Models for Ordering Multiple Products Subject to Multiple Constraints, Quantity and Freight Discounts

One of the most important responsibilities of a supply chain manager is to decide “how much” (or “many”) of inventory items to order and how to transport them. This paper presents four mixed-integer linear programming models to help supply chain managers make these decisions for multiple products subject to multiple constraints when suppliers offer quantity discounts and shippers offer freight discounts. Each model deals with one of the possible combinations of all-units, incremental quantity discounts, all-weight and incremental freight discounts. The models are based on a piecewise linear approximation of the number of orders function. They allow any number of linear constraints and determine if independent or common (fixed) cycle ordering has a lower total cost. Results of computational experiments on an example problem are also presented.

Optimal EOQ Model for Deteriorating Items Considering the Incremental Quantity Discounts and Shortages

In this present paper, a deterministic lot size model is developed for deteriorating items with incremental quantity discounts. It is assumed that shortages are permitted to occur and fully backlogged. A simple solution procedure is shown for determining the optimal order lot size and the optimal order cycle. A numerical example is used to illustrate how the solution procedure works.

Examining the association between delay discounting,delay aversion and physical activity in Chinese adults with type-2 diabetes mellitus

BACKGROUND The role of physical activity in diabetes is critical,influencing this disease's development,man-agement,and overall outcomes.In China,22.3%of adults do not meet the minimum level of physical activity recommended by the World Health Organization.Therefore,it is imperative to identify the factors that contributing to lack of physical activity must be identified.AIM To investigate the relationship among delay discounting,delay aversion,glycated hemoglobin(HbA1c),and various levels of physical activity in Chinese adults diagnosed with type 2 diabetes mellitus(T2DM).METHODS In 2023,400 adults with T2DM were recruited from the People's Hospital of Linxia Hui Autonomous Prefecture of Gansu Province.A face-to-face questionnaire was used to gather demographic data and details on physical activity,delay discounting,and delay aversion.In addition,HbA1c levels were measured in all 400 participants.The primary independent variables considered were delay discounting and delay aversion.The outcome variables included HbA1c levels and different intensity levels of physical activity,including walking,moderate physical activity,and vigorous physical activity.Multiple linear regression models were utilized to assess the relationship between delay discounting,delay aversion,and HbA1c levels,along with the intensity of different physical activity measured in met-hours per week.RESULTS After controlling for the sample characteristics,delay discounting was negatively associated with moderate physical activity(β=-2.386,95%CI:-4.370 to-0.401).Meanwhile,delay aversion was negatively associated with the level of moderate physical activity(β=-3.527,95%CI:-5.578 to-1.476)in the multiple linear regression model,with statistically significant differences.CONCLUSION Elevated delay discounting and increased delay aversion correlated with reduced levels of moderate physical activity.Result suggests that delay discounting and aversion may influence engagement in moderate physical activity.This study recommends that health administration and government consider delay discounting and delay aversion when formulating behavioral intervention strategies and treatment guidelines involving physical activity for patients with T2DM,which may increase participation in physical activity.This study contributes a novel perspective to the research on physical activity in adults with T2DM by examining the significance of future health considerations and the role of emotional responses to delays.

Tunneling, Information Asymmetry, and Private Placement Discounts

Private placement has become an increasingly important method of equity refinancing for regulators, listed companies, and investors. This paper analyzes factors influencing private placement discounts based on the controlling shareholder＇s opportunistic behavior and information asymmetry. Our findings indicate that the type of subscriber is a key determinant of the private placement discount, particularly when the subscriber is the controlling shareholder. Asymmetric information between listed companies and investors is another important determinant： The higher the degree of information asymmetry, the greater the private placement discounts.

Equilibrium dividend strategies in the dual model with a random time horizon

This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.

