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The sequential and stochastic assignment problem (SSAP) has wide applications in logistics, finance, and health care management, and has been well studied in the literature. It assumes that jobs with unknown values arrive according to a stochastic process. Upon arrival, a job's value is made known and the decision-maker must immediately decide whether to accept or reject the job and, if accepted, to assign it to a resource for a reward. The objective is to maximize the expected reward from the available resources. The optimal assignment policy has a threshold structure and can be computed in polynomial time. In reality, there exist situations in which the decision-maker may postpone the accept/reject decision. In this research, we study the value of postponing decisions by allowing a decision-maker to hold a number of jobs which may be accepted or rejected later. While maintaining this queue of arrivals significantly complicates the analysis, optimal threshold policies exist under mild assumptions when the resources are homogeneous. We illustrate the benefits of delaying decisions through higher profits and lower risk in both cases of homogeneous and heterogeneous resources. 27Sakaguchi [24] extends the work of Albright [2] to the case in which jobs are finite in number and arrive according to a non-homogeneous Poisson process. Sakaguchi [25] permits the number of available resources to be unknown. Albright [3] studies the "secretary problem" where the best M secretaries are to be selected from N available secretaries. The model in this work assumes the value of the secretaries come from different distributions, with two successive secretaries' values governed by a Markov Chain. Nakai [15,16] studies the case with the distribution of resources varying according to a partially observable Markov process. Albright [4] considers the case when the parameters of the distribution of the job value are not fully known and allows the parameters to be updated through a Bayesian model. Kennedy [12] permits job values to be dependent. Righter [20] studies the case where each person has independent deadlines and compares this model with the discount model. Righter [21] permits the arrival rate, the job's value, and the variability of job values to change according to independent Markov processes. Additionally, Albright and Derman [1] and Saario [23] studied the asymptotic results of the SSAP.The dynamic and stochastic knapsack problem (DSKP) with homogeneous sized items studied by Kleywegt and Papastavrou [13] is closely related to SSAP. By setting the costs appropriately, the threshold policy developed there holds for the SSAP with homogeneous resources. Nikolaev and Jacobson [17] extended the results of the SSAP and the DSKP to the case with a random number of arrivals.A variety of applications utilize the SSAP. For example, the resource can be replaced by houses to sell and jobs can be replaced by purchase offers with random values arriving at random times. Elfving [7] uses this interpretation for the case with M = 1. McLa...

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This article generalizes the dynamic and stochastic knapsack problem by allowing the decision-maker to postpone the accept/reject decision for an item and maintain a queue of waiting items to be considered later. Postponed decisions are penalized with delay costs, while idle capacity incurs a holding cost. This generalization addresses applications where requests of scarce resources can be delayed, for example, dispatching in logistics and allocation of funding to investments. We model the problem as a Markov decision process and analyze it through dynamic programming. We show that the optimal policy with homogeneoussized items possesses a bithreshold structure, despite the high dimensionality of the decision space. Finally, the value (or price) of postponement is illustrated through numerical examples.

One perhaps surprising outcome of E-Commerce has been the emergence of speculators who resell products via the web. These speculators create retail shortages for popular products (e.g., toys) by removing them from store shelves in bulk and then selling them at inflated prices through secondary channels; e.g., on sites such as eBay. This article examines the impact of such speculation on ordering decisions in a two-stage manufacturer-retailer supply chain. The equilibrium results of the proposed model demonstrate a range of outcomes: in some cases both the retailer and manufacturer benefit from speculators, whereas in other cases, both may be hurt by a high number of speculators. The proposed model provides insight on when it is best for the manufacturer to take measures to preclude a high degree of speculation.