A Note on Determining Optimal Selling Price and Lot Size Under All-Unit Quantity Discounts

A recent study conducted by Abad [1] described a method of determining the optimal price and lot size when the supplier offers all-unit quantity discounts. The author developed a procedure using centralized and decentralized approaches. According to the author's suggestion, further study is necessary to determine if the decentralized approach always provides an optimal solution. In the present study, an attempt is made to investigate the uniformity between the centralized and decentralized approaches and to verify whether the decentralized approach always yields optimal solutions.     

An Inventory Model with Planned Shortages and Price Dependent Demand

Previous research has yielded a procedure for a retailer to determine the optimal lot size and selling price when a supplier offers all-unit quantity discounts and demand is a decreasing function of price. In this paper, we extend that research by allowing for shortages. An algorithm is presented that determines the optimal lot size, order level, and selling price for a class of demand functions, including the constant price-elasticity and linear demand functions.     

Parental substance misuse and statutory child protection in England: Risk factors and outcomes

Parental substance misuse is a significant child welfare issue and associated with increased risk of child maltreatment. The aim of the present study was to understand what social care outcomes children who live with parental substance misuse have, and to assess factors associated with those social care outcomes over a two-year period. The paper reports on a retrospective longitudinal study of 299 children all living with parental substance misuse and referred to one local authority in England. Data were collected from children's social work case files about procedural social care outcomes and factors which may be associated with those outcomes. Using cluster analysis, a new typology of children's longitudinal trajectories through the children's social care system was developed, consisting of five distinct types. Analysis indicated that some children received too little intervention from children's social care despite ongoing concerns, while other children were potentially unnecessarily caught up in the social care system. Factors associated with children having the poorest outcomes were: caregiver instability resulting from substance misuse, parenting capacity and household instability. The study's findings indicate that some children who live with parental substance misuse are at significant risk of harm, but others are not and may be better supported through non-statutory services such as early help.