Probabilistic Audit in a Revenue Sharing Contract Under Asymmetric Demand Information

A two-echelon supply chain comprising a supplier and a retailer, coordinated by a revenue-sharing contract has been studied. The supplier knows the realized demand only from a sales report submitted by the retailer at the end of each decision period. Possession of private information about the market demand allows the retailer to under-report sales. To protect revenue loss from this under-reporting, the supplier uses audit probabilistically to check the retailer’s dishonesty. Unlike designing a mechanism for the supplier to elicit private information from the retailer, which has been predominantly discussed in the literature, this study proposes a policy where the players can improve their expected profit compared to what they would have earned when the retailer had to reveal truthful information. Our study finds that the supplier benefits from the retailer’s dishonesty, provided dishonesty is limited with the help of a probabilistic audit process. Both players' expected profits are higher in our proposed policy than what they would earn under a truth-inducing policy. These findings suggest that future studies focus on achieving social welfare instead of concentrating only on truth-inducing mechanisms. A numerical analysis of the optimization problem is performed to find the optimal audit probability. Our results will help a manager in a supplying firm design a revenue-sharing contract when she cannot observe her retailer’s revenue without an audit

Patterns in abundance and diversity of faecally dispersed parasites of tiger in Tadoba National Park, central India

BACKGROUND: Importance of parasites in ecological and evolutionary interactions is being increasingly recognized. However, ecological data on parasites of important host species is still scanty. We analyze the patterns seen in the faecal parasites of tigers in the Tadoba National Park, India, and speculate on the factors and processes shaping the parasite community and the possible implications for tiger ecology. RESULTS: The prevalence and intensities were high and the parasite community was dominated by indirect life cycle parasites. Across all genera of parasites variance scaled with the square of the mean and there was a significant positive correlation between prevalence and abundance. There was no significant association between different types of parasites. CONCLUSIONS: The 70 samples analyzed formed 14 distinct clusters. If we assume each of the clusters to represent individual tigers that were sampled repeatedly and that resident tigers are more likely to be sampled repeatedly, the presumed transient tigers had significantly greater parasite loads than the presumed resident ones

Deterministic and stochastic descriptions of gene expression dynamics

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012

A New Green Labeling Scheme for Agri-Food Supply Chains: Equilibrium and Information Sharing under Uncertainties

Even though organic farming is perceived worldwide as the most eco-friendly agricultural method, its significantly lower yield compared to conventional farming poses a major challenge in ensuring food security for the ever-increasing world population. On the other hand, the adverse environmental impacts of conventional agriculture due to the uncontrolled use of key farm inputs like fertilizer and irrigation water cannot be overlooked. In this context, we develop a new eco-label to promote an efficient agricultural method that provides the right balance between yield and environmental impacts through the optimal use of these farm inputs. The proposed eco-label is applied to a game-theoretic model of a farmer-retailer supply chain under demand and yield uncertainties. We consider the demand as a function of the product’s retail price, greenness, and quality; and model yield using a crop-response function. The analytical results derived help optimize the farm inputs, retail prices, and order quantity so that the stakeholders’ profits are maximized. We also investigate the effects of yield information sharing in this supply chain and find that the stakeholders must share yield information when environmentally conscious consumers dominate the market

A New Green Labeling Scheme for Agri-Food Supply Chains: Equilibrium and Information Sharing under Uncertainties

Even though organic farming is perceived worldwide as the most eco-friendly agricultural method, its significantly lower yield compared to conventional farming poses a major challenge in ensuring food security for the ever-increasing world population. On the other hand, the adverse environmental impacts of conventional agriculture due to the uncontrolled use of key farm inputs like fertilizer and irrigation water cannot be overlooked. In this context, we develop a new eco-label to promote an efficient agricultural method that provides the right balance between yield and environmental impacts through the optimal use of these farm inputs. The proposed eco-label is applied to a game-theoretic model of a farmer-retailer supply chain under demand and yield uncertainties. We consider the demand as a function of the product’s retail price, greenness, and quality; and model yield using a crop-response function. The analytical results derived help optimize the farm inputs, retail prices, and order quantity so that the stakeholders’ profits are maximized. We also investigate the effects of yield information sharing in this supply chain and find that the stakeholders must share yield information when environmentally conscious consumers dominate the market

Mathematical model to mitigate planning fallacy and to determine realistic delivery time

Planning fallacy is the tendency to underestimate the duration of a task due to the optimistic bias of individuals. We design a mechanism from the principal's perspective (an original equipment manufacturer (OEM)) to mitigate the optimistic bias of agents (a contract manufacturer (CM) and a supplier) in a serial supply chain. The OEM determines the deadline of agents by explicitly factoring the agent's planning fallacy in the model through the cost under-estimation factor. Further, we prove that threshold based incentives are better than lump-sum bonus to motivate the supplier and the CM to mitigate procrastination of task. Keywords: Planning fallacy, Procrastination, Optimistic bias, Behavioural operation

Determining expected behaviour of fraudsters for a continuous audit system

This research attempts to determine the behaviour of fraudsters in a continuous audit system where the fraudsters have multiple options for committing fraud. The system is modelled as a Continuous Time Markov Chain where the state changes are caused by the fraudster's actions. The model uses a dynamic game with probabilistic transitions to determine the expected behaviour of the fraudster

Moving towards “mobile warehouse”: Last-mile logistics during COVID-19 and beyond

Supply chains in general and last-mile logistics in particular, have been disrupted due to COVID-19. Though several innovative last-mile logistics solutions have been proposed in the past, they possess certain limitations, especially during COVID-19 motivating the need for an alternative last-mile logistics solution. We present a review of literature related to last-mile logistics and supply chain disruptions to identify the limitations of existing last-mile delivery practices during COVID-19. Using a stylized analytical model, we then propose that “mobile warehouse” can be an effective solution to last-mile logistics issues faced during COVID-19 and beyond under certain conditions. A mobile warehouse is a truck dedicated to a particular geographical location and carries the inventory of various products based on the estimated demand requirements for these products in that geographical location. We provide the condition under which the B2C e-commerce providers find it profitable to adopt a truck as a mobile warehouse to sell high demand items quickly