Optimal Production and Marketing Planning

This paper presents an integrated production, marketing and inventory model which determines the production lot size, marketing expenditure and products selling price. Our model is highly nonlinear and non-convex and cannot be solved directly. Therefore, Geometric Programming (GP) is used to locate the optimal solution of the proposed model. In our GP implementation, we use a transformed dual problem in order to reduce the model to an optimization of an unconstrained problem in a single variable and the resulting problem is solved using a simple line search. We analyze the solution in different cases in order to study the behaviour of the model and for each case, a numerical example is used to demonstrate the implementation of our analysis.     

Gas phase pyrolysis of some cyclic dithioketals

A detailed analysis of the gas phase pyrolysis of 1,4-dithiaspiro[4,4]nonane(I), 1,5-dithiaspiro(5.4)decane(II), 1,4-dithiaspiro(4.5)decane(III), and 1,5-(5,5)undecane(IV) is presented. Pyrolysis resulted primarily in cleavage of the molecules to thiocyclopentanone and thiocyclohexanone. The products observed are discussed in relation to the effect of ring size in cyclic dithioketals. A definite correlation was noted between the thermal and their electron-impact-induced fragmentations of these materials.     

Effect of frit size on sintering, crystallization and electrical properties of wollastonite glass-ceramics

Wollastonite glass-ceramics were prepared through pressureless sintering. The sinterability of the prepared samples of the glassy powder in the system (SiO₂-CaO-Na₂O-Fe₂O₃-WO₃) was investigated in the temperature range 720-900 °C and soaking time of 180 min. The influence of the increase in the glass powder particle size on the sinterability and dielectric properties of the glass-ceramic samples was studied.The sintered specimens were characterized by scanning electron microscopy (SEM) and X-ray diffraction (XRD) methods. XRD analysis revealed that wollastonite was the main crystalline phase in the sintered glass-ceramics. Dielectric properties such as dielectric constant and dielectric loss were measured via a network analyzer at 10 GHz.It was observed that the increase of the glassy powder particle size improved the sinterability and dielectric properties of the glass-ceramic specimens. Wollastonite glass-ceramics with 16 μm particle size had maximum constant and minimum loss (ε_r = 10.10 and tan δ = 0.005) compared with the other glass-ceramics.     

Competitive online algorithms for resource allocation over the positive semidefinite cone

We consider a new and general online resource allocation problem, where the goal is to maximize a function of a positive semidefinite (PSD) matrix with a scalar budget constraint. The problem data arrives online, and the algorithm needs to make an irrevocable decision at each step. Of particular interest are classic experiment design problems in the online setting, with the algorithm deciding whether to allocate budget to each experiment as new experiments become available sequentially. We analyze two greedy primal-dual algorithms and provide bounds on their competitive ratios. Our analysis relies on a smooth surrogate of the objective function that needs to satisfy a new diminishing returns (PSD-DR) property (that its gradient is order-reversing with respect to the PSD cone). Using the representation for monotone maps on the PSD cone given by Löwner’s theorem, we obtain a convex parametrization of the family of functions satisfying PSD-DR. We then formulate a convex optimization problem to directly optimize our competitive ratio bound over this set. This design problem can be solved offline before the data start arriving. The online algorithm that uses the designed smoothing is tailored to the given cost function, and enjoys a competitive ratio at least as good as our optimized bound. We provide examples of computing the smooth surrogate for D-optimal and A-optimal experiment design, and demonstrate the performance of the custom-designed algorithm.     

Equivalence relations among inequalities for some relative operator entropies

Positivity - The relative operator entropy has properties like operator means. In addition, the relative operator entropy has entropy-like properties. In this paper, we prove a Loewner–Heinz...     

Optimization of maintenance policy under warranty length‐based demand with consideration of both manufacturer and buyer satisfaction

This study proposes a model to optimize postsale services consisting of four factors: (a) the basic warranty length, (b) the extended warranty length, (c) the preventive maintenance level, and (d) the preventive maintenance interval. Furthermore, consumer demand for the product and extended warranty are considered as functions of the length of the basic warranty and extended warranty periods, respectively. Because buyer dissatisfaction with a product can lead to the loss of potential buyers and the switch of current customers to the competitors, both manufacturer and buyer satisfaction are considered in the model. Three comparative studies are done for showing the effectiveness of the model. The first one compares the results of simultaneous optimization from the two perspectives of manufacture and customer with the single‐objective optimization results from each of the mentioned viewpoints. The second comparison studies the provision of extended warranty contract in the proposed model, and the third comparison investigates the effect of preventive maintenance actions on the results of the model.     

Preparation,Characterization and Controlled Release Investigation of Biocompatible pH-Sensitive PVA/PAA Hydrogels

In the present research hydrogel films based on polyvinyl alcohol (PVA) and polyacrylic acid (PAA) blend, with various crosslink densities, have been prepared through different thermal treatment. The results of FTIR and DSC confirmed quality and quantity of conclusion on miscibility of PVA/PAA blends, respectively. Besides, biocompatibility of the samples has been proved in cytotoxicity tests using L929 cells, according to ISO10993–5. Water uptake of the hydrogel blends is measured. pH sensitivity properties of blends are studied with and without boiling in NaOH solutions where the effect of swelling in water before boiling has also been investigated. Preswellings in water and NaOH concentration have been found to be mainly effective on pH sensitivity of PVA/PAA blends. Biocompatibility and pH sensitivity behavior make these hydrogels appropriate candidates to orally deliver drugs such as insulin and peptides that can be released in basic pH of intestine. The stability of these films in acidic solutions and its expansion and also the consequent release of drugs in basic solutions have been studied by using Teofilin as a model drug by UV-spectrophotometeric measurements.