the demand rates are proportional withtime. In this paper, he did not suggest an optimal solution to the model but, rather, an approximate method by assumed equal replenishment periods. Goswami and Chauduri  considered a modelwith linear demand rates. They also suggested an approximate replenishment schedule. This is concerned with the development of amelioratinginventory models. The amelioratinginventory is the inventory of foods whose utility increases over the time by ameliorating activation. This study is performed according to areas; one is an economic order quantity (EOQ) model for the items whose utility is ameliorating in accordance with Weibull distribution, and the other is a partial selling quantity (PSQ) model developed for selling the surplus inventory accumulated by ameliorating activation with linear demand. Numerical examples to show the effect of amelioratingrateoninventory polices are illustrated.
Weiss (1980) first developed an inventorymodel by considering continuous review system and assumed that demand follows a Poisson distribution. Later, Liu and Lian (1999) generalized the main results of Weiss. According to their assumption demand shortage is fully backordered and they generalized the model to a stationary renewal process instead of a Poisson demand. Gurler and Ozkaya (2003) made a necessary amendment of Liu and Lian results. Later, Gurler and Ozkaya (2008) developed their own model by considering the life span of a batch as a random variable. Berk and Gurler (2008) developed a general approach known as (Q, r) policy which is an optimal policy for many continuous review inventory systems of nonperishable items. Tekin (2001) ameliorated the problem to some extent by making necessary revisions of the (Q, R) policy by proposing a (Q, R, T) policy. According to this policy, a refill order of amount Q is placed every time the available inventory level falls to r, or when T amounts of time have passed since the last occasion the inventory position reaches Q, whichever happens first. Chiu and Wang (2007) developed an EPQ modelwith the consideration of scrap, rework and stochastic machine breakdowns. They assumed random breakdown of machine and no resumption (NR) policy in their proposed model. Then total production-inventory cost functions were derived respectively for both EPQ models with breakdown and without breakdown and these cost functions were integrated and renewal reward theorem was used to cope with the variable cycle length. The authors concluded that the optimal runtime falls within the range of bounds and is determined by using the bisection method that is based on the intermediate value theorem. Chiu et al. (2011) derived a mathematical model for solving manufacturing runtime problem with the consideration of constant demandrate, constant production rate, random defective rate and stochastic machine breakdown.
variable ratedependenton the duration of waiting time up to the arrival of next lot. In both the models, the deterioration rate follows a three-parameter Weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. The corresponding models have been formulated and solved by considering the transportation cost for replenishing the items. Two numerical examples have been given to illustrate the results and the significant features of the result are discussed. Finally, based on these examples, the effects of different parameters on the initial stock level, shortage level (in case of secondmodel only), cycle length along with the optimal profit, sensitivity analyses have been performed considering one parameter at a time keeping other parameters at their original values.
The economic order quantity (EOQ) model is widely used by practitioners as a decision making tool for the control of inventory. In general, the objective of inventory management deals with minimization of the inventory carrying cost. Therefore it is important to determine the optimal stock and optimal time of replenishment of inventory to meet the future demand. An inventorymodelwith stock at the beginning and shortages allowed, but then partially backlogged was developed by Lin et al. . Urban  developed an inventorymodel that incorporated financing agreements with both suppliers and customers using boundary condition. Yadav et al.  established an inventorymodel of deteriorating itemswith two warehouse and stock dependentdemand. Wu et al.  applied the Newton method to locate the optimal replenishment policy for EPQ modelwith present value. Roy and Chaudhuri  established an EPLS modelwith a variable production rate and demand depending on price. Huang  developed an EOQ model to compare the interior local minimum and the boundary local minimum.
element in a set while later is concerned with the degree of uncertainty by which an element belongs to a set. In an inventory control model, Petrovic and Sweeney (1994) fuzzified the demand, lead time and inventory level into triangular fuzzy numbers. They used the fuzzy proposition method to obtain the optimal order quantity. Ishii and Konno (1998) introduced fuzziness in shortage cost by an L- shape fuzzy number when demand is stochastic. Gen et al. (1997) expressed the input data by fuzzy numbers, where they used interval mean value concept to solve an inventory problem. Yao and Chiang (2003) considered an inventorymodelwith total demand and storing cost as triangular fuzzy numbers. They performed the defuzzification by centroid and signed distance methods. Mondal and Maiti (2002) applied genetic algorithms (GAs) to solve a multi-item fuzzy EOQ model. Maiti and Maiti (2006) dealt with a fuzzy inventorymodelwith two warehouses under possibility constraints. Mahapatra and Maiti (2006) formulated a multi-item, multi-objective inventorymodel for deteriorating itemswith stock- and time-dependentdemandrate over a finite time horizon in fuzzy stochastic environment. Halim et al. (2008) developed a fuzzy inventorymodel for perishable itemswith stochastic demand, partial backlogging and fuzzy deterioration rate. The model is further extended to consider fuzzy partial backlogging factor. Goni and Maheswari (2010) discussed the retailer’s ordering policy under two levels of delay payments considering the demand and the selling price as triangular fuzzy numbers. They used graded mean integration representation method for defuzzification.
