Competition and Coordination in a Two‐Channel Supply Chain

We study competition and coordination in a supply chain in which a single supplier both operates a direct channel and sells its product through multiple differentiated retailers. We study analytically the supply chain with symmetric retailers and find that the supplier prefers to have as many retailers as possible in the market, even if the retailers' equilibrium retail price is lower than that of the supplier, and even if the number of retailers and their cost or market advantage prevent sales through the direct channel. We find that the two‐channel supply chain may be subject to inefficiencies not present in the single‐channel supply chain. We show that several contracts known to coordinate a single‐channel supply chain do not coordinate the two‐channel supply chain; thus we propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the two‐channel supply chain with symmetric retailers. We provide some analytical results for the supply chain with asymmetric retailers and propose an efficient solution approach for finding the equilibrium. We find numerically that the supplier still benefits from having more retailers in the market and that linear quantity discount contracts can mitigate supply chain inefficiency, though they no longer achieve perfect coordination.     

Benefits of Hybrid Lateral Transshipments in Multi‐Item Inventory Systems under Periodic Replenishment

Lateral transshipments are a method of responding to shortages of stock in a network of inventory‐holding locations. Conventional reactive approaches only seek to meet immediate shortages. The study proposes hybrid transshipments which exploit economies of scale by moving additional stock between locations to prevent future shortages in addition to meeting immediate ones. The setting considered is motivated by retailers who operate networks of outlets supplying car parts via a system of periodic replenishment. It is novel in allowing non‐stationary stochastic demand and general patterns of dependence between multiple item types. The generality of our work makes it widely applicable. We develop an easy‐to‐compute quasi‐myopic heuristic for determining how hybrid transshipments should be made. We obtain simple characterizations of the heuristic and demonstrate its strong cost performance in both small and large networks in an extensive numerical study.     

Efficiency or Competition? A Structural Econometric Analysis of Canada's AWS Auction and the Set‐Aside Provision

In 2008, Industry Canada auctioned 105 MHz of spectrum to a group of bidders that included incumbents and potential new entrants into the Canadian mobile phone market, raising $4.25 billion. In an effort to promote new entry, 40 MHz of spectrum was set‐aside for new entrants. In order to estimate the implicit cost of the set‐aside provision, we estimate the parameters of the bidders' profit function via a maximum match estimator based on the notion of pairwise stability in matches. We find that all telecommunications firms valued both geographic complementarities across auction licenses as well as absolute spectrum. Under a reasonable alternative scenario, our results indicate that the set‐aside led to a total profit loss of approximately 10%.     

Effect of Inventory Information Discrepancy in a Drop‐Shipping Supply Chain

This article investigates the impact of information discrepancy between a drop‐shipper and an online retailer on the drop‐shipping supply chain performance. The inventory information misalignment between them contributes to the failure of order fulfillment and demand satisfaction, and hence the associated penalties are incurred. In this article, we first analyze the penalties of ignoring such information discrepancy on both the drop‐shipper and the online retailer. We then assess the impact of information discrepancy on both parties when the drop‐shipper understands the existence of the information discrepancy but is not able to eliminate the errors. The numerical experiments indicate that both parties can have significant amount of the percentage cost reductions if the information discrepancy can be eliminated, and the potential savings are substantial especially when the errors have large variability. Furthermore, we observe that the online retailer is more vulnerable to information discrepancy than the drop‐shipper, and the drop‐shipper is likely to suffer from the online retailer's underestimation of the physical inventory level more than the problem of its overestimation. Moreover, even if eliminating errors is not possible, both parties could still benefit from taking the possibility of errors into consideration in decision making.     

On evaluating how well a biomarker can predict treatment response with survival data

One of the objectives of personalized medicine is to take treatment decisions based on a biomarker measurement. Therefore, it is often interesting to evaluate how well a biomarker can predict the response to a treatment. To do so, a popular methodology consists of using a regression model and testing for an interaction between treatment assignment and biomarker. However, the existence of an interaction is not sufficient for a biomarker to be predictive. It is only necessary. Hence, the use of the marker‐by‐treatment predictiveness curve has been recommended. In addition to evaluate how well a single continuous biomarker predicts treatment response, it can further help to define an optimal threshold. This curve displays the risk of a binary outcome as a function of the quantiles of the biomarker, for each treatment group. Methods that assume a binary outcome or rely on a proportional hazard model for a time‐to‐event outcome have been proposed to estimate this curve. In this work, we propose some extensions for censored data. They rely on a time‐dependent logistic model, and we propose to estimate this model via inverse probability of censoring weighting. We present simulations results and three applications to prostate cancer, liver cirrhosis, and lung cancer data. They suggest that a large number of events need to be observed to define a threshold with sufficient accuracy for clinical usefulness. They also illustrate that when the treatment effect varies with the time horizon which defines the outcome, then the optimal threshold also depends on this time horizon.     

A strong law of large numbers for independent random variables under non-additive probabilities

Abstract

Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.     

Exploring Parameter Relations for Multi‐Stage Models in Stage‐Wise Constant and Time Dependent Hazard Rates

Single cohort stage‐frequency data are considered when assessing the stage reached by individuals through destructive sampling. For this type of data, when all hazard rates are assumed constant and equal, Laplace transform methods have been applied in the past to estimate the parameters in each stage‐duration distribution and the overall hazard rates. If hazard rates are not all equal, estimating stage‐duration parameters using Laplace transform methods becomes complex. In this paper, two new models are proposed to estimate stage‐dependent maturation parameters using Laplace transform methods where non‐trivial hazard rates apply. The first model encompasses hazard rates that are constant within each stage but vary between stages. The second model encompasses time‐dependent hazard rates within stages. Moreover, this paper introduces a method for estimating the hazard rate in each stage for the stage‐wise constant hazard rates model. This work presents methods that could be used in specific types of laboratory studies, but the main motivation is to explore the relationships between stage maturation parameters that, in future work, could be exploited in applying Bayesian approaches. The application of the methodology in each model is evaluated using simulated data in order to illustrate the structure of these models.     

Inference in Semi‐Parametric Dynamic Models for Repeated Count Data

This paper deals with a longitudinal semi‐parametric regression model in a generalised linear model setup for repeated count data collected from a large number of independent individuals. To accommodate the longitudinal correlations, we consider a dynamic model for repeated counts which has decaying auto‐correlations as the time lag increases between the repeated responses. The semi‐parametric regression function involved in the model contains a specified regression function in some suitable time‐dependent covariates and a non‐parametric function in some other time‐dependent covariates. As far as the inference is concerned, because the non‐parametric function is of secondary interest, we estimate this function consistently using the independence assumption‐based well‐known quasi‐likelihood approach. Next, the proposed longitudinal correlation structure and the estimate of the non‐parametric function are used to develop a semi‐parametric generalised quasi‐likelihood approach for consistent and efficient estimation of the regression effects in the parametric regression function. The finite sample performance of the proposed estimation approach is examined through an intensive simulation study based on both large and small samples. Both balanced and unbalanced cluster sizes are incorporated in the simulation study. The asymptotic performances of the estimators are given. The estimation methodology is illustrated by reanalysing the well‐known health care utilisation data consisting of counts of yearly visits to a physician by 180 individuals for four years and several important primary and secondary covariates.