Abstract
These equations depict the following inventory situation. A nonnegative order for a single product is to be placed at the beginning of each of an infinite sequence of equally spaced periods into the future, labeled 0, 1, 2, .. Demands depleting the inventory form a nonnegative sequence of independent identically distributed random variables 40, 1, '2, * . For analytic convenience the distribution is assumed to possess a continuous positive density function 0(4) on [0, oo). An order zi placed at the beginning of period i arrives after a fixed Aperiod lag at the beginning of period i + A, and is relabeled Y(i + ), which explains (4). The pipeline vector qi at the beginning of period i consists of the inventory on hand at that point xi together with the sequence of outstanding orders to arrive in succeeding periods Y(i+ 1), Y(i+ 2)' ... , Y(i+ -1) If demand in a given period exceeds inventory on hand, two extreme cases are considered. In model I, also called the no backlogging or the lost sales case, no customer will wait, so the inventory level is conveniently thought of as being nonnegative; it is recursively generated by (5a). In model II, also called the backlogging case, all customers
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.