Discount Rate Parameters Research Articles

An integrated optimization model for procurement and production lot sizing and scheduling problems

Abstract Lot sizing is a prevalent issue within manufacturing companies, where determining the optimal procurement and production lot sizes is crucial for maximizing profits. This problem has become more complex, given that numerous suppliers can provide the same raw materials with different prices and quantity discount schemes. A company should also determine optimal carriers to deliver materials to the company’s warehouse. In a manufacturing process, the company should determine the optimal production lot size and its schedules. In this paper, a model was developed to solve simultaneously procurement and production lot sizing, as well as production scheduling problems. The model encompasses multiple suppliers offering quantity discounts, aiming to maximize company profit by accounting for various costs, including procurement, production, inventory, and quality costs. A case study is taken from a company producing noodles and its related derivative products to illustrate the application of the model. Based on the optimization results, the company obtained a total profit of IDR. 14,656,550,000 or $950,921.30 (the exchange rate of $1 at IDR. 15,413). The sensitivity analysis results show that the objective function is sensitive to changes in the purchase cost, sale revenue, and discount rate parameters. The decision variables for accepted product demand, product quantity, and the starting and completion time of product family are only sensitive to changes in certain parameters. Meanwhile, the decision variables for product inventory, product backlog, raw material inventory, and purchased raw material quantity are sensitive to the changes in all the analyzed parameters.

The decade after tomorrow: Estimation of discount rates from realistic temporal decisions over long time horizons

Understanding trade-offs across time is important in many areas of economics, but eliciting and estimating the parameters of discounting processes is difficult. We implement a novel stated choice approach to measuring discount rates that combines desirable elements of laboratory experiments and market behavior studies. We use a decadal time frame and exogenous variation in payment attributes to identify private consumption discount rate parameters that are consistent with the observed choice patterns. Imposing exponential discounting implies that people discount the future in a manner consistent with market interest rates, but we find substantial heterogeneity that varies with observable respondent characteristics. Relaxing the time consistent discounting assumption provides empirical evidence against declining discount rates.

On the Optimization of Bayesian D-Efficient Discrete Choice Experiment Designs for the Estimation of QALY Tariffs That Are Corrected for Nonlinear Time Preferences

ObjectivesThis article explains how to optimize Bayesian D-efficient discrete choice experiment (DCE) designs for the estimation of quality-adjusted life year (QALY) tariffs that are unconfounded by respondents' time preferences. MethodsThe calculation of Bayesian D-errors is explained for DCE designs that allow for the disentanglement of respondents' time and health-state preferences. Time preferences are modelled via an exponential, hyperbolic, or power discount function and the performance of the proposed DCE designs is compared with that of several conventional DCE designs that do not take nonlinear time preferences into account. ResultsBased on the achieved D-error, asymptotic standard error, and estimated sample size to obtain statistically significant estimates of the discount rate parameters, the proposed designs outperform the conventional DCE designs. ConclusionsWe recommend that applied researchers use appropriately optimized DCE designs for the estimation of QALY tariffs that are corrected for time preferences. The TPC-QALY software package that accompanies this article makes the recommended designs easily accessible for health-state valuation researchers.

Testing the Traditional CCAPM in the US: A Revisit

This study re-examines the traditional consumption-based capital asset pricing model (CCAPM) by largely updating US monthly samples of consumption and stock market return and following the methodology of generalized method of moments (GMM) with instrumental variables of Hansen and Singleton (1982). As a result, our investigations reveal the following facts for the US stock market. First, 1) in the cases of the CCAPM with consumption for nondurable goods and the CCAPM with consumption for nondurable goods and services, their discount rate parameters almost always take similar values that are slightly less than one. Next, 2) their risk aversion parameters more stably take small minus values in the CCAPM with consumption for nondurable goods than in the CCAPM with consumption for nondurable goods and services. Third, 3) in our empirical examinations, all estimated CCAPMs with two kinds of consumption are not rejected by the J-tests.

A Re-examination of the Consumption-based Capital Asset Pricing Model: The Case of US and Japan

This paper re-tests the classic consumption-based capital asset pricing model (CCAPM) by extending US quarterly samples and adding the Japanese case. Using the generalized method of moments (GMM) methodology developed by Hansen and Singleton (1982), we obtain the following findings. (1) First, in the case of the CCAPM with consumption for nondurable goods in the US, the discount rate parameters generally show plausible values; however, the risk aversion parameters show unstable values in general. Further, by the J -tests, the estimated CCAPMs with consumption for nondurable goods in the US are always supported. (2) Second, in the case of the CCAPM with consumption for nondurable goods and services in the US, although the parameters of discount rate generally show plausible values, the risk aversion parameters are unstable. In addition, judging the results of the J -tests, all estimated CCAPMs with consumption for nondurable goods and services in the US are supported. (3) Finally, as for the CCAPM with private final consumption expenditures in Japan, the parameters of discount rate take plausible values; on the other hand, the risk aversion parameter values are unstable in general. Regarding the model validity, our estimated CCAPMs for Japan are mostly supported by the J -tests.

New designs for research in delay discounting

AbstractThe two most influential models in delay discounting research have been the exponential (E) and hyperbolic (H) models. We develop a new methodology to design binary choice questions such that exponential and hyperbolic discount rates can be purposefully manipulated to make their rate parameters orthogonal (Pearson’s R = 0), negatively correlated (R = –1), positively correlated (R = +1), or to hold one rate constant while allowing the other to vary. Then we extend the method to similarly contrast different versions of the hyperboloid model. The arithmetic discounting model (A), which is based on differences between present and future rewards rather than their ratios, may easily be made orthogonal to any other pair of models. Our procedure makes it possible to design choice stimuli that precisely vary the relationship between different discount rates. However, the additional control over the correlation between different discount rate parameters may require the researcher to either restrict the range that those rate parameters can take, or to expand the range of times the participant must wait for future rewards.

Testing for Dynamic Misspecification of Input Demand Functions: An Application to Canadian Agriculture

Previous applications of the inter‐temporal quadratic adjustment cost model in agriculture have failed to consider information gained from pre‐testing in choosing an appropriate specification for dynamic demand of quasi‐fixed inputs. A test strategy is outlined taking account of this information in order to consistently estimate adjustment cost and discount rate parameters. Canadian agricultural data are used in the empirical analysis. Test results suggest that the intertemporal quadratic adjustment cost model is inappropriate for modeling dynamic demand for land, labor and machinery.

Note—Optimal Long-Run Equilibrium Advertising Level for the Blattberg-Jeuland Model

The purpose of this note is to formulate and solve a dynamic optimization problem based on the Blattberg-Jeuland advertising model. Also examined is the behavior of the optimal long-run equilibrium level of advertising with respect to changes in some important parameters of the problem. In particular, a new interesting result, showing that the equilibrium optimal level of advertising for the B-J model is a nonmonotone function of the rate of decay parameter, is derived. That is, the equilibrium optimal level of advertising is an increasing function of the rate of decay for smaller rates of decay and a decreasing function for larger rates of decay than a critical rate of decay. This phenomenon is analogous to a sink effect and is intuitively appealing. It is also shown that the equilibrium optimal level of advertising is a decreasing function of the insertion cost and discount rate parameters. Finally, the framework presented in this note is also useful in analyzing further extensions of the problem solved here.