A produce‐to‐stock system with advance demand information and secondary customers

We consider a manufacturer (i.e., a capacitated supplier) that produces to stock and has two classes of customers. The primary customer places orders at regular intervals of time for a random quantity, while the secondary customers request a single item at random times. At a predetermined time the manufacturer receives advance demand information regarding the order size of the primary customer. If the manufacturer is not able to fill the primary customer's demand, there is a penalty. On the other hand, serving the secondary customers results in additional profit; however, the manufacturer can refuse to serve the secondary customers in order to reserve inventory for the primary customer. We characterize the manufacturer's optimal production and stock reservation policies that maximize the manufacturer's discounted profit and the average profit per unit time. We show that these policies are threshold‐type policies, and these thresholds are monotone with respect to the primary customer's order size. Using a numerical study we provide insights into how the value of information is affected by the relative demand size of the primary and secondary customers. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A load-sharing model: The linear breakdown rule

An n-component parallel system is subjected to a known load program. As time passes, components fail in a random manner, which depends on their individual load histories. At any time, the surviving components share the total load according to some rule. The system's life distribution is studied under the linear breakdown rule and it is shown that if the load program is increasing, the system lifetime is IFR. Using the notion of Schur convexity, a stochastic comparison of different systems is obtained. It is also shown that the system failure time is asymptotically normally distributed as the number of components grows large. All these results hold under various load-sharing rules; in fact, we show that the system lifetime distribution is invariant under different load-sharing rules.