Multi-product lot scheduling with backordering and shelf-life constraints

In this paper, we revisit the economic lot scheduling problem (ELSP), where a family of products is produced on a single machine, or facility, on a continual basis. Our focus is on the determination of a feasible production schedule, including the manufacturing batch size of each item. We assume that total backordering is permissible and that each of the products has a limited post-production shelf life. Several studies examining this problem have suggested a rotational common cycle approach, where each item is produced exactly once every cycle. To ensure schedule feasibility, we resort to the technique of reducing individual production rates and allow the flexibility of producing any item more than once in every cycle, in conjunction with appropriate timing adjustments. In order to solve this more generalized model, which is NP hard, we suggest a two-stage heuristic algorithm. A numerical example demonstrates our solution approach.     

A decision support system for a third-party coordinator managing supply chain with demand uncertainty

Global supply chains reduce cost but increase lead times, complexities and uncertainties. Retailers in consumer products industry are getting shorter lead time to respond to market demand. To meet this challenge, many rely on third party supply chain managers (SCMs) for economically supplying required quantities of finished products quickly. However, due to shorter ‘time to market’, the SCM has to procure raw materials and start production process based on expected demand. Since SCM absorbs financial penalties associated with under- and over-estimation of demand from retailer, finding an optimal production lot size and product customisation strategy are essential to an SCM's operation. We develop a profit maximisation model and provide a close-form solution that allows an SCM to calculate optimal production lot size. The model is used to examine profitability of postponing product customisation. Finally, the effect of demand variation on SCM's profitability is explored.     

Probabilistic Modeling of Flood Hazard and its Risk Assessment for Eastern Region of India

This article models flood occurrence probabilistically and its risk assessment. It incorporates atmospheric parameters to forecast rainfall in an area. This measure of precipitation, together with river and ground parameters, serve as parameters in the model to predict runoff and subsequently inundation depth of an area. The inundation depth acts as a guide for predicting flood proneness and associated hazard. The vulnerability owing to flood has been analyzed as social vulnerability $(V_S)$, vulnerability to property $(V_P)$, and vulnerability to the location in terms of awareness $(V_A)$. The associated risk has been estimated for each area. The distribution of risk values can be used to classify every area into one of the six risk zones—namely, very low risk, low risk, moderately low risk, medium risk, high risk, and very high risk. The prioritization regarding preparedness, evacuation planning, or distribution of relief items should be guided by the range on the risk scale within which the area under study falls. The flood risk assessment model framework has been tested on a real‐life case study. The flood risk indices for each of the municipalities in the area under study have been calculated. The risk indices and hence the flood risk zone under which a municipality is expected to lie would alter every day. The appropriate authorities can then plan ahead in terms of preparedness to combat the impending flood situation in the most critical and vulnerable areas.     

Economic analysis of demand uncertainty and delayed information sharing in a third-party managed supply chain

Designers and retailers in consumer products industry are faced with high demand volatility and potential loss of profit from design piracy. Many retailers rely on third-party supply chain managers (SCMs) to manage global supply chains. A SCM starts raw materials procurement and production process based on expected demand and takes financial risks associated with demand uncertainty. But a retailer often delays sharing product design information with SCM forcing it to expedite production and distribution processes incurring additional financial penalties. To analyse economic impact of delayed information sharing under uncertain demand, we develop a mathematical model. Our model indicates that higher demand volatility lessens the effect of penalty associated with delayed information sharing for retailers. The model also shows that for a given demand volatility, per-unit premium increases asymptotically for a retailer compared to marginal production cost increase for SCM. Such findings are not intuitive for SCMs or retailers.     

Bayesian analysis of generalized odds-rate hazards models for survival data

In the analysis of censored survival data Cox proportional hazards model (1972) is extremely popular among the practitioners. However, in many real-life situations the proportionality of the hazard ratios does not seem to be an appropriate assumption. To overcome such a problem, we consider a class of nonproportional hazards models known as generalized odds-rate class of regression models. The class is general enough to include several commonly used models, such as proportional hazards model, proportional odds model, and accelerated life time model. The theoretical and computational properties of these models have been re-examined. The propriety of the posterior has been established under some mild conditions. A simulation study is conducted and a detailed analysis of the data from a prostate cancer study is presented to further illustrate the proposed methodology.     

