Discrete Dynamic Programming Model Research Articles

Accept or reject a ride? This is the problem

PurposeOnline ride-hailing platforms match drivers with passengers by receiving ride requests from passengers and forwarding them to the nearest driver. In this context, the low acceptance rate of offers by drivers leads to friction in the process of driver and passenger matching. What policies by the platform may increase the acceptance rate and by how much? What factors influence drivers' decisions to accept or reject offers and how much? Are drivers more likely to turn down a ride offer because they know that by rejecting it, they can quickly receive another offer, or do they reject offers due to the availability of outside options? This paper aims to answer such questions using a novel dataset from Tapsi, a ride-hailing platform located in Iran.Design/methodology/approachThe authors specify a structural discrete dynamic programming model to evaluate how drivers decide whether to accept or reject a ride offer. Using this model, the authors quantitatively measure the effect of different policies that increase the acceptance rate. In this model, drivers compare the value of each ride offer with the value of outside options and the value of waiting for better offers before making a decision. The authors use the simulated method of moments (SMM) method to match the dynamic model with the data from Tapsi and estimate the model's parameters.FindingsThe authors find that the low driver acceptance rate is mainly due to the availability of a variety of outside options. Therefore, even hiding information from or imposing fines on drivers who reject ride offers cannot motivate drivers to accept more offers and does not affect drivers' welfare by a large amount. The results show that by hiding the information, the average acceptance rate increases by about 1.81 percentage point; while, it is 4.5 percentage points if there were no outside options. Moreover, results show that the imposition of a 10-min delay penalty increases acceptance rate by only 0.07 percentage points.Originality/valueTo answer the questions of the paper, the authors use a novel and new dataset from a ride-hailing company, Tapsi, located in a Middle East country, Iran and specify a structural discrete dynamic programming model to evaluate how drivers decide whether to accept or reject a ride offer. Using this model, the authors quantitatively measure the effect of different policies that could potentially increase the acceptance rate.

The shadow price of nitrogen

PurposeThe most recent and prestigious scientific research shows that nitrogen leaching caused by over-used nitrogen fertilizer rapidly acidifies all soil types in China, revolutionizing the basic understanding of the mechanism of soil acidification. The purpose of this paper is to study the impact of nitrogen on soil acidity over the long run, which is the shadow price of nitrogen.Design/methodology/approachIn a discrete dynamic programming model, this paper compares the nitrogen application and soil pH between optimal nitrogen control that takes the shadow price of nitrogen into consideration and myopic nitrogen control that ignores that shadow price. Using a five-year panel experimental data on a rapeseed-rice rotation, this paper simulates and numerically solves the dynamic model.FindingsBoth theoretically and empirically, this paper shows that the over-use of nitrogen and the decline in soil pH are explained by ignorance of the shadow price of nitrogen. Compared with optimal nitrogen control, myopic nitrogen control applies more nitrogen in total, resulting in lower soil pH. In addition, over-use in the first season contributes to soil acidification and the carry-over effects mitigate that problem.Originality/valueThis paper enriches the literature by extending the study of the environmental impact of nitrogen leaching to its impact on the long-term loss in agricultural production, providing a new theoretical framework in which to study soil acidification rather than conventionally treating soil acidification as a secondary consequence of acid rain, and showing the possibility of using nitrogen control to mitigate soil acidification when lime applications are not feasible due to socio-economic constraints.

Carbon sequestration and the optimal forest harvest decision under alternative baseline policies

The choice of a baseline against which to evaluate changes in carbon stocks is a critical component of any forest carbon offset market. In this paper, we use a discrete dynamic programming model and data from a lodgepole pine (Pinus contorta Douglas ex Loudon) stand in northeastern British Columbia, Canada, to demonstrate that different baselines have little or no effect on optimal harvest decision but can have a large impact on economic returns to a landowner. The results reveal that the magnitude of the financial return to the landowner is dependent on the starting conditions of both the predetermined baseline and the proposed carbon offset project. The study also shows that when given the choice between alternative baselines, a landowner will always choose a fixed baseline over a business-as-usual baseline.

Intergenerational long-term effects of preschool-structural estimates from a discrete dynamic programming model

This paper formulates a structural dynamic programming model of preschool investment choices of altruistic parents and then empirically estimates the structural parameters of the model using the NLSY79 data. The paper finds that preschool investment significantly boosts cognitive and non-cognitive skills, which enhance earnings and school outcomes. It also finds that a standard Mincer earnings function, by omitting measures of non-cognitive skills on the right-hand side, overestimates the rate of return to schooling. From the estimated equilibrium Markov process, the paper studies the nature of within generation earnings distribution, intergenerational earnings mobility, and schooling mobility. The paper finds that a tax-financed free preschool program for the children of poor socioeconomic status generates positive net gains to the society in terms of average earnings, higher intergenerational earnings mobility, and schooling mobility.

