Replenishment Time Research Articles

A simple model of the inner-hair-cell ribbon synapse accounts for mammalian auditory-nerve-fiber spontaneous spike times

The initial neural encoding of acoustic information occurs by means of spikes in primary auditory afferents. Each mammalian primary auditory afferent (type-I auditory-nerve fiber; ANF) is associated with only one ribbon synapse in one receptor cell (inner hair cell; IHC). The properties of ANF spike trains therefore provide an indirect view of the operation of individual IHC synapses. We showed previously that a point process model of presynaptic vesicle pool depletion and deterministic exponential replenishment, combined with short postsynaptic neural refractoriness, accounts for the interspike interval (ISI) distributions, serial ISI correlations, and spike-count statistics of a population of cat-ANF spontaneous spike trains. Here, we demonstrate that this previous synapse model produces unrealistic properties when spike rates are high and show that this problem can be resolved if the replenishment of each release site is stochastic and independent. We assume that the depletion probability varies between synapses to produce differences in spontaneous rate and that the other model parameters are constant across synapses. We find that this model fits best with only four release sites per IHC synapse, a mean replenishment time of 17 ms, and absolute and mean relative refractory periods of 0.6 ms each. This model accounts for ANF spontaneous spike timing better than two influential, comprehensive models of the auditory periphery. It also reproduces ISI distributions from spontaneous and steady-state driven activity from other studies and other mammalian species. Adding fractal noise to the rate of depletion of each release site can yield long-range correlations as typically observed in long spike trains. We also examine two model variants having more complex vesicle cycles, but neither variant yields a markedly improved fit or a different estimate of the number of release sites. In addition, we examine a model variant having both short and long relative refractory components and find that it cannot account for all aspects of the data. These model results will be beneficial for understanding ribbon synapses and ANF responses to acoustic stimulation.

Pricing and lot-sizing policies for perishable products with advance-cash-credit payments by a discounted cash-flow analysis

A contractor often requests a customer pay an advance payment when signing a contract to install a new roof. A cash payment to cover the contractor's materials cost is then required upon delivery of the materials to do the job. Then, the contractor grants the customer a credit payment to pay the remainder of the total cost after the work is completed and satisfactory. Hence, an advance-cash-credit (ACC) payment scheme is commonly used in real world business transactions. This paper develops a supplier-retailer-customer chain in which the retailer receives an upstream ACC payment from the supplier while in return offers a downstream cash-credit (some in cash and the rest in credit) payment to customers. Additionally, today's health-conscious consumers judge product freshness through its expiration date because the freshness of a perishable product degrades with time. As a result, the demand for perishable products is influenced by the combined effect of selling price and product freshness linked to expiration date. Taking time value of money into consideration, then an inventory model by using a discounted cash-flow analysis is developed. Furthermore, the present value of total annual profit is demonstrated that is strictly concave in unit price and strictly pseudo-concave in replenishment time, which simplifies the search for the global solution to a local maximum. Finally, a sensitivity analysis is conducted and several managerial insights are obtained.

A stochastic production inventory model for deteriorating items with products’ finite life-cycle

The article deals with a production inventory system for deteriorating items where the production rate of the system is a random variable within a finite range and the unit production cost depends on production lotsize as well as the rate of production. In the model, the maximum life-cycle of the products is finite and all the products are totally expired at the end of the life-time of the product. Shortages are allowed and partially backlogged. The backlogging rate is depended on length of the waiting time for the next replenishment. The main objective is to find out the optimal production lot-size such that the average expected cost per unit time of the inventory system is minimum. The different cases according to the value of the product’s life-time, production run-time and cycle length of the system are discussed analytically and numerically. A numerical example and its sensitivity analysis along with its managerial insights are presented to illustrate the behavior of the proposed production-inventory model.

