Optimal decision policy for a retailer in a stochastic manufacturing process involving a rework process for defective items and two-level trade credit finance

Contraction Mappings in the Theory Underlying Dynamic Programming

In this paper, we applied a dynamic programming model for the optimization of Consolidated University Academic Salary Structure II (CONUASS II) for the overall interest of the academic staff and the Nigerian University System at large; the focus of this research was on the decision policy that would help to enhance the living conditions of lecturers in the Nigerian universities thereby averting frequent strikes and disruption of academic calendars; strikes delay students and affect their features; hence, anything that can stabilize the university education in Nigeria will contribute immensely to the economic growth and stability of the country. For us to achieve these objectives, we applied dynamic programming and developed an optimal decision policy to obtain the best optimal policy needed for the highest-ranking cadre in the academic to achieve optimal remuneration of at least twice their per annum salary with subsequent adjustment in the other cadres’ salaries accordingly; the researchers applied the optimal decision policy and obtained (1, 1, 1, 1, 1, 1, 2, 2, 0, 0) that optimizes the academic staff's earnings with a promotion to level 08 instead of remaining at the bar with many steps. If this policy is applied, a professor at the bar will grow to level 08 and will earn up to at least double his annual salary (N13,658,325) instead of the current stagnating salary of (N6,020,163) per annum at the bar; this will make the lecturers happy and discharge their duties with commitments thereby addressing the perennial strikes in the Nigerian universities.

We consider how local and global decision policies interact in stopping time problems such as quickest time change detection. Individual agents make myopic local decisions via social learning, that is, each agent records a private observation of a noisy underlying state process, selfishly optimizes its local utility and then broadcasts its local decision. Given these local decisions, how can a global decision maker achieve quickest time change detection when the underlying state changes according to a phase-type distribution? This paper presents four results. First, using Blackwell dominance of measures, it is shown that the optimal cost incurred in social-learning-based quickest detection is always larger than that of classical quickest detection. Second, it is shown that in general the optimal decision policy for social-learning-based quickest detection is characterized by multiple thresholds within the space of Bayesian distributions. Third, using lattice programming and stochastic dominance, sufficient conditions are given for the optimal decision policy to consist of a single linear hyperplane, or, more generally, a threshold curve. Estimation of the optimal linear approximation to this threshold curve is formulated as a simulation-based stochastic optimization problem. Finally, this paper shows that in multiagent sensor management with quickest detection, where each agent views the world according to its prior, the optimal policy has a similar structure to social learning.

In this paper, we applied dynamic programming model for optimization of Consolidated University Academic Salary Structure II (CONUASS II) for the overall interest of the academic staff and the Nigerian University System. Our focus was on the decision policy that would help to enhance the living condition of lecturers in the Nigerian universities thereby averting frequent strikes and disruption of academic calendars. The frequent and incessant strikes delay students and impacts negatively to their feature; hence, anything that could be done to stabilize the university education in Nigeria will contribute immensely to the economic growth and stability of the country. To achieve this, we applied dynamic programming and developed an optimal decision policy which was applied to obtain the best optimal policy needed for the highest ranking cadre in the academic to achieve optimal remuneration of at least twice their per annum salary with subsequent adjustment in the other cadres’ salaries accordingly. Applying the optimal decision policy, we obtained (1, 1, 1, 1, 1, 1, 2, 2, 0, 0) which optimizes the academic staff’s earning with a promotion to level 08 instead of remaining at bar with many steps. If this policy is implemented, a professor at the bar will grow to level 08 and will therefore earn up to at least double of his/her annual salary (N13,658,325) instead of the current stagnating salary of (N6,020,163) per annum at the bar. This will make the lecturers to be happy and discharge their duties with commitments and thereby addressing the perennial strikes in the Nigerian universities.

The traditional economic order quantity models usually assume that the purchasing cost must be paid for the items as soon as the items are received. However, in practice trade credit is one of the main measures to promote the sale of goods. On the other hand, the retailer would offer the trade credit period to his/her customers. That is a two-level trade credit. In this paper, we develop an EPQ model for deteriorating items under two-level trade credit, where the demand rate of the items is dependent on the current stock level, and the inventory system with inventory-level-dependent demand rate is further extended. Then we provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could make the average cost per unit time to a minimum. Easy solution methods are shown to find the optimal replenishment policy of the considered problem and some theoretical evidences are provided for retailers to make the practical inventory decision. At last, numerical examples are presented to illustrate the developed model.

