A supplement to an EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales return

Hsu and Hsu (2013a) established a closed-form solution for an EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns, where the customers who return the defective items will receive full price refunds; i.e., the returned items are not replaced with good items. In this note, we extend Hsu and Hsu's (2013a) work to consider the case that returned items are replaced with good items. A closed-form solution is developed for the optimal order size and the maximum shortage level. Numerical examples are provided to show the differences in the optimal solutions when returned items are replaced, and when they are not

Economic Design of Acceptance Sampling Plans in a Two-Stage Supply Chain

Supply Chain Management, which is concerned with material and information flows between facilities and the final customers, has been considered the most popular operations strategy for improving organizational competitiveness nowadays. With the advanced development of computer technology, it is getting easier to derive an acceptance sampling plan satisfying both the producer’s and consumer’s quality and risk requirements. However, all the available QC tables and computer software determine the sampling plan on a noneconomic basis. In this paper, we design an economic model to determine the optimal sampling plan in a two-stage supply chain that minimizes the producer’s and the consumer’s total quality cost while satisfying both the producer’s and consumer’s quality and risk requirements. Numerical examples show that the optimal sampling plan is quite sensitive to the producer’s product quality. The product’s inspection, internal failure, and postsale failure costs also have an effect on the optimal sampling plan

An Integrated Vendor-Buyer Cooperative Inventory Model for Items with Imperfect Quality and Shortage Backordering

We develop a model to determine an integrated vendor-buyer inventory policy for items with imperfect quality and planned back orders. The production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor delivers the items to the buyer in small lots of equally sized shipments. Upon receipt of the items, the buyer will conduct a 100% inspection. Since each lot contains a variable number of defective items, shortages may occur at the buyer. We assume that shortages are permitted and are completely back ordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected total annual integrated cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer

A precise measurement of the Z -boson double-differential transverse momentum and rapidity distributions in the full phase space of the decay leptons with the ATLAS experiment at √s = 8 TeV

This paper presents for the first time a precise measurement of the production properties of the Z boson in the full phase space of the decay leptons. This is in contrast to the many previous precise unfolded measurements performed in the fiducial phase space of the decay leptons. The measurement is obtained from proton–proton collision data collected by the ATLAS experiment in 2012 at s=8 TeV at the LHC and corresponding to an integrated luminosity of 20.2 fb-1. The results, based on a total of 15.3 million Z-boson decays to electron and muon pairs, extend and improve a previous measurement of the full set of angular coefficients describing Z-boson decay. The double-differential cross-section distributions in Z-boson transverse momentum pT and rapidity y are measured in the pole region, defined as 80<mℓℓ<100 GeV, over the range |y|<3.6. The total uncertainty of the normalised cross-section measurements in the peak region of the pT distribution is dominated by statistical uncertainties over the full range and increases as a function of rapidity from 0.5–1.0% for |y|<2.0 to 2-7% at higher rapidities. The results for the rapidity-dependent transverse momentum distributions are compared to state-of-the-art QCD predictions, which combine in the best cases approximate N4LL resummation with N3LO fixed-order perturbative calculations. The differential rapidity distributions integrated over pT are even more precise, with accuracies from 0.2–0.3% for |y|<2.0 to 0.4–0.9% at higher rapidities, and are compared to fixed-order QCD predictions using the most recent parton distribution functions. The agreement between data and predictions is quite good in most cases

A note on

Wee et al. (2007) developed an optimal inventory model. In this technical note, we point out a contradiction between Wee et al.'s model and their assumption. A corrected model is developed based on their assumption. Numerical examples show that in terms of the two decision variables, there is a significant difference between the corrected model and Wee et al.'s model. The results also show that that the penalty of using Wee et al.'s model can be significant under certain situations