Optimal replenishment time for retailer under partial upstream prepayment and partial downstream overdue payment for quadratic demand

ABSTRACTIn competitive edge, the proffer of delay payment is of great consequence tool to boost the market demand by exerting influence of more customers. In opposition to, merchandiser may be asked to pay some per cent of purchasing cost before receiving products to reduce the risk of cancellation of order. In this article, optimal replenishment time for merchandiser under partial upstream prepayment and partial downstream overdue payment is presented under quadratic demand with three different models: (1) without deterioration, (2) with constant deterioration and (3) maximum fixed-lifetime deterioration as loss of utility is the real situation of products like fruits, vegetables, juices, etc., and to reduce deterioration of the product, merchandiser spends capital on preservation technology to preserve the item. Quadratic demand is suitable for the products for which demand increases initially and afterward it starts to decrease. The decision policies are analysed for the merchandiser. The objective is to minimize merchandiser’s total cost with respect to decision variables. The models are supported with numerical examples. Sensitivity analysis is carried out to derive insights for decision maker.

Optimal pricing and replenishment policies for instantaneous deteriorating items with backlogging and trade credit under inflation

In this paper we develop an economic order quantity model to investigate the optimal replenishment policies for instantaneous deteriorating items under inflation and trade credit. Demand rate is a linear function of selling price and decreases negative exponentially with time over a finite planning horizon. Shortages are allowed and partially backlogged. Under these conditions, we model the retailer’s inventory system as a profit maximization problem to determine the optimal selling price, optimal order quantity and optimal replenishment time. An easy-to-use algorithm is developed to determine the optimal replenishment policies for the retailer. We also provide optimal present value of profit when shortages are completely backlogged as a special case. Numerical examples are presented to illustrate the algorithm provided to obtain optimal profit. And we also obtain managerial implications from numerical examples to substantiate our model. The results show that there is an improvement in total profit from complete backlogging rather than the items being partially backlogged.

Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization

We investigate a two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and stock-dependent demand under inflationary conditions. Shortages are allowed. The backlogging rate is variable and depends on the waiting time for the next replenishment. This paper seeks to determine an optimal replenishment policy that minimizes the present value of the total cost per unit time. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution are found. The corresponding problems are formulated and solved with particle swarm optimization. Numerical experimentation and post-optimality analysis are conducted.

The Effect of the Safety Stock on the Occurrence Probability of the Stock Shortage

Abstract The objective of the logistics management is to guarantee the stock level required for the adequate handling of production at the lowest possible level of costs and risks. The main purpose of the paper is to present the relations between stock level and risk of shortages. As a result of the research, the introduction of the safety stock is the solution to cover the effects of the uncertain factors in the supply chain. The theoretical approach of the model assumes a deterministic operational environment, in practice, however, there are several unpredictable factors influencing the operation of the production company. By using the periodic and continuous review models, the paper presents the effects of demand changes and stochastic length of replenishment time on the risk of stock availability. We need to quantify a service level which determines the accepted probability of the shortage occurrence.

Continuous Flow 1H and 13C NMR Spectroscopy in Microfluidic Stripline NMR Chips.

Microfluidic stripline NMR technology not only allows for NMR experiments to be performed on small sample volumes in the submicroliter range, but also experiments can easily be performed in continuous flow because of the stripline’s favorable geometry. In this study we demonstrate the possibility of dual-channel operation of a microfluidic stripline NMR setup showing one- and two-dimensional 1H, 13C and heteronuclear NMR experiments under continuous flow. We performed experiments on ethyl crotonate and menthol, using three different types of NMR chips aiming for straightforward microfluidic connectivity. The detection volumes are approximately 150 and 250 nL, while flow rates ranging from 0.5 μL/min to 15 μL/min have been employed. We show that in continuous flow the pulse delay is determined by the replenishment time of the detector volume, if the sample trajectory in the magnet toward NMR detector is long enough to polarize the spin systems. This can considerably speed up quantitative measurement of samples needing signal averaging. So it can be beneficial to perform continuous flow measurements in this setup for analysis of, e.g., reactive, unstable, or mass-limited compounds.

