Mixture Of Distribution Functions Research Articles

Optimization Problems in Forming a Mixture of Distribution Functions of Operating Times to Failure of Elements of Technical Systems

Optimization Problems in Forming a Mixture of Distribution Functions of Operating Times to Failure of Elements of Technical Systems

Minimax Distribution-Free Procedure for Mixture Inventory Model with Variable Lead Time and a Service Level Constraint by Reducing Order Cost

SYNOPTIC ABSTRACTAs supply chains have become more extended in recent years, coordination and information sharing among supply chain members to improve system efficiency have attracted much interest. In order to achieve a higher degree of coordination and automation among the supply chain parties, the supply chain sometimes invests in reducing the ordering cost to streamline and speed up transactions via the application of information technology. If the ordering cost per order could be reduced effectively, then the total relevant cost per unit time could be automatically improved. In this study, we investigate a continuous review inventory model involving controllable lead time for the mixtures of distributions of the lead time demand, subject to a service level constraint in order to accommodate more practical features of the real inventory systems. Further, ordering cost can be reduced by an investment in which the optimal inventory control approach is shaped to account for the service level restriction.We assume that any mixture of distribution functions of the lead time demand gives only known finite, first two moments, but its probability distribution is unknown, and we apply a minimax distribution-free procedure to find the optimal solution. Moreover, a computational algorithm with the help of a computer code using the software MATLAB 7.0 is developed to solve the problem. A numerical example is presented to illustrate the theoretical results, and a sensitivity analysis is performed with respect to the various system parameters. Through sensitivity analysis, some observations and managerial implications are presented.

The pyrolysis process of wood biomass samples under isothermal experimental conditions—energy density considerations: application of the distributed apparent activation energy model with a mixture of distribution functions

This work deals with the isothermal pyrolysis of Pine and Beech wood samples and kinetic studies, using the thermo-analytical technique, at five different operating temperatures. Pyrolysis processes were investigated by using the distributed apparent activation energy model, which involves the complex mixture of different continuous distribution functions. It was found that decomposition processes of wood pseudo-components take place in different conversion areas during entire pyrolyses, whereby these areas, as well as the changes in apparent activation energy (E a) values, are not the same for softwood and hardwood samples. Bulk density (Bden) and energy density (ED) considerations have shown that both biomass samples suffer from low Bden and ED values. It was concluded that pyrolysis can be used as a means of decreasing transportation costs of wood biomass materials, thus increasing energy density. The “pseudo” kinetic compensation effect was identified, which arises from kinetic model variation and wood species variation. In the current extensive study, it was concluded that primary pyrolysis refers to decomposition reactions of any of three major constituents of the considered wood samples. Also, it was established that primary reactions may proceed in parallel with simultaneous decomposition of lignin, hemicelluloses and cellulose in the different regions of wood samples, depending on the operating temperature. It was established that endothermic effects dominate, which are characterized with devolatilization and formation of volatile products. It has been suggested that the endothermic behavior that arises from pyrolyses of considered samples may indicate the endothermic depolymerization sequence of cellulose structures.

Computational procedure of optimal inventory model involving controllable backorder rate and variable lead time with defective units

This article considers that the number of defective units in an arrival order is a binominal random variable. We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity and lead time are decision variables. In our studies, we also assume that the backorder rate is dependent on the length of lead time through the amount of shortages and let the backorder rate be a control variable. In addition, we assume that the lead time demand follows a mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. Furthermore, we develop an algorithm procedure to obtain the optimal ordering strategy for each case. Finally, three numerical examples are also given to illustrate the results.