A note on the deterministic EPQ with partial backordering

In a recent paper published in Omega [Pentico DW, Drake MJ, Toews C. The deterministic EPQ with partial backordering: a new approach. Omega 2009; 37(3):624–36], the authors proposed an EPQ model with partial backordering. In the EPQ model, a critical value of backordering rate was developed, below which the optimal production policy is either to lose all sales or meet all demand, above which the optimal policy is to allow stockouts with partial backordering and meet fractional demand. However, there exists a flaw in the critical value of backordering rate, which will be amended in this note.     

The deterministic EPQ with partial backordering: A new approach

Several authors have developed models for the EOQ when only a percentage of stockouts will be backordered. Most of these models are complicated, with equations unlike those for the EOQ with full backordering. In this paper we extend work by Pentico and Drake [The deterministic EOQ with partial backordering: a new approach. European Journal of Operational Research 2008; in press] that developed equations for the EOQ with partial backordering that are more like those for the EOQ with full backordering to develop a comparable model for the EPQ with partial backordering.     

A note on “The EPQ with partial backordering and phase-dependent backordering rate”

Pentico et al. [The EPQ with partial backordering and phase-dependent backordering rate. Omega 2011;39(5):574-7] recently proposed an EPQ model with partial backordering. They tried to determine the minimum average total cost per year from the three cases: to lose all sales, to meet all demand, and to allow stockouts with partial backordering. In this paper, we solve the same model without differential calculus and present a different decision procedure. Without the comparison of those costs, a numerical example is illustrated to determine the optimal production policy by our criteria.     

The EPQ with partial backordering and phase-dependent backordering rate

In previous work we established a closed-form optimal stocking strategy for an EPQ model with partial backordering at a constant rate β. Here we extend this work to allow for the possibility that the percentage of demand backordered will increase when production starts again. We show how our previous model can be adapted to find the optimal decision variable values for this new assumption and develop the condition that the initial value of β must meet for partial backordering to be optimal.     

A supplement to the EPQ with partial backordering and phase-dependent backordering rate

In this note, we extend Pentico et al. (2011)'s [1] EPQ model where the authors considered two different backordering rates during shortage period; they assumed the backordering rate increases only from the start of production phase. We propose two models that allow the backordering rate to increase anytime during the production phase, and thus provide more flexibility for decision-makers to vary the backordering rate.     

An EOQ model with partial delayed payment and partial backordering

In many transactions concerning selling and buying, a specified delay of payment is offered or accepted by the seller. This can be regarded as a kind of discount and has potential consequences for the order size. These kinds of effects are not explicitly incorporated in the classical formulas for economic order quantities (EOQ). In this research we consider an EOQ problem under partial delayed payment. A fraction of the purchasing cost must be paid at the beginning of the period and the remaining amount can be paid later. Shortages are permitted and occur as a combination of backorders and lost sales. The aim of this paper is to determine the order and shortage quantities.     

Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

In this paper, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock. Shortages are allowed and, during the stockout period, only a fraction of demand is partially backordered. The backordering cost includes a fixed cost and a cost linearly dependent on the length of time for which backorder exists. A solution procedure is developed for determining the optimal inventory policy. Moreover, to illustrate the effects of some parameters on the optimal policy and the minimum total inventory cost, a numerical study is developed.     

Optimal inventory model for items with imperfect quality and shortage backordering

In this study, we develop an optimal inventory model for items with imperfect quality and shortage backordering. Such implicit assumption is reasonable in view of the fact that poor-quality items do exist during production. They are usually picked up during the screening process and are withdrawn from stock instantaneously. It is assumed that all customers are willing to wait for new supply when there is a shortage. The analysis shows that our model is a generalization of the models in current literatures. An algorithm and numerical analysis developed show that our model always results in better performance.     

On the fruitfulness of the concept of partial organization: A rejoinder to Apelt et al.

This short paper responds to Apelt et al.’s (2017) comments on Ahrne et al.'s (2016) proposal of extending the concept of organization to any decided social orders and thereby putting organization studies at the centre of the social sciences. We highlight some misunderstandings about the aims of this proposal and discuss Apelt et al.’s own proposal of re-focusing organization studies on formal organizations based on Niklas Luhmann's systems theory.     

On the Rank-Based Selection Strategy for the Group Interview Problem*

For the so-called group interview problem in which several groups of choice alternatives are presented sequentially to the decision maker, the optimal selection strategy is derived that minimizes the expected rank of the selected choice or purchased product. For the case in which the sequence of groups can be rearranged by the decision maker, a simple heuristic procedure is proposed for obtaining a near-optimal sequence of groups, and the performance of the heuristic procedure in a Monte Carlo simulation is accessed. According to the heuristic procedure, the consumer is advised to visit smaller stores first and then move to larger stores later to increase the likelihood of finding a better product. Finally, the optimal selection strategy and the heuristic procedure are compared with those proposed by Chun, Moskowitz, and Plante (1993) and the problem of locating a new store in an area where there are several competing stores is discussed. The optimal selection strategy and the heuristic procedure can be applied to many sequential decision problems such as the consumer search and purchase process.     

On the optimality of the TLS algorithm for solving the online-list scheduling problem with two job types on a set of multipurpose machines

In this paper we study the optimality of the TLS algorithm for solving the online scheduling problem of minimizing the makespan on a set of m multipurpose machines, where there are two different job types and each job type can only be processed on a unique subset of machines. The literature shows that the TLS algorithm is optimal for the special cases where either m=2 or where all processing times are restricted to unity. We show that the TLS algorithm is optimal also for the special cases where the job processing times are either job type or machine set dependent. For both cases, the optimality of the TLS algorithm is proven by showing that its competitive ratio matches the lower bound for any processing set and processing time parameters.     

On Intergenerational Equity and Its Clash with Intragenerational Equity and on the Need for Policies to Guide the Regulation of Disposal of Wastes and Other Activities Posing Very Long-Term Risks

This article begins with some history of the derivation of 40 CFR Part 191, the U.S. Environmental Protection Agency (EPA) standard that governs the geologic disposal of spent nuclear fuel and high-level and transuranic radioactive wastes. This is followed by criticisms of the standard that were made by a Sub-Committee of the EPA Science Advisory Board, by the staff of the U.S. Nuclear Regulatory Commission, and by a panel of the National Academies of Science and Engineering. The large disparity in the EPA approaches to regulation of disposal of radioactive wastes and disposal of hazardous, long-lived, nonradioactive chemical waste is illustrated. An examination of the intertwined matters of intergenerational equity and the discounting of future health effects follows, together with a discussion of the conflict between intergenerational equity and intragenerational equity. Finally, issues related to assumptions in the regulations concerning the future state of society and the biosphere are treated, as is the absence of any national philosophy or guiding policy for how to deal with societal activities that pose very long-term risks.