On entropies for random partitions of the unit segment

summary:We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions

Food supplements’ non-conformity in Europe – Poland: a case study

Background: Mislabelling and substitution of ingredients in food supplements is a growing concern for regulators, businesses and consumers. Whilst there is a body of literature that has considered food and drink substitution and mislabelling, there is limited published research on the compliance of food supplements with regulatory requirements. Scope and Approach: Using secondary data, the aim of this research was to identify the main factors influencing food supplements non-compliance in the European Union (EU) but with specific emphasis on Poland. The sources of data in this review were: (1) the register of pro-health foods maintained by the Chief Sanitary Inspector (GIS) in Poland; (2) unpublished data from the European Commission DG Health and Food Safety (EC DG SANTE); (3) the EU Food Fraud Network and the Administrative Assistance and Cooperation System (EU FFN & AAC) Reports; (4) the Polish Trade Inspection (IH) Report; and (5) the Rapid Alert System for Food and Feed (RASFF) Portal. Key findings and conclusions: The level of food supplements non-compliance with stated legal requirements especially mislabelling is identified in this research. Policy needs to be strengthened both at the EU level, where overarching regulatory governance can be introduced, and also in individual member states, such as Poland, where situational socio-economic factors such as health-care provision, the associated absorptive capacity of the food supplements’ market and the level of ability of national institutions to institute effective regulatory and market governance influence the incidence of food supplements

Comparison of the Purchasing Behaviour of Polish and United Kingdom Consumers in the Organic Food Market during the COVID-19 Pandemic

The main objective of the study was to compare young consumer purchasing behaviour towards organic food in Poland (PL) and the United Kingdom (UK), countries with different levels of organic market maturity. The study was conducted by means of an online survey questionnaire during the COVID-19 pandemic between December 2020 and February 2021. The sample consisted of 862 PL and 161 UK consumers. 31% of PL respondents and 58.4% of UK respondents indicated they purchase organic products. Descriptive statistics, the Mann–Whitney U test and the two proportion Z test were used for statistical analyses. The results indicate that young consumers pay particular attention to the freshness and quality of consumed products. Concern for their own health and that of their loved ones, as well as the desire to eat better-quality products were the main motivations for the respondents to purchase organic products. Organic vege-tables and fruits, eggs, dairy products, and meat and meat products, were among the most frequently purchased products in the studied cohorts. Experts (e.g., a dietitian, physician) were declared to be the first source of information concerning food products for young consumers. Next, family members were indicated. Social media content (PL respondents) and information from websites managed by institutions (UK respondents) were mentioned as the third source. UK consumers preferred short supply chains. The present study can be used by government bodies and companies to select the most effective communication channels for education and advertising and to develop effective commercial strategies aimed at young consumers

Satisficing Newsvendor Problem with the Optimism Coefficient

In this research note the satisficing newsvendor problem is considered which is defined as the maximization of the probability of exceeding the expected profit multiplied by a positive constant. This constant called optimism coefficient can be chosen by the firm’s management either based on their preference or the market conditions. The coefficient indicates whether there is a low or high optimistic decision maker. For the general demand distribution the results are significantly dependent on this coefficient

Barter Exchange as the Way to Deal with Excess Inventory : Newsvendor Problem with Multiplicative Demand

Barter exchange has been growing in popularity during the coronavirus pandemic. This article considers bartering introduced to the newsvendor model with multiplicative demand. The objective of the model is to specify the order quantity and retail price to maximize the expected profit. We distinguish cases with the co-movement of prices of exchanged products and without it. In the first case, we calculate a precise optimal solution to the problem. In the latter case, we prove the existence of an optimal solution and give the conditions under which it is unique. We examine the sensitivity analysis of the results which is illustrated in numerical examples. The analysis revealed that the greater the commission, the lower the optimal profit. We make a conclusion that barter exchange can help the retailer to improve the profit. (original abstract

Goal Setting in the Newsvendor Problem with Uniformly Distributed Demand

In the paper we introduce the newsvendor problem with a satisficing-level objective, which is defined as maximization of the probability of exceeding the moving target. This target is defined as the expected profit, multiplied by a positive constant. The constant is chosen by the management and it indicates whether the low or the high goal should be achieved. We obtain closed form solutions of this newsvendor model with uniformly distributed demand. Additionally, we consider a bicriteria problem with the satisficing- -level and the classical objective

Bicriteria Optimization in the Newsvendor Problem with Exponentially Distributed Demand

In this paper exponential distribution is implemented as a demand distribution in newsvendor model with two different and conflicting goals. The first goal is the standard objective of maximization of the expected profit. The second one is to maximize the probability of exceeding the expected profit, called survival probability. Using exponential distribution as the demand distribution allows us to obtain the exact solutions. Also for this distribution we can study the monotonicity of survival probability with respect to various model parameters analytically. Additional results are obtained when various sets of the parameters are considered. Finally, the bicriteria index which combines these conflicting objectives is optimized which gives the compromise solution. Moreover, in order to illustrate theoretical results, we present numerical examples and graphs of auxiliary functions

Bicriteria Optimization in the Risk-Adjusted Newsvendor Problem

In this paper, we study the newsvendor problem with various degrees of risk tolerance. We consider bicriteria optimization where the first objective is the classical maximization of the expected profit and the second one is the satisficing-level objective. The results depend on the risk coefficient and are different for a risk-neutral, a risk-averse, and a risk-seeking retailer. We find the compromise solution of the bicriteria newsvendor problem numerically, since the two objectives are mutually conflicting. The formulas obtained are illustrated with exponentially distributed demand

The Pandemic-Type Demand Shocks in the Mean-Variance Newsvendor Problem

The paper considers the negative pandemic-type demand shocks in the mean-variance newsvendor problem. It extends the previous results to investigate the case when the actual additive demand may attain negative values due to high prices or considerable, negative demand shocks. The results indicate that the general optimal solution may differ to the solution corresponding exclusively to the non-negative realizations of demand