Joint Initial Stocking and Transshipment—Asymptotics and Bounds

A common problem faced by many firms in their supply chains can be abstracted as follows. Periodically, or at the beginning of some selling season, the firm needs to distribute finished goods to a set of stocking locations, which, in turn, supply customer demands. Over the selling season, if and when there is a supply‐demand mismatch somewhere, a re‐distribution or transshipment will be needed. Hence, there are two decisions involved: the one‐time stocking decision at the beginning of the season and the supply/transshipment decision throughout the season. Applying a stochastic dynamic programming formulation to a two‐location model with compound Poisson demand processes, we identify the optimal supply/transshipment policy and show that the optimal initial stocking quantities can be obtained via maximizing a concave function whereas the contribution of transshipment is of order square‐root‐of T. Hence, in the context of high‐volume, fast‐moving products, the initial stocking quantity decision is a much more important contributor to the overall profit. The bounds also lead to a heuristic policy, which exhibits excellent performance in our numerical study; and we further prove both the bounds and the heuristic policy are asymptotically optimal when T approaches infinity. Extension to multiple locations is also discussed.     

Optimal repeated measurements designs for comparing test treatments with a control

A-optimal and mv optimal repeated measurments designs for comparing serveral test treatments with a control are considered. the models considered are basically of two types: without preperides and the cirular model. It is shown known that some known strongly balanced uniform repeated measurements designs can be modified to obtain optimal designs for this problem. Some other methods of finding optimal designs are also given.     

Cutting Experimental Designs into Blocks

Most experimental material in agriculture and industry is heterogeneous in nature and therefore its statistical analysis benefits from blocking. Many experiments are restricted in time or space, and again blocking is useful. This paper adopts the idea of orthogonal blocking of Box & Hunter (1957) and applies it to optimal blocking designs. This approach is then compared with the determinant-based approach described in the literature for constructing block designs.     

Rejoinder to 'Ahmed, M.S. (1998). A note on regression-type estimators using multiple auxiliary information.'

In the estimators t ₃ , t ₄ , t ₅ of Mukerjee, Rao & Vijayan (1987), b _{y x} and b _{y z} are partial regression coefficients of y on x and z , respectively, based on the smaller sample. With the above interpretation of b _{y x} and b _{y z} in t ₃ , t ₄ , t ₅ , all the calculations in Mukerjee at al. (1987) are correct. In this connection, we also wish to make it explicit that b _{x z} in t ₅ is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t ₃ , t ₄ , t ₅ , as given in Ahmed (1998 Section 3) are computed assuming that our b _{y x} and b _{y z} are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t ₀ , quoted also in Ahmed (1998), is no better than t ₅ of Mukerjee at al. (1987).     

Sharing beliefs and the absence of betting in the Choquet expected utility model

Choquet expected utility maximizers tend to behave in a more “cautious” way than Bayesian agents, i. e. expected utility maximizers. We illustrate this phenomenon in the particular case of betting behavior. Specifically, consider agents who are Choquet expected utility maximizers. Then, if the economy is large, Pareto optimal allocations provide full insurance if and only if the agents share at least on prior, i. e., if the intersection of the core of the capacities representing their beliefs is non empty. In the expected utility case, this is true only if they have a common prior. Received: July 2000; revised version: May 2001     

How to combine pareto optimality with liberty considerations

I argue that the liberty condition of Sen's important impossibility of a Paretian liberal result is not a condition that liberals (or libertarians) would accept. The problem is that an appropriate liberty condition must be formulated in terms of consent - not in terms of preference. To formulate an adequate condition the framework needs to expand from collective choice rules (which only take information about preferences as input) to rights-based social choice rules (which also take as input information about which options have been consented to and which would violate someone's rights). I formulate a more adequate liberty condition based on the notion of consent that is acceptable to liberals, and then show that Pareto optimality is incompatible even with that condition. I then show how the liberty condition can be weakened in a plausible manner, and describe an interesting class of theories - rights-based Paretian theories - that satisfy the Pareto optimality requirement while being sensitive to liberty considerations.     

Rank-order tests for the parallelism of several regression surfaces

For testing the hypothesis that several (s?2) linear regression surfaces X_ki=α_k+β_kc_ki+Z_ki (k=1,…,s) are parallel to one another, i.e., β₁=?=β_s, a class of rank-order tests are considered. The tests are shown to be asymptotically distribution-free, and their asymptotic efficiency relative to the general likelihood ratio test is derived. Asymptotic optimality in the sense of Wald is also discussed.     

Repeated measurements designs - a review

Any experiment in which one or more of the experimental units is used more than once is called a repeated measurements experiment. The associated design of a repeated measurements experiment is referred to as a repeated measurements design. This review covers some known results on repeated measurements designs. Emphasis is placed on the impact of optimal design theory. Some construction methods for these designs are presented. Hedayat and Afsarinejad (1975) has an extensive bibliography of earlier literature. A bibliography of these designs published after 1974 is provided at the end of this paper.     

A note on a modified double stage shrinkage estimator

A modified double stage shrinkage estimator has been proposed for the single parameter θ of a distribution function _Fθ. It is shown to be locally better in comparison to the usual double stage shrinkage estimator in the sense of smaller mean squared error in a certain neighbourhood of prior estimate θ_o of θ.