Adaptive Optimization for Forest-level Timber Harvest Decision Analysis

Optimal decision policy for a retailer in a stochastic manufacturing process involving a rework process for defective items and two-level trade credit finance

With the increase of world population and industrial growth of developing countries, demand for energy, in particular electric power, has gone up at an unprecedented rate over the last four decades. To meet the demand, electric power generation by use of fossil fuel has increased enormously thereby producing increased quantity of greenhouse gases contributing more and more to atmospheric pollution which, climate Scientists believe, can adversely affect the global climate, and health and welfare of world population. In view of these, there is global awareness of looking for alternate sources of energy such as natural gas, hydropower, wind, solar, geothermal and finally biomass etc. It is recognized that this requires replacement of existing infrastructure with new systems, which cannot be achieved overnight. Optimal control theory has been widely used for the last five decades in diverse areas of physical sciences, medicine, engineering, economics and social sciences. The main motivation of this article is to use this theory to find the optimum strategy (decision or policy) for integration of all currently available renewable energy sources with the existing electric power generating systems with the ultimate goal of elimination of fossil fuel. Eight main energy sources such as Coal, Petroleum, Natural Gas, Conventional Hydro, Wind, Solar, Geothermal and Biomass are considered in a dynamic model. The state of the dynamic model represents the level of power generation from each of the sources at any time t. The proposed objective function is based on the desired target level of power generation from each of the available sources at the end of the plan period while reducing the production of greenhouse gasses. Pontryagin Minimum principle is used to determine the optimal control or decision policy. Official released data from the U.S. Energy Information Administration is used as a case study. Based on this data and a mathematical model proposed in a paper (Miah, Ahmed and Chowdhury, 2012) published by Energy Economics combined with the minimum principle, an optimal policy is presented for integration of renewable energy sources to the national power grid.

This paper investigates the optimal replenishment policy for the retailer with the ramp type demand and demand dependent production rate involving the trade credit financing, which is not reported in the literatures. First, the two inventory models are developed under the above situation. Second, the algorithms are given to optimize the replenishment cycle time and the order quantity for the retailer. Finally, the numerical examples are carried out to illustrate the optimal solutions and the sensitivity analysis is performed. The results show that if the value of production rate is small, the retailer will lower the frequency of putting the orders to cut down the order cost; if the production rate is high, the demand dependent production rate has no effect on the optimal decisions. When the trade credit is less than the growth stage time, the retailer will shorten the replenishment cycle; when it is larger than the breakpoint of the demand, within the maturity stage of the products, the trade credit has no effect on the optimal order cycle and the optimal order quantity.

We investigate the structure of optimal policies in general multiperiod multiasset consumption-investment problems in the presence of transfer costs. A number of objectives such as utility of a consumption stream, utility of terminal wealth, and multiattribute utility are encompassed by the formulation. The general problem is first formulated as a stochastic dynamic program. The one-period subproblems are then analyzed using convex duality theory. The principal result is the characterization of a not necessarily convex of no for each period. If in any period the entering asset position is in this set, no transactions are made. Each point of the set is the vertex of a cone such that if the entering asset position is outside the set, the optimal policy is to move to the vertex of the cone in which the entering asset position lies. It is shown that the region of no transactions is a connected set and that it is a cone when the utility function is assumed to be positively homogeneous. In the latter case, the optimal decision policy and induced utility IN THIS PAPER we study a general class of multiperiod, multiasset investmentconsumption problems. Our purpose is to characterize the structure of optimal policies in the presence of transaction costs. Related problems have been studied by several authors, e.g., Constantinides [2, 3], Fama [5], Eppen and Fama [4], Kamin [7], Magill and Constantinides [10], Zabel [17], Hakansson [6], Merton [11], Samuelson [14], and Mukherjee and Zabel [12], and in these papers optimal policies have been characterized for a number of special cases. Our methodology significantly generalizes and sharpens many of the above results. For example, much of the previous work has been limited to the two-asset case or to particular utility functions, whereas our formulation allows any number of assets and general concave utility functions. The principal result of this paper, in the case of proportional transaction costs and concave utility functions, is the characterization of the optimal policy in each period and the set of entering asset positions from which no transactions should be made. This set or of no (RNT) can take on many forms ranging from a simple halfline to a nonconvex set. (See examples in Section 3.)