An Integrated Pricing and Inventory Model for Deteriorating Products in a two stage supply chain under Replacement and Shortage

In this paper a two-stage supply chain including a wholesaler and a retailer is investigated. In which retailer acts as a vendor and sells the products to the final customers. This chain only produces a single deteriorating product with constant deteriorating rate. Demand in this chain is deterministic and lead time for replenishment and replacement of retailer’s stock is considered to be zero. The objective of this study is to maximize total chain’s profit by determining the optimal values of retailer’s selling price () and order cycle length (). Since due to deterioration, a part of the initial stock is deteriorated, so the retailer residuals (recycles) the deteriorated part and replace healthy product as needed instead. Two scenarios with shortage and without shortage assumption are developed. Finally numerical examples are presented to show the applicability of the proposed models and sensitivity analyze on some parameter’s values is conducted.

Integrated planning of spare parts and service engineers with partial backlogging

In this paper, we consider the integrated planning of resources in a service maintenance logistics system in which spare parts supply and service engineers deployment are considered simultaneously. The objective is to determine close-to-optimal stock levels as well as the number of service engineers that minimize the total average costs under a maximum total average waiting time constraint. When a failure occurs, a spare part and a service engineer are requested for the repair call. In case of a stock-out at spare parts inventory, the repair call will be satisfied entirely via an emergency channel with a fast replenishment time but at a high cost. However, if the requested spare part is in stock, the backlogging policy is followed for engineers. We model the problem as a queueing network. An exact method and two approximations for the evaluation of a given policy are presented. We exploit evaluation methods in a greedy heuristic procedure to optimize this integrated planning. In a numerical study, we show that for problems with more than five types of spare parts it is preferable to use approximate evaluations as they become significantly faster than exact evaluation. Moreover, approximation errors decrease as problems get larger. Furthermore, we test how the greedy optimization heuristic performs compared to other discrete search algorithms in terms of total costs and computation times. Finally, in a rather large case study, we show that we may incur up to 27% cost savings when using the integrated planning as compared to a separated optimization.

Retrial inventory model with negative customers and multiple working vacations

This paper analyses a continuous review (s, S) inventory system at a service facility, wherein an item demanded by a customer is issued after performing service on the item. Primary arrivals follow a Poisson distribution and they may turn out to be positive or negative and then enter into the orbit. The orbiting demands compete for service according to an exponential distribution. The server takes multiple working vacations at zero inventory. Replenishment times, vacation times, service times during regular busy periods and vacation periods are exponentially distributed. A matrix analytic method is used for the steady-state distribution of the model. Various performance measures and cost analyses are shown with numerical results.

Deterministic inventory model for items with linear demand, variable deterioration and partial backlogging

A deterministic inventory model is developed for a deteriorating item having linear demand and variable deterioration rate. Shortages are allowed and partially backlogged. In developing the model we have assumed that the rate of backlogging is variable and dependent on the waiting time for the next replenishment. The objective of the model is to develop an optimal policy that minimises the total average cost. Suitable numerical example has been discussed to understand the problem. Sensitivity analysis has been carried out to show the effect of changes in the parameter on the optimum total average cost.

An EOQ model for non-instantaneous deteriorating items with partial backlogging and permissible delay in payments under inflation

In this paper, an economic order quantity (EOQ) model for non-instantaneous deteriorating items with permissible delay in payments under the effect of inflation and time value of money is presented. The demand is considered as a deterministic function which includes selling price and advertisement cost. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. The objective of this model is to minimise the total inventory cost of the retailer by finding the optimal length of time in which there is no inventory shortage and finding the optimal order quantity. Numerical examples are given to justify the model. Sensitivity analysis of the model with respect to several system parameters has been carried out and the implications are discussed in detail.

Deterministic inventory model for items with linear demand, variable deterioration and partial backlogging

A deterministic inventory model is developed for a deteriorating item having linear demand and variable deterioration rate. Shortages are allowed and partially backlogged. In developing the model we have assumed that the rate of backlogging is variable and dependent on the waiting time for the next replenishment. The objective of the model is to develop an optimal policy that minimises the total average cost. Suitable numerical example has been discussed to understand the problem. Sensitivity analysis has been carried out to show the effect of changes in the parameter on the optimum total average cost.

A partially backlogged EPQ model with demand dependent production and non-instantaneous deterioration

The present paper deals with a production inventory system for non-instantaneous deteriorating items with demand dependent production rate. It is assumed that demand rate is exponentially increasing function of time. Shortages are considered and partially backordered at a rate of decreasing function of waiting time for next replenishment. Herein, two cases for life time approach regarding the production stopping time point have been studied separately. The numerical examples have been provided separately to illustrate each case. Finally, sensitivity analysis has also been made to show the behaviour of presented model in each case.

