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In most of the inventory models, a single stock is considered where items are served for the customers. In this paper, two stocks are considered for efficient stock management, One is for fresh items and another is for returned items. Two models are considered here, first model is developed for non-perishable items where the second one is for perishable items. The models are more appropriate where warranties are provided for a fixed time duration after sale for fresh items. Moreover, inventories whose are kept in the stock may not have finite shelf-life that are also considered here in model-II such as milk, meat, vegetables, radioactive materials, volatile liquids. In model-II, we have considered that the inventory decay in a constant rate $\theta $. It is assumed that inventory level for both the fresh and returned items are pre-determined. When inventory level reaches at re-order point s, a replenishment takes place with parameter $\gamma $. The demands that arrive for fresh items and returned items follow Poisson process with parameter $\lambda $ $\&$ $\delta $ respectively. Service will be provided with Poisson process for returned items with parameter $\mu$. The joint probability distribution for inventory level of returned items and for fresh items are obtained in the steady state analysis. Some systems characteristics of two models are derived here and the results are illustrated with the help of numerical examples.

In this study, ductile mode cutting of silicon wafer materials has been carried out using an ultra-precision lathe with single crystal diamond cutters and the wear characteristics of the tool and the effect of its different diamond crystal orientations were investigated. Experimental results indicated that wear occurred mainly on the flank face of the tool and the wear pattern was typically mechanical abrasive wear, adhesive wear and possible thermo-chemical wear. At higher cutting distance, crater wear with small grooves in the vicinity of cutting edge was observed on the tool rake face. However, given the highly anisotropic nature in properties of diamond, wear resistance of a diamond tool varies with the crystal planes as well as crystal directions on the same plane. From this study, it is found that in terms of tool flank wear (VBmax) resistance, the tool life of the diamond cutter with crystal orientations {1 0 0} as the rake and {1 1 0} as the flank planes, was much longer than those of the diamond cutters with other crystal orientations as the rake and flank planes.

Wear in diamond tools is a crucial factor in ultra-precision machining. However, as is well known, single crystal diamond possesses strong anisotropy. Its mechanical and physical properties vary with crystallographic orientation. In this study, tool wear investigation was carried out on nano-scale ductile cutting of silicon using an ultra-precision lathe with single crystal diamond tools. The wear characteristics of single point diamond tools and the effect of diamond crystallographic orientation were investigated. Experimental results indicate that gradual wear occurred mainly on the flank face of the tool. A very smooth wear mark on the rake face was also seen. The machining data show that wear resistance of the tool and tool life were greater when the crystallographic orientation of the rake face was {1 1 0} than when it was {1 0 0} or {1 1 1}. The thrust force on the diamond tool was lower when the rake face crystallographic orientation was {1 1 0} than when it was some other orientation. For all the crystallographic orientations studied in the diamond tools, gradual tool flank wear had no significant effect on the surface roughness of machined silicon work material.