We consider the problem of approximating optimal stationary control policies by quantized control. Stationary quantizer policies are introduced and it is shown that such policies are “-optimal among stationary policies under mild technical conditions. Quantitative bounds on the approximation error in terms of the rate of the approximating quantizers are also derived. Thus, one can search for”-optimal policies within quantized control policies. These pave the way for applications in optimal design of networked control systems where controller actions need to be quantized, as well as for a new computational method for the generation of approximately optimal Markov decision policies in general (Borel) state and action spaces for both discounted cost and average cost infinite horizon optimal control problems.

In this paper, we want to investigate the retailer's optimal replenishment policy with defective items under cash discount and two levels of trade credit policy. Mathematical models have been derived for determining the retailer's optimal inventory cycle time so that the annual total profit is maximized. Finally, numerical examples are given to illustrate the theorem and obtain some managerial phenomena.

We are witnessing an increasing use of data-driven predictive models to inform decisions in high-stakes situations, from lending and hiring to university admissions. As decisions have implications for individuals and society, there is increasing pressure on decision makers to be transparent about their decision policies. At the same time, individuals may use knowledge, gained by transparency, to invest effort strategically in order to maximize their chances of receiving a beneficial decision. Our goal is to find decision policies that are optimal in terms of utility in such a strategic setting. First, we characterize how strategic investment of effort by individuals leads to a change in the feature distribution. Using this characterization, we show that, in general, optimal decision policies are hard to find in polynomial time, and there are cases in which deterministic policies are suboptimal. Then, we demonstrate that, if the cost individuals pay to change their features satisfies a natural monotonicity assumption, we can narrow down the search for the optimal policy to a particular family of decision policies with a set of desirable properties, which allow for a highly effective polynomial time-heuristic search algorithm using dynamic programming. Finally, under no assumptions on the cost, we develop an iterative search algorithm that is guaranteed to converge to locally optimal decision policies. Experiments on synthetic and real credit card data illustrate our theoretical findings and show that the decision policies found by our algorithms achieve higher utility than those that do not account for strategic behavior. This paper was accepted by Vivek Farias, data science. Funding: This work was supported by Machine Learning Cluster of Excellence [EXC #2064/1, Project #390727645], H2020 European Research Council [Grant 945719], and Bundesministerium für Bildung und Forschung [Grant 01IS18039B]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.02567

Optimal fishery harvesting rules under uncertainty

In this study, we investigate pricing policy and coordination conditions in an online-to-offline supply chain considering corporate environmental responsibility and lateral inventory transshipment. First, we provide demand functions to capture effects of price, corporate environmental responsibility level, and preference degree of the consumer to online channel. Then, we build profit functions and develop three joint pricing and corporate environmental responsibility-level decision models for centralized decision (Scenario CD), retailer Stackelberg game (Scenario RS), and manufacturer Stackelberg game (Scenario MS). Furthermore, we determine the optimal decision policies by solving developed models, and conduct sensitivity analysis of significant factors. Finally, we use a revenue-sharing contract to realize supply chain coordination and find coordination conditions for Scenario RS and MS, and further show the impacts of revenue-sharing rate and investment cost sensitivity on the conditions using numerical studies. We find that optimal joint decision policies can be affected by significant factors to a varying degree. In certain conditions, the revenue-sharing contract can coordinate online-to-offline supply chains considering corporate environmental responsibility and lateral inventory transshipment. Our study proposes a new decision problem, constructs new joint decision models, determines new optimal joint policies, conducts new coordination analysis, and thus contributes to the research on supply chain operations considering corporate environmental responsibility and lateral inventory transshipment.