules. Under certain conditions, several previous findings based on static models do not hold. In particular, component commonality does not always generate inventory benefits under certain commonly used allocation rules. We provide insight on when component commonality generates inventory benefits and when it may not. We further establish some asymptotic properties that connect component lead times and costs to the impact of component commonality. Through numerical studies, we demonstrate the value of commonality and its sensitivity to various system parameters in between the asymptotic limits. In addition, we show how to evaluate the system under a new allocation rule, a modified version of the standard first-in-first-out rule.

Dynamic procurement in a capacitated supply chain facing uncertain demand

In an environment where a buyer procures capacity from a capacitated supplier through a wholesale price contract, the impact of timing of the decisions and of additional demand information on the supplier's pricing and the buyer's procurement decisions are investigated. As the selling season approaches, the buyer and the supplier have better information about the demand process. It is questioned as to what degree waiting until the demand uncertainty is resolved—given that such an option is feasible—is the best alternative for the supply chain partners. The main model is a two-period dynamic pricing/procurement game where the supplier sets wholesale prices dynamically; he sets the second period price after seeing the demand state as well as the buyer's first period procurement quantity. Two single-period models based on the information available to the players prior to their decisions are also studied. For each model, the subgame perfect Nash equilibrium is found in a closed form and the players' behaviors are analyzed to determine the impact of the additional information and trading periods on their welfare. The supplier's optimal capacity decision is also considered. Several additional insights are obtained through numerical experiments.