Analysis of cure rate survival data under proportional odds model

Due to significant progress in cancer treatments and management in survival studies involving time to relapse (or death), we often need survival models with cured fraction to account for the subjects enjoying prolonged survival. Our article presents a new proportional odds survival models with a cured fraction using a special hierarchical structure of the latent factors activating cure. This new model has same important differences with classical proportional odds survival models and existing cure-rate survival models. We demonstrate the implementation of Bayesian data analysis using our model with data from the SEER (Surveillance Epidemiology and End Results) database of the National Cancer Institute. Particularly aimed at survival data with cured fraction, we present a novel Bayes method for model comparisons and assessments, and demonstrate our new tool’s superior performance and advantages over competing tools.     

A JOINT ECONOMIC-LOT-SIZE MODEL FOR PURCHASER AND VENDOR

In a typical purchasing situation, the issues of price, lot sizing, etc., usually are settled through negotiations between the purchaser and the vendor. Depending on the existing balance of power, the end result of such a bargaining process may be a near-optimal or optimal ordering policy for one of the parties (placing the other in a position of significant disadvantage) or, sometimes, inoptimal policies for both parties. This paper develops a joint economic-lot-size model for a special case where a vendor produces to order for a purchaser on a lot-for-lot basis under deterministic conditions. The focus of this model is the joint total relevant cost. It is shown that a jointly optimal ordering policy, together with an appropriate price adjustment, can be beneficial economically for both parties or, at the least, does not place either at a disadvantage.     

Theory of mind and peer relationships: The role of social anxiety

Recent research has shown that individual differences in theory of mind (ToM) during middle childhood are linked with individual differences in children's peer relationships. The present longitudinal study investigated this association more deeply, exploring the potential mediating role played by children's social anxiety. We tested a group of 66 children (11.5 years old at Time 1) three times over one year after their transition to secondary school. Over and above language, SES and stability in individual differences, ToM performance shortly after starting secondary school (Time 1) predicted higher peer acceptance, as well as lower peer rejection, one year later (Time 3) via lower levels of social anxiety over time (Time 2). This study extends our knowledge about the links between social understanding and interpersonal relations in middle childhood. The results suggest that ToM may play an important role in children's adjustment when confronting new social contexts.     

Expenditure patterns of older Americans, 2001-2009

PRE- AND POSTRETIREMENT EXPENSES: Before retirement, people pay FICA taxes, incur work-related expenses, and set aside money for retirement. But after retirement, most people have different financial obligations, and, as a result, retirees may still be able to maintain their level of preretirement well-being with very different income levels. Studying income, expenditures, and wealth-holding patterns together provides a more complete idea of how people are doing in terms of being able to afford retirement than arbitrary estimates such as income replacement ratios. UNIQUE DATA: This Issue Brief examines the expenditure patterns of the older section of the population. It uses data from the Consumption and Activities Mail Survey (CAMS), a supplement to the Health and Retirement Study (HRS), conducted by the Institute for Social Research at the University of Michigan, contains detailed expenditure data on 32 categories, and follows the same group of individuals over eight years In addition, the income and wealth data available in the HRS are used to establish the financial standing of older households. DECLINING EXPENSES: Household expenses steadily decline with age. With the age 65 expenditure as a benchmark, household expenditure falls by 19 percent by age 75, 34 percent by age 85, and 52 percent by age 95. HOME EXPENSES: Home and home-related expenses remain the single largest spending category for older Americans. On average, those over age 50 spend around 40-45 percent of their budget on home and home-related items. RISING HEALTH CARE EXPENSES: Health-related expenses are the second-largest component in the budget of older Americans. It is the only component which steadily increases with age. Health care expenses capture around 10 percent of the budget for those between 50-64, but increase to about 20 percent for those age 85 and over. DEMOGRAPHIC GROUPS: Singles, blacks, and high school dropouts do not have a sound financial standing in retirement. Their expenditures exceed their income and they hold very little financial wealth. The bottom income quartile, which includes mostly these demographic groups, has the weakest financial standing in retirement. LONG-TERM CARE and PRIVATE HEALTH INSURANCE: Long-term care and some form of private health insurance coverage have a significant effect on increased spending by older households.     

On the representation of preference orders on sequence spaces

A set of sufficient conditions for representability of preference orders on real sequence spaces is analyzed. In particular, monotonicity and continuity of the order is not assumed. Two applications are worked out to demonstrate how such a result might be useful.