An optimal hybrid emission control system in a multiple compliance period model

We characterize an optimal hybrid policy for pollutant emissions that includes a permit price ceiling and emission cap in a multi-period model. Previous studies have primarily focused on a hybrid policy of emission regulation that included an emission cap and permit price ceiling in a single period model, we extend this literature by developing such an optimal hybrid model in a multi-period framework where banking and borrowing of emission permits is allowed. In our model, we compare the case of a regulator who sets the emission cap and price ceiling to be consistent with a long run emission objective with the case of a regulator who occasionally is motivated to deviate from the optimal long run regulatory policy in order to correct for unexpected but exceptionally high emissions. Using a discrete dynamic programming model with stochastic emissions, we show that the hybrid model gives the regulator a degree of freedom in making an optimal price and quantity choice.

Intergenerational Long Term Effects of Preschool: Structural Estimates from a Discrete Dynamic Programming Model

This paper formulates a structural dynamic programming model of preschool investment choices of altruistic parents and then empirically estimates the structural parameters of the model using the NLSY79 data. The paper finds that preschool investment significantly boosts cognitive and non-cognitive skills, which enhance earnings and school outcomes. It also finds that a standard Mincer earnings function, by omitting measures of non-cognitive skills on the right hand side, overestimates the rate of return to schooling. From the estimated equilibrium Markov process, the paper studies the nature of within generation earnings distribution and intergenerational earnings and schooling mobility. The paper finds that a tax financed free preschool program for the children of poor socioeconomic status generates positive net gains to the society in terms of average earnings and higher intergenerational earnings and schooling mobility.

An Optimal Hybrid Emission Control System in a Multiple Compliance Period Model

Previous studies have primarily focused on a hybrid policy of emission regulation that included an emission cap and permit price ceiling in a single period model, we extend this literature by developing such an optimal hybrid model in a multi-period framework where banking and borrowing of emission permits is allowed. In our model, we compare the case of a regulator who sets the emission cap and price ceiling to be consistent with a long run emission objective with the case of a regulator who occasionally is motivated to deviate from the optimal long run regulatory policy in order to correct for unexpected but exceptionally high emissions. Using a discrete dynamic programming model with stochastic emissions, we show that the hybrid model gives the regulator a degree of freedom in making an optimal price and quantity choice.

An Optimization Distribution Model of Initial Emission Permits

Improving the allocation efficiency of environmental capacity is an important way to realize the coordination of a country's economic growth and environmental quality level. This paper simulates the economic environment of the real society and establishes discrete dynamic programming model about the initial distribution of the emissions permits, and adopts the inverse-deducing method studying the allocation efficiency of the initial emission permits from the perspective of economic benefit of the distribution of emission permits. At last, it points out that we can realize benefit maximization if limited regional environmental capacity can be distributed with a scientific and reasonable way in industries which own different value creation.

Intergenerational Long Term Effects of Preschool - Structural Estimates from a Discrete Dynamic Programming Model

This paper formulates a structural dynamic programming model of preschool investment choices of altruistic parents and then empirically estimates the structural parameters of the model using the NLSY79 data. The paper finds that preschool investment significantly boosts cognitive and non-cognitive skills, which enhance earnings and school outcomes. It also finds that a standard Mincer earnings function, by omitting measures of non-cognitive skills on the right hand side, overestimates the rate of return to schooling. From the estimated equilibrium Markov process, the paper studies the nature of within generation earnings distribution and intergenerational earnings and schooling mobility. The paper finds that a tax financed free preschool program for the children of poor socioeconomic status generates positive net gains to the society in terms of average earnings and higher intergenerational earnings and schooling mobility.

Intertemporal Stable Pension Funding

This paper proposes a discrete dynamic programming model to maintain pension contribution in a stable level. By assuming an intertemporal stable contribution rate, we derive an algorithm to calculate the optimal contribution that requires less exogenous information and produces more stable results. Our simulation results further confirm that our model helps pension fund managers to make more stable contributions and further reduce the contribution risk for the defined benefit pension fund than the traditional algorithms do.

Intertemporal Stable Pension Funding

This paper proposes a discrete dynamic programming model to maintain pension contribution in a stable level. By assuming an intertemporal stable contribution rate, we derive an algorithm to calculate the optimal contribution that requires less exogenous information and produces more stable results. Our simulation results further confirm that our model helps pension fund managers to make more stable contributions and further reduce the contribution risk for the defined benefit pension fund than the traditional algorithms do.

