In this paper, we derive mutual information based upper and lower bounds on the number of nonadaptive group tests required to identify a given number of “healthy” items from a large population containing a small number of “defective” items. We show that an impressive reduction in the number of tests is achievable compared to the approach of first identifying all the defective items and then pic...

The goal of non-adaptive group testing is to identify at most d defective items from N items, in which a test of a subset of N items is positive if it contains at least one defective item, and negative otherwise. However, in many cases, especially in biological screening, the outcome is unreliable due to biochemical interaction; i.e., noise. Consequently, a positive result can change to a negat...

We consider an efficiently decodable non-adaptive group testing (NAGT) problem that meets theoretical bounds. The problem is to find a few specific items (at most d) satisfying certain characteristics in a colossal number of N items as quickly as possible. Those d specific items are called defective items. The idea of NAGT is to pool a group of items, which is called a test, then run a test on ...

In this paper, Economic Order Quantity ( ) based model for non-instantaneous deteriorating items with imperfect quality, permissible delay in payments and inflation is proposed. We adopt a time-dependent demand function. Also, the effects of time value of money are studied using the Discounted Cash Flow approach. Moreover, we assume that orders may contain a random proportion of defective items...

In this paper we consider a single machine system that produces items part of which are defective. The defective items produced in a time period, consisting of several equal cycles, are accumulated and are all reworked in the last cycle of this period called the rework cycle. At the end of the rework cycle the whole process will start all over again. The first significant objective of this stud...

We study the problem of planning the production of new and recovering defective items of the same product manufactured on the same facility. Items of the product are produced in batches. The processing of a batch includes two stages. In the first work stage, all items of a batch are manufactured and good quality items go to the inventory to satisfy given demands. In the second rework stage, som...

In practice the items received in a lot may contain defective items, and the screening process to eliminate the defective items may involve both a Type I and a Type II error. Due to the defective items and the inspection errors, shortages may sometimes occur. In this paper, we develop an economic order quantity model with imperfect quality items, inspection errors, shortage backordering, and sa...

The problem of scheduling the production of new and recoverable defective items of the same product manufactured on the same facility is studied. Items are processed in batches. Each batch comprises two sub-batches processed consecutively. In the first subbatch, all the items are newly manufactured. Some of them are of the required good quality and some are defective. The defective items are re...