Inventory control with partial batch ordering

In an in¯nite-horizon, periodic-review, single-item production/inventory system with random demand and back-ordering, we study the feature of batch ordering, where a separate ¯xed cost is associated for each batch ordered. Contrary to majority of the literature on this topic, we do not restrict the order quantities to be integer multiples of the batch size and instead allow the possibility of partial batches, in which case the ¯xed cost for ordering the batch is still fully charged. We build a model that particu- larly takes the batch ordering cost structure into account. We introduce an alternative cost accounting scheme to analyze the problem, and we discuss several properties of the optimal solution. Based on the analysis of a single-period problem and a multi-period lower-bound problem, we study two heuristic policies for the original partial batch or- dering problem, both of which perform very well computationally for a wide range of problem parameters. Finally, we compare the performance of the optimal policy to the performance of the best full-batch-size ordering policy to quantify the value of partial ordering °exibility

Inventory control with multiple setup costs

We consider an infinite-horizon, periodic-review, single-item production/inventory system with random demand and backordering, where multiple setups are allowed in any period and a separate fixed cost is associated for each setup. Contrary to the majority of the literature on this topic, we do not restrict the order quantities to be integer multiples of the exogenously given batch size and instead allow the possibility of partial batches, in which case the fixed cost for ordering the batch is still fully charged. We build a model that particularly takes the batch-ordering cost structure into account. We introduce an alternative cost-accounting scheme to analyze the problem, which we use to develop a computationally efficient optimal solution method and several properties of the optimal solution. In addition, we propose two heuristic policies, both of which perform extremely well computationally

On 'Optimal Bidding in a Uniform Price Auction with Multi-Unit Demand'

On 'Optimal Bidding in a Uniform Price Auction with Multi-Unit Demand

Electronic density of states derived from thermodynamic critical field curves for underdoped La-Sr-Cu-O

Thermodynamic critical field curves have been measured for $La_{2-x}Sr_{x}CuO_{4+\delta}$ over the full range of carrier concentrations where superconductivity occurs in order to determine changes in the normal state density of states with carrier concentration. There is a substantial window in the $H-T$ plane where the measurements are possible because the samples are both thermodynamically reversible and the temperature is low enough that vortex fluctuations are not important. In this window, the data fit Hao-Clem rather well, so this model is used to determine $H_c$ and $\kappa_c$ for each temperature and carrier concentration. Using N(0) and the ratio of the energy gap to transition temperature, $\Delta (0)/k_BT_c$, as fitting parameters, the $H_c vs T$ curves give $\Delta (0)/k_BT_c \sim 2.0$ over the whole range of $x$. Values of N(0) remain rather constant in the optimum-doped and overdoped regime, but drops quickly toward zero in the underdoped regime.

On the Statistical Distribution of Epidermal Papillomata in Mice

IN a previous investigation reported from this laboratory (Ball and McCarter, 1960) it was noted that tumours produced in the skin of the CFW mouse by treatment with 7,12-dimethylbenz(a)anthracene (DMBA) and croton oil, were not distributed among the mice in accordance with the expected Poisson's distribution. Animals bearing no tumours and those bearing many were much more numerous than expected. A quantitative analysis of induced primary adenomatous pulmonary tumours in mice was reported by Polissar and Shimkin (1954). They showed that the occurrence of such tumours was subject to Poisson's distribution and that deviations from this distribution could be attributed to heterogeneity of susceptibility in the animals. We have now analyzed the data obtained in our laboratory in three populations of mice undergoing epidermal carcinogenesis. MATERIALS AND METHODS Strain CFW.-These mice were females, purchased from Carworth Farms Inc., New City, New York. They were housed in groups of 10 in acrylic plastic boxes with stainless steel tops. The bedding was sawdust. Water and Purina Fox Chow Cubes were freely available. Strain CFW/D.-This strain originated when, through error, a male was included among the female CFW mice purchased from the supplier in 1958. Since that time, brother-sister mating has been carried out with a view to obtaining a single inbred line. Litters selected for brother-sister mating were chosen on the basis of health, number in the litter and even distribution of the sexes and not for sensitivity to carcinogenesis. The mice were in the thirteenth and fourteenth inbred generations when used. They were cared for as described above. Strain I.-This strain was obtained several years ago through the kindness of Dr. H. B. Andervont. The mice had been mated brother-to-sister for 71 to 72 generations when the experiment was begun. Chemicals. 7,1 2-dimethylbenz(a)anthracene and benzo((a)pyrene were obtained from Eastman Organic Chemicals. Croton oil was obtained from Bush and Co., Canada. Paraffin oil viscosity 125/135 NF was a product of Fisher Scientific Co., Montreal, Canada. Meprobamate (Miltown) was kindly supplied by Dr. F. M

Gaugino condensation scale of one family hidden SU(5)', dilaton stabilization and gravitino mass

The hidden SU(5)' with one family, 10 and 5-bar, breaks supersymmetry dynamically. From the effective Lagrangian approach, we estimate the hidden sector gaugino candensation scale, the dilaton stabilization and the resulting gravitino mass. In some models, this gravitino mass can be smaller than the previous naive estimate. Then, it is possible to raise the SU(5)' confining scale above 10^{13} GeV.Comment: 8 pages, 4 figure

A semi-small decomposition of the Chow ring of a matroid

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring, recovering the main result of [AHK18]. We also show that a similar semi-small orthogonal decomposition holds for the augmented Chow ring of M