Two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and permissible delay in payments under inflation

In this paper, two-warehouse economic order quantity (EOQ) model for non-instantaneous deteriorating items with permissible delay in payments under the effect of inflation and time value of money is presented in which the demand is considered as a deterministic function of selling price and advertisement cost. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This model aids in minimising the total inventory cost by finding the optimal intervals and the optimal order quantity. Furthermore, numerical examples are provided to illustrate the proposed model, sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.

Two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and permissible delay in payments under inflation

In this paper, two-warehouse economic order quantity (EOQ) model for non-instantaneous deteriorating items with permissible delay in payments under the effect of inflation and time value of money is presented in which the demand is considered as a deterministic function of selling price and advertisement cost. Also in this model, shortages are allowed and partially backlogged. The backlogging rate is dependent on the waiting time for the next replenishment. This model aids in minimising the total inventory cost by finding the optimal intervals and the optimal order quantity. Furthermore, numerical examples are provided to illustrate the proposed model, sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.

HadGEM2-AO 기후모델에 따른 과거와 미래의 동아시아 강수량에 대한 육지 증발량의 영향

Land evaporation contribution to precipitation over East Asia is studied to understand terrestrial moisture source of continental precipitation. Moisture recycling of precipitation relying on terrestrial evaporation is estimated based on the analysis method of Van der Ent et al. (2010). We utilize HadGEM2-AO simulations for the period of 1970~1999 and 2070~2099 from RCP8.5. Globally, 46% of terrestrial precipitation is depending from continental evaporation. 58% of terrestrial evaporation returns as continental precipitation. Over East Asia, precipitation has been affected by local evaporation and transported moisture. The advection of upwind continental evaporation results from the prevailing westerlies from the midwestern of Eurasian continent. For the present-day period, about 66% of the precipitation over the land of East Asia originates from land evaporation. Regionally, the ratios change and the ratios of precipitation terrestrial origin over the Northern inland and Southern coast of East Asia are 82% and 48%, respectively. Seasonally, the continental moisture recycling ratio is larger during summer (JJA) than winter (DJF). According to RCP8.5, moisture recycling ratio is expected to change. At the end of the 21st century, the impact of continental moisture sources for precipitation over East Asia is projected to be reduced by about 5% compared to at the end of 20th century. To understand the future changes, moisture residence time change is investigated using depletion and replenishment time.

Dynamic pricing and periodic ordering for a stochastic inventory system with deteriorating items

In this paper, we consider a problem of the dynamic pricing and the periodic ordering for deteriorating items with a stochastic inventory level depending on the stock-dependent demand and the selling price. In the model to be established, both shortages and remains are allowed, and the backlogging rate is variable and dependent on the waiting time for the next replenishment. Combined with the dynamic pricing, a stochastic dynamic optimization model, which maximizes the total profit, is developed. Based on the dynamic programming principle, the stochastic control model is transformed into a Hamilton–Jacobi–Bellman (HJB) equation. We show that there exists an optimal replenishment cycle length with an optimal inventory level at start of cycle. Moreover, the optimal pricing strategies are given. In addition, the finite difference scheme with the semi-smooth Newton method is proposed to solve the HJB equation numerically, and some numerical simulations are presented to illustrate the theoretical results. The sensitivity analysis of the optimal solution with respect to the major parameters is carried out and some managerial insights are proposed.

Pricing policy for declining demand using item preservation technology.

We have designed an inventory model for seasonal products in which deterioration can be controlled by item preservation technology investment. Demand for the product is considered price sensitive and decreases linearly. This study has shown that the profit is a concave function of optimal selling price, replenishment time and preservation cost parameter. We simultaneously determined the optimal selling price of the product, the replenishment cycle and the cost of item preservation technology. Additionally, this study has shown that there exists an optimal selling price and optimal preservation investment to maximize the profit for every business set-up. Finally, the model is illustrated by numerical examples and sensitive analysis of the optimal solution with respect to major parameters.