Poke And Delayed Drink Intertemporal Choice Task(POKE-ADDICT):An open-source behavioral apparatus for intertemporal choice testing in rodents

Advancements in neuroscience research present opportunities and challenges,requiring substantial resources and funding.To address this,we describe here“Poke And Delayed Drink Intertemporal Choice Task(POKE-ADDICT)”,an open-source,versatile,and cost-effective apparatus for intertemporal choice testing in rodents.This allows quantification of delay discounting(DD),a cross-species phenomenon observed in decision making which provides valuable insights into higher-order cognitive functioning.In DD,the subjective value of a delayed reward is reduced as a function of the delay for its receipt.Using our apparatus,we implemented an effective intertemporal choice paradigm for the quantification of DD based on an adjusting delayed amount(ADA)algorithm using mango juice as a reward.Our paradigm requires limited training,a few 3D-printed parts and inexpensive electrical components,including a Raspberry Pi control unit.Furthermore,it is compatible with several in vivo procedures and the use of nose pokes instead of levers allows for faster task learning.Besides the main application described here,the apparatus can be further extended to implement other behavioral tests and protocols,including standard operant conditioning.In conclusion,we describe a versatile and cost-effective design based on Raspberry Pi that can support research in animal behavior,decision making and,more specifically,delay discounting.

浅谈传粉生物学中几个术语的含义及其中文译名

准确理解外来的专业术语并给予合适的中文译名 ,不仅有助于推动学科的发展 ,而且有利于同行之间的交流。传粉生物学是近年来在我国迅速发展的一个生态学与进化生物学的分支领域。本文讨论了该学科中的几个重要术语的含义和它们的中文译名 ,建议将pollendiscounting和seeddiscounting译为“花粉折损”和“种子折损” ,herkogamy译为“雌雄异位” ,trade_off译为“权衡”。

Real option pricing method for R&D investment under changing risk-free rate and discount rate

The polynomial spline model, which belongs to the static term structure model of interest rates, is studied. Every cash flow of the project is discounted relatively accurately by obtaining the discount rate from the static term structure model of interest rates. A simple basic model, which belongs to the dynamic term structure model, is studied, and the option pricing formula under changing risk-free rates is obtained by bringing it into the option pricing formula. Both dynamic and static term structure models are estimated by the use of the data of buy-back rates and the Shanghai Stock Exchange, and an example is given to compare the differences between the traditional method and the method under the changes in the interest rates and the discount rates.

Selling Luxury Brands in Online Private Sales Multibrand Retailers--An Exploratory Study of Consumers’Perspective

With Internet changing the luxury business landscape,new players have emerged such as the Online Private Sales Retailers(OPSRs).These offer online buyers with a choice of limited-time sales to help companies get rid of their overstocks.Luxury brands are no exception.No research has been conducted about how luxury consumers relate with such websites,hence this paper.In an exploratory fashion,interviews with luxury buyers who also buy online on OPSRs,are conducted to get insights on consumers’perceptions and luxury brand equity that selling through OPSRs may have.We find that appropriate product and brand help consumers forget that they are buying brands’unsold stocks,that transferring the luxury webmospheres would be positively perceived,that consumers from these websites are looking for benefits such as freedom of use and brand discovery,rather than personalized offers,that multiple discounts on several OPSRs may damage the luxury-perception of a brand,that the private sales members consider the service to be good enough for the demanded price,and that personalized invitations can help increase online consumers’feelings of desirability and exclusivity.The paper concludes with practical recommendations for both luxury companies and OPSRs.

Privacy preserving supply chain quantity discount contract design

The development and deployment of privary preserving supply chain quantity discount contract design can allow supply chain collaborations to take place without revealing any participant＇s data to others, reaping the benefits of collaborations wbile avoiding the drawbacks of privacy information disclosure. First, secure multi-party computation protocols are applied in the joint-ordering policy between a single supplier and a single retailer, the joint-ordering policy can be conducted without disclosing private cost information of any of the other supply chain partners. Secondly, secure multi-party computation protocols are applied in the privacy preserving supply chain quantity discount contract design between a single supplier and a single retailer. The information disclosure analyses of the algorithm show that： the optimal quantity discount of the jointordering policy can be conducted without disclosing private cost information of any of the other supply chain partners; the above protocol can be implemented without mediators; the privacy preserving quantity discount algorithm can be mutually verifiable and has solved the problem of asymmetric information.