Optimal Banknote Replenishing Policy by an Issuing Bank

The minimal total cost replenishing policy for legal banknotes by the Bank of Israel (a ‘Federal’ Issuing Bank) was determined in three stages: (a) the market demand for banknotes of different denominations for a planning horizon of 10 years was evaluated using regression analysis; (b) the periodic supply of the banknotes to the market was estimated from the incremental market demand and the need to replace worn out banknotes; and (c) a total cost discrete Dynamic Programming model was constructed to find the optimal ordering quantities of banknotes, under the constraints of maximal storage and maximal order size capacities.

Optimal banknote replenishing policy by an issuing bank

The minimal total cost replenishing policy for legal banknotes by the Bank of Israel (a ‘Federal’ Issuing Bank) was determined in three stages: (a) the market demand for banknotes of different denominations for a planning horizon of 10 years was evaluated using regression analysis; (b) the periodic supply of the banknotes to the market was estimated from the incremental market demand and the need to replace worn out banknotes; and (c) a total cost discrete Dynamic Programming model was constructed to find the optimal ordering quantities of banknotes, under the constraints of maximal storage and maximal order size capacities.

Reply to comment by glenn gotz on “the dynamics of job separation: The case of federal employees”

The comment by Glenn Gotz discusses the advantages of a dynamic programming model under uncertainty relative to our model. We have no major disagreement with Gotz on what those advantages are. However, the advantages of our model relative to a programming model could be more clearly brought out, particularly the advantages of computation that largely motivated our model choice. In this short reply we would like to clarify the differences between the two models in behavioural assumptions and in computational difficulty, and to delineate for the practitioner the trade-offs that must be faced by any analyst. Since the trade-offs we discuss are present in all discrete dynamic programming models under uncertainty, not just in our application, our discussion should be useful to a fairly wide audience. To begin we shall state concisely a simple genetic optimal stopping model of the type discussed by Gotz but using slightly different notation to be more consistent with that in the programming literature. In the simplest optimal stopping program the agent (the individual in our case) begins in a particular state (working for the Federal government, for example) and must choose when to change to an alternative state (e.g. to leave the government). It is assumed that the individual cannot return if he leaves, although allowing that possibility would not change the nature of the trade-offs we discuss below. We also assume a finite horizon. Letting L denote the choice to leave and S the choice to stay, the values of leaving and staying, respectively, can be written as follows:

Aqueduct and Reservoir Capacities for Distribution Systems

The determination of the design capacity and operation policy of water delivery systems for farming areas is complicated by the temporal variability of demands and the corresponding use of delivery capacity, the probabilistic occurrence of supplies, the spatial distribution of users, and losses in the distribution systems. This paper develops a general method to integrate the choices of delivery system capacity and of conjunctively operated local reservoir capacities (the decisions of delivery system operators and farmers) to make more efficient use of water resources. The method consists of using the results from local economic optimization models of farm water requirements and benefits in a discrete dynamic programming model of the delivery system to determine the most efficient method of distributing limited water supplies. In previous papers, the writers have worked with intrayearly probabilistic supplies and transportation losses. The main improvments here are that the method: (1) Allows variable pea...

A Model for Corporate Debt Maturity Decisions

Whenever the firm must borrow funds, it must also decide maturity of the new debt. Yet, the decision models which have dealt with the debt maturity decision have done so almost incidentally, as an extension of the decision to exercise the call provision on outstanding bonds ([6], [10], [23]). There has been little direct examination of the corporate debt maturity decision. In an attempt to fill this gap, this paper is an exploration of the debt maturity decision for a firm which is concerned with minimizing the present value of the expected costs of borrowing. This paper develops a discrete dynamic programming model of the debt maturity decision, in a world where interest rates follow a finite Markov process, and where the yield curve is formed from expectations regarding the future course of interest rates. With this optimization model, the influence on the debt maturity strategy of variables such as flotation costs and liquidity premiums will be explored. There will be no consideration of the risks associated with alternative borrowing strategies.

A Generalized Discrete Dynamic Programming Model

This paper considers a stationary discrete dynamic programming model that is a generalization of the finite state and finite action Markov programming problem. We specify conditions under which an optimal stationary linear decision rule exists and show how this optimal policy can be calculated using linear programming, policy iteration, or value iteration. In addition we allow the parameters of the problem to be random variables and indicate when the expected values or these random variables are certainty equivalents.

Turnpike Theory in Deterministic Discrete Dynamic Programming with Discount Factor Greater than One

Previously known results concerning the structure of optimal policies will be applied here to derive turnpike theorems for the deterministic discrete dynamic programming model with discount factor greater than one.