Parameter values for lot size and quality level via CAE simulation, statistical method, and mathematical programming

Because of the stochastic nature of production systems, it is necessary to first build an uncertainty model for subsequent real applications. Moreover, process parameter planning, quality design, and production inventory management are interdependent elements. In this research, a computer simulation model via computer-aided engineering (CAE) was developed to determine the optimal process parameters, lot size, and back order intervals for an integrated process design and inventory management system with simultaneous quality and cost considerations. Based on the estimated process time and costs obtained using CAE, the derived production rate and unit cost were then used for production inventory applications. In consideration of the uncertainty factor, the response surface method (RSM) was employed to analyze the output, namely the total costs incurred in employing the proposed approach, as well as the inputs, which include the cutting parameters, production quantity, and back order intervals. After the RSM was used to obtain the response functions, which represent the output of the collective interests, the mathematical programming (MP) was formulated based on the response functions to determine the optimal process parameters, process quality levels, production order quantities, and back order intervals. The total cost per set time unit was minimized by determining the required quality level, process parameter values, Economic Production Quantity (EPQ), and back order intervals. A cutting example was chosen to demonstrate the proposed approach. Two cases were used for comparison: the Integrated Case (the proposed approach herein) and the Disintegrated Case.

Inventory models with integrated time dependent demands for deteriorating items – in third and fourth order equations.

. Inventory models with integrated time-dependent demands for deteriorative items are considered in this study. The demand models found in the literature include constant, linear, quadratic, exponential, price dependent, and stock dependent among others. To wit, no study exists that uses integrated time-dependent demands. Three models are developed: The first model uses continuously compounded demands, the second model uses linear demands integrated with continuously compounded demands, and the third model uses quadratic demands integrated with continuously compounded demands. Mathematical models are delineated for each model and relevant examples are provided to elucidate the proposed procedure. The objective herein is to obtain optimum order quantities and order intervals concerning the overall cost. Sensitivity analysis is provided for each of the three models. The necessary data was generated using Visual Basic 6.0.. Inventory models with integrated time-dependent demands for deteriorative items are considered in this study. The demand models found in the literature include constant, linear, quadratic, exponential, price dependent, and stock dependent among others. To wit, no study exists that uses integrated time-dependent demands. Three models are developed: The first model uses continuously compounded demands, the second model uses linear demands integrated with continuously compounded demands, and the third model uses quadratic demands integrated with continuously compounded demands. Mathematical models are delineated for each model and relevant examples are provided to elucidate the proposed procedure. The objective herein is to obtain optimum order quantities and order intervals concerning the overall cost. Sensitivity analysis is provided for each of the three models. The necessary data was generated using Visual Basic 6.0.

Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization

We consider the robust standard quadratic optimization problem (RStQP), in which an uncertain (possibly indefinite) quadratic form is optimized over the standard simplex. Following most approaches, we model the uncertainty sets by balls, polyhedra, or spectrahedra, more generally, by ellipsoids or order intervals intersected with subcones of the copositive matrix cone. We show that the copositive relaxation gap of the RStQP equals the minimax gap under some mild assumptions on the curvature of the aforementioned uncertainty sets and present conditions under which the RStQP reduces to the standard quadratic optimization problem. These conditions also ensure that the copositive relaxation of an RStQP is exact. The theoretical findings are accompanied by the results of computational experiments for a specific application from the domain of graph clustering, more precisely, community detection in (social) networks. The results indicate that the cardinality of communities tend to increase for ellipsoidal uncertainty sets and to decrease for spectrahedral uncertainty sets.

Susceptibility of Selected Tea Shoots to Oviposition by Empoasca onukii (Hemiptera: Cicadellidae) and Feasibility of Egg Removal with Harvesting

The Empoasca onukii (Hemiptera: Cicadellidae) female lays its eggs inside the epidermis of the tea plant shoots. This has led to speculation that shoot harvesting could represent a method of egg removal. To verify the validity of this hypothesis, we sought to determine which part of the shoot was used for the oviposition and how the value of the harvested shoot affects the cost of the egg removal. In this study, four tea cultivars were chosen to examine the preferences for the site of oviposition. In addition, a mathematical model was used to describe the correlation between the economic value of the selected shoot and eggs laid within the shoot. Our study revealed that the pest preferred the 3rd and 4th leaf order intervals of the shoot as the oviposition sites, and the oviposition preferences was dependent on the leaf order interval class across all tea cultivars. In addition, a significant negative exponential relationship was found between the economic value of the selected shoot and the percentage of the eggs laid within the shoot, indicating that egg removal through shoot harvesting was limited. The findings of this study could be used to better understand the role of shoot harvesting in egg removal and would provide new insights into the understanding of the incidence of this pest.