Estimation of lung cancer burden in Australia,the Philippines,and Singapore:an evaluation of disability adjusted life years

Objective: Lung cancer is one of the leading cancers and major causes of cancer mortality worldwide. The economic burden associated with the high mortality of lung cancer is high, which accounts for nearly $180 billion on a global scale in 2008. This paper aims to understand the economic burden of lung cancer in terms of disability adjusted life years(DALY) in Australia, the Philippines, and Singapore.Methods: The years of life lost(YLL) and years lost due to disability(YLD) were calculated using the formula developed by Murray and Lopez in 1996 as part of a comprehensive assessment of mortality and disability for diseases, injuries and risk factors in 1990 and projected to 2020. The same formula is represented in the Global Burden of Disease template provided by the World Health Organization. Appropriate assumptions were made when data were unavailable and projections were performed using regression analysis to obtain data for 2015.Results: The total DALYs due to lung cancer in Australia, the Philippines, and Singapore were 91,695, 38,584, and 12,435,respectively, and the corresponding DALY rates per a population of 1,000 were 4.0, 0.4, and 2.2, respectively, with a discount rate of 3%. When researchers calculated DALYs without the discount rate, the burden of disease increased substantially; the DALYs were 117,438 in Australia, 50,977 in the Philippines, and 16,379 in Singapore. Overall, YLL or premature death accounted for more than 95% of DALYs in these countries.Conclusions: Strategies for prevention, early diagnosis, and prompt treatment must be devised for diseases where the major burden is due to mortality.

The compound Poisson risk model with dependence under a multi-layer dividend strategy

In this paper, a compound Poisson risk model with time-dependent claims is studiedunder a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber- Shiu function is derived and solved. Asymptotic formulas of the ruin probability are obtained when the claim size distributions are heavy-tailed.

ON THE RENEWAL RISK MODEL WITH INTEREST AND DIVIDEND

We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.

Applying a salinity response function and zoning saline land for three fi eld crops: a case study in the Hetao Irrigation District, Inner Mongolia, China

Salinity is one of the major abiotic factors affecting the growth and productivity of crops in Hetao Irrigation District, China. In this study, the salinity tolerances of three local crops, wheat （Triticum aestinum L.）, maize （Zea mays L.） and sunflower （Helianthus annuus L.）, growing in 76 farm fields are evaluated with modified discount function. Salinity ecological zones appropriate for these local crops are characterized and a case study is presented for crop salinity ecological zoning. The results show that the yield reductions of wheat, maize and sunflower when grown in saline soils are attributed primarily to a reduction in spikelet number, 1 000-grain weight and seed number per head, respectively. Sunflower is the most tolerant crop among the three which had a salinity tolerance index （ST-index） of 12.24, followed by spring maize and spring wheat with ST-Indices of 9.00 and 7.43, respectively. According to the crop salinity tolerance results, the arable land in the Heping Village of this district was subdivided into four salinity ecological zones： the most suitable, suitable, sub-suitable and unsuitable zones. The area proportion of the most suitable zone for wheat, maize and sunflower within the Heping Village was 27.5, 46.5 and 77.5%, respectively. Most of the most suitable zone occurred in the western part of the village. The results of this study provide the scientific basis for optimizing the local major crop distribution and improving cultural practices management in Hetao Irrigation District.

