Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

One person in the battlefield is not a warrior: Self-construal, perceived ability to make a difference, and socially responsible behavior

We suggest that cultivating an individual's connectedness to others promotes sociallyresponsible behavior both directly and indirectly through increased perceived abilityto make a difference. Individuals whose interdependent self is more prominent feel theyhave more of an impact on larger scale societal outcomes and, therefore, engage more insocially responsible behaviors than do individuals whose independent self is moreprominent. We test these hypotheses in two experiments in which participants makefinancial contributions or exert an effort for a social cause. In a survey, we find thatperceived effectiveness mediates the effect of self-construal on socially responsibleconsumption.

When to carry eccentric products? Optimal retail assortment under consumer returns

To understand whether retailers should consider consumer returns when merchandising, we study howthe optimal assortment of a price-taking retailer is influenced by its return policy. The retailer selects itsassortment from an exogenous set of horizontally differentiated products. Consumers make purchase andkeep/return decisions in nested multinomial logit fashion. Our main finding is that the optimal assortmenthas a counterintuitive structure for relatively strict return policies: It is optimal to offer a mix of the mostpopular and most eccentric products when the refund amount is sufficiently low, which can be viewed asa form of risk sharing between the retailer and consumers. In contrast, if the refund is sufficiently high, orwhen returns are disallowed, optimal assortment is composed of only the most popular products (a commonfinding in the literature). We provide preliminary empirical evidence for one of the key drivers of our results:more eccentric products have higher probability of return conditional on purchase. In light of our analyticalfindings and managerial insights, we conclude that retailers should take their return policies into accountwhen merchandising.