Optimal Utilization of Ports’ Free-of-Charge Times in One Distribution Center and Multiple Ports Inventory Systems

In this paper, we consider a distribution system consisting of one distribution center (DC), a set of ports, and a set of retailers, in which the product is distributed to the retailers from the DC through the ports by the water transport, and study inventory management for the distribution system with considering the effect of the free storage periods provided by the ports. Inventory management for the distribution system is to determine the order intervals of the DC and the retailers while minimizing the inventory ordering and holding costs. Focusing on stationary and integer-ratio policies, we formulate this inventory management problem as an optimization problem with a convex objective function and a set of integer-ratio constraints and present O(Nlog⁡N) time algorithm to solve the relaxed problem (relaxing the integer-ratio constraints) to optimality, where N is the number of the retailers. We prove that the relaxed problem provides a lower bound on average cost for all the feasible policies (containing dynamic policies) for this inventory management problem. By using the optimal solution of the relaxed problem, we build a stationary integer-ratio policy (a power-of-two policy) for this inventory management problem and prove that the power-of-two policy can approximate the optimal inventory policy to 83% accuracy.

Fractional Modeling for Quantitative Inversion of Soil-Available Phosphorus Content

The study of field spectra based on fractional-order differentials has rarely been reported, and traditional integer-order differentials only perform the derivative calculation for 1st-order or 2nd-order spectrum signals, ignoring the spectral transformation details between 0th-order to 1st-order and 1st-order to 2nd-order, resulting in the problem of low-prediction accuracy. In this paper, a spectral quantitative analysis model of soil-available phosphorus content based on a fractional-order differential is proposed. Firstly, a fractional-order differential was used to perform a derivative calculation of original spectral data from 0th-order to 2nd-order using 0.2-order intervals, to obtain 11 fractional-order spectrum data. Afterwards, seven bands with absolute correlation coefficient greater than 0.5 were selected as sensitive bands. Finally, a stepwise multiple linear regression algorithm was used to establish a spectral estimation model of soil-available phosphorus content under different orders, then the prediction effect of the model under different orders was compared and analyzed. Simulation results show that the best order for a soil-available phosphorus content regression model is a 0.6 fractional-order, the coefficient of determination (), root mean square error (RMSE), and ratio of performance to deviation (RPD) of the best model are 0.7888, 3.348878, and 2.001142, respectively. Since the RPD value is greater than 2, the optimal fractional model established in this study has good quantitative predictive ability for soil-available phosphorus content.

OWNR problem with variable replenishment and inventory holding costs and quantity discounts

We consider an inventory/distribution system consisting of one warehouse and N retailers (OWNR). Warehouse replenishes its orders from external supplier and supplies all orders of retailers. The objective of this paper is to maximise supply chain benefits of the whole system. To achieve this objective SENYIGIT and AKKAN’s heuristic algorithm is used. We assume that demand is constant and deterministic; shortages are not allowed and lead times are negligible. Total system cost consists of order-quantity-dependent replenishment and inventory holding cost parameters, and quantity discounts are applicable. The main idea of new heuristic is to compare replenishment and inventory holding costs while manipulating the order quantity by order intervals of locations. While balance condition is searched by new version of SENYIGIT and AKKAN’s heuristic algorithm, quantity discounts and replenishment costs will reduce costs of whole systems. Capital limit constraint is also included to the model of objective function. The algorithm is developed for quantity discounts and 100 datasets randomly generated for the system that contains five retailers and the solutions were obtained by developed heuristic. Keywords: Supply chain management, two echelon inventory systems, integer-ratio policies, quantity discounts, heuristic method, variable cost parameters.