Study of evaluation method for the overseas oil and gas investment based on risk compensation

The overseas oil and gas investment evaluation is one of the core tasks in overseas investment of oil and gas companies,among which risk evaluation and benefit evaluation are the most important.This paper sets forth transmission paths of risk factors to the investment benefit by identifying 14 overseas oil and gas investment risks in four categories.On the basis of the concept of risk compensation,different compensation mechanisms specific to each risk are designed.The risk and benefit are integrated objectively to develop a comprehensive evaluation model by correcting the recoverable reserve,adjusting benefit evaluation parameters such as investments on exploration and development,and compensating for the changes in risk factors with time through dynamic discount rate.Moreover,two cases studies,namely the evaluations of Project A in Sudan and comparison among Blocks A–G,are used to describe usage method and applicable scope of such evaluation model,respectively.According to the results,oil price is a key influencing factor for enterprise internal risk and industrial risk.Risk compensation reduces comprehensive benefit of overseas oil and gas investment and undermines the investment feasibility and priority of blocks.The research findings of this paper are free from the effects of some subject factors and avoid multi-objective decision making,and also avoid the undesired repeated calculation of risk factors.

Evidence combination method in time domain based on reliability and importance

In order to achieve the information fusion in the time domain based on the evidence theory, an evidence combination method in the time domain based on reliability and importance is proposed according to the idea of evidence discount. Firstly, the distortion of the time-domain evidence is judged based on single exponential smoothing. The real-time reliability of the evidence at the adjacent time is obtained by the real-time reliability assessment method of the evidence based on the credibility decay model.Then, the relative importance of the evidence at the adjacent time is obtained by comprehensively considering improved conflict degree and uncertainty. Finally, based on the criterion of evidence discount and the Dempster’s rule of combination, the evidence combination is carried out to achieve the sequential combination of time-domain evidence. The numerical simulation and analysis show that this method has fully embodied the dynamic characteristics of time-domain evidence combination, and it has strong processing ability for conflict information and anti-disturbing ability.The proposed method has good applicability to information fusion in the time domain.

EXPECTED DISCOUNTED PENALTY FUNCTION OF ERLANG(2) RISK MODEL WITH CONSTANT INTEREST

The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.

The evolution of cooperation in public good game with deposit

The emergence of cooperation still remains a fundamental conundrum in the social and behavior sciences.We introduce a new mechanism,deposit mechanism,into theoretical model to explore how this mechanism promotes cooperation in a well-mixed population.Firstly,we extend the common binary-strategy combination of cooperation and defection in public good game by adding a third strategy,namely,deposit cooperation.The players with deposit cooperation strategy pay a deposit in advance to obtain the benefits of public good at a lower contributions compared with the players with cooperation strategy,when the provision of public good is successful.Then,we explore the evolution of cooperation in the public good game with deposit by means of the replicator dynamics.Theoretical computations and stimulations show that the deposit mechanism can promote cooperation in a well-mixed population,and the numbers of equilibrium point are determined by variables of public good game.On the one hand,when the coexistence of cooperators and defectors is the stable equilibrium point in the evolutionary system,increasing the threshold of public good and adopting the weak altruism way for share benefits can enhance the level of cooperation in the population.On the other hand,if the coexistence of deposit cooperators and defectors is the stable equilibrium point,it is effective to promote the deposit cooperation by lowering the values of discount and deposit,and raising the threshold of public good.

Choice of discount rate in reinforcement learning with long-delay rewards

In the world, most of the successes are results of longterm efforts. The reward of success is extremely high, but before that, a long-term investment process is required. People who are “myopic” only value short-term rewards and are unwilling to make early-stage investments, so they hardly get the ultimate success and the corresponding high rewards. Similarly, for a reinforcement learning(RL) model with long-delay rewards, the discount rate determines the strength of agent’s “farsightedness”.In order to enable the trained agent to make a chain of correct choices and succeed finally, the feasible region of the discount rate is obtained through mathematical derivation in this paper firstly. It satisfies the “farsightedness” requirement of agent. Afterwards, in order to avoid the complicated problem of solving implicit equations in the process of choosing feasible solutions,a simple method is explored and verified by theoreti cal demonstration and mathematical experiments. Then, a series of RL experiments are designed and implemented to verify the validity of theory. Finally, the model is extended from the finite process to the infinite process. The validity of the extended model is verified by theories and experiments. The whole research not only reveals the significance of the discount rate, but also provides a theoretical basis as well as a practical method for the choice of discount rate in future researches.

OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER

In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.