A Generalized Stochastic Cost–Volume–Profit Model

Cost–volume–profit (CVP) analysis is a widely used decision tool across many business disciplines. The current literature on stochastic applications of the CVP model is limited in that the model is studied under the restrictive forms of the Gaussian and Lognormal distributions. In this paper we introduce the Mellin Transform as a methodology to generalize stochastic modeling of the CVP problem. We demonstrate the versatility of using the Mellin transform to model the CVP problem, and present a generalization of the CVP model when the contribution margin and sales volume are both defined by continuous random distributions.

Determining the Spatial Pattern of Blackleg Diseased Potato Plants in the Field and Simulated Post-Harvest Tuber Infections in Potato Crates

Experiments were carried out in 2012 and 2013 to answer two basic questions in the testing of potato blackleg causing agents before and after harvest. Firstly, what is the spatial distribution of symptomatic plants in the field. Secondly, what is the distribution of infected tubers over the crates and the resulting detection probability using the standard method of collecting 200 tubers from the top crates in storage. In both years, ten farmers were equipped with a global positioning system (Garmin GPSMAP 62) and asked to register the position of blackleg diseased plants every time they scouted their potato lot for diseases. To answer the second question, potatoes marked with four nails (only visible internally after harvest) and potatoes with a different skin colour were added to one-hectare (ha) fields of seed potatoes in different patterns of aggregation ranging from random, to aggregated distribution, up to one big hotspot prior to harvest. The invisibly marked tubers were used for the unbiased collection of twenty 200-tuber samples from the storage crates, while the coloured skin tubers were used to ascertain, when the potatoes were graded, the distribution of ‘infected’ potatoes over the storage crates. The experiment was carried out with 0.05 and 0.1% disease incidence, in 2012 and 2013, respectively. Twenty two out of 26 fields proved to have a random pattern of diseased plants at harvest, which indicates that the blackleg diseased plants came into the field as infected seed potatoes. Two of the four aggregated patterns detected, started out as random distributions but became aggregated later in time, indicating spread in the field. A random spatial pattern in the field at harvest proved to result in a uniform distribution of infected tubers in the crates and, consequently, sampling of only the top crates for the 200-tuber sample does not introduce any bias. Fifty percent of the infected farmer lots were detected by the Nederlandse Algemene Keuringsdienst inspectors performing their official field surveys, which was a better performance than the 18% detection obtained by the standard 200-tuber sampling method. Only 6 out of 80 samples from the ‘infected’ lots with 0.05% disease incidence level, and 22 out of 80 samples at the 0.1% disease incidence level were detected by the latter method. It was concluded that intensifying the field survey would be cheaper and more successful than enlarging the tuber sample size to increase the probability for detection of infected seed lots.

New Kernel Function for the Approximation of Third Order Derivatives

A new kernel function is developed to approximate the third order derivative by mean of the Smoothed Particle Hydrodynamics (SPH) method. It has the advantage to be efficiently used with gridded data and random distributions. Due to the discrepancy of the particles in the former distribution, we extended the use of the CSPM method for the approximation of third order derivatives. Our new kernel function provides three accurate numerical schemes, in conjunction with the trapezoidal rule, Simpson’s rule and the CSPM method respectively.

A simple justification of effective models for conducting or fluid media with dilute spherical inclusions

We present a gentle approach to the justification of effective media approximations, for PDE’s set outside the union of n ≫ 1 spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as n → + ∞ by simple arguments.

Stochastic Chebyshev Goal Programming Mixed Integer Linear Model for Sustainable Global Production Planning

Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective mixed-integer optimization model is developed to ensure production efficiency in uncertainty conditions and satisfy the requirements of sustainable development. The efficiency of the production system is ensured through objective functions that optimize backorder quantity, machine uptime and customer satisfaction. The other three objective functions of the proposed model are related to optimization of profits, emissions, and employment changing. The objective functions respectively represent the three elements of sustainable development: economy, environment, and sociality. The proposed model also assures the production manager’s discretion over whether or not to adopt production options such as backorder, overtime, and employment of temporary workers. At the same time, the resource limits of the above options can also be adjusted according to the situation of each production facility via the model’s parameters. The solutions that compromise the above objective functions are determined with the Chebyshev goal programming approach together with the weights of the goals. The model is applied to the multinational production system of a Southeast Asian supplier in the textile industry. The goal programming solution of the model shows an improvement in many aspects compared to this supplier’s manufacturing practices under the same production conditions. Last but not least, the study develops different scenarios based on different random distributions of uncertainty demand and different weights between the objective functions. The analysis and evaluation of these scenarios provide a reference basis for managers to adjust the production system in different situations. Analysis of uncertain demand with more complex random distributions as well as making predictions about the effectiveness of scenarios through the advantages of machine learning can be considered in future studies.