Researchers started to develop inventory systems allowing time variability in one or more than one parameters. Dave and Patel  discussed an inventorymodel for replenishment. This was followed by another model by Dave  with variable instantaneous demand, discrete opportunities for replenishment and shortages. Bahari- Kashani  discussed a heuristic modelwithtime-proportional demand. An Economic Order Quantity (EOQ) model for deteriorating itemswith shortages and linear tend in demand was studied by Goswami and Chaudhuri . On all these inventory systems, the deterioration rate is a constant.
The Economic Order Quantity (EOQ) model developed by Harris in 1915 was popularized by Wilson in 1934 (Hariga, 1995), while Taft introduced the Economic Production Quantity (EPQ) model in 1918. Ghare and Shrader (1963) was the first to extend the classical EOQ formula to include exponential decay, wherein a constant fraction of on hand inventory is assumed lost due to deterioration. Misra (1975) developed the first production lot size model in which both constant and variable rate of deterioration were considered (Raafat, 1991). In subsequent models, the deterioration rates of the items vary from exponential distribution to gamma, normal or Weibull distributions. According to Nahmias (1982), the exponential decay can be derived by assuming that a constant fraction of on-hand stock is lost (i.e. deteriorates) each period regardless of the age distribution of inventory. Hence, those models with exponential deterioration rate are classified as having constant deterioration rate while those with Weibull, normal or other distribution are considered as having variable rate of deterioration (Urban 2005). There are also different Production-inventory models with constant deterioration rate (Maity & Maiti, 2005; Hedjar et al., 2004; Yang & Wee, 2003; Yu, 2007; Alfares et al., 2005; Jaggi et al., 2011). A generalized model in which deterioration and production varies continuously withtime was developed by Balkhi (2001) while Lo et al. (2007) developed an integrated production inventorymodelwith varying rate of deterioration, imperfect production processes and inflation. Other models with varying deterioration rate include Pal et al., (2008) and Sridevi et al. (2010).
mal replenishment time for a linearly increasing demand pattern. Barbosa and Friedman and Henery respec- tively extended the demand pattern to a power demand form and a log-concave function. Hariga and Goyal and Teng extended Donaldson’s work by considering various types of shortages. For deteriorating items such as medicine, volatile liquids and blood banks, Dye developed the inventorymodel under the circumstances where shortages are allowed and backlogging rate linearly depends on the total number of customers in the waiting line during the shortage period. However, there still re- main many problems associated with replenishment poli- cies for retailers that should theoretically be solved to provide them with eﬀective indices. We focus on a case where special display goods[11, 12, 13] are dealt in. The special display goods are heaped up in the end displays or special areas at retail store. Retailers deal in such special display goods with a view to introducing and/or exposing new products or for the purpose of sales promotions in many cases. They are sold at a fast velocity when their quantity displayed is large, but are sold at a low veloc- ity when their quantity becomes small. Baker and Baker and Urban dealt with a similar problem, but they expressed the demandrate simply as a function of a polynomial form without any practical meaning. Our previous work has developed an inventorymodel for the special display goods with a seasonal demandrate over a ﬁnite time horizon to determine the optimal re- plenishment policy, which maximizes the retailer’s total proﬁt. However, the salvage value which is the dis- posal value of unsold inventory at the end of the season was assumed to be equal to the purchase cost. In this study, we relax this restriction on the salvage value in order to derive a more general solution. Numerical ex- amples are presented to illustrate the theoretical under- pinnings of the proposed model.
fuzziness of ordering cost and holding cost. Roy and Maiti (1997) presented a fuzzy EOQ modelwithdemand-dependent unit cost under limited storage capacity considering different parameters as fuzzy sets with suitable membership function. Kao and Hsu (2002), Dutta, Chakraborty, and Roy (2005) studied single period inventorymodelwith fuzzy demand and fuzzy random variable demand, respectively, and developed models for optimum order quantity in terms of cost. Syed and Aziz (2007) modeled inventorymodel without shortage under fuzzy environment. Ordering and holding costs were considered as fuzzy triangular numbers, and optimum order quantity was developed using signed distance method. Wang et al. (2007) developed the model of fuzzy economic order quantity without backordering. Holding cost and set-up cost were considered as fuzzy in nature and the model was developed for keeping the credibility of total cost in the planning period below certain budget level. Vijayan and Kumaran (2008) investigated continuous review and periodic review inventory models under fuzzy environment, where the membership function distribution took a trapezoidal form. Gani and Maheswari (2010) discussed the retailer’s ordering policy under two levels of delay payments considering the demand and the selling price as triangular fuzzy numbers. They used graded mean integration representation method for defuzzification. Singh et al. (2011) and Malik and Singh (2011) utilized soft computing techniques for modeling of inventory under price dependentdemand and variable demand, respectively. In the same year, Mahata and Mahata (2011) applied fuzzy EOQ model to supply chains and Rong (2011) developed EOQ model by treating the holding cost, shortage cost and ordering cost per unit as uncertain variables. Based on above mentioned situations, this paper considers the retailer’s optimal policy for non- instantaneous deteriorating itemswith permissible delay in payments under different scenarios in fuzzy environment. The paper discusses all the possible cases which may arise and yet not considered in the previous inventory models under permissible delay in payments. Further, this paper also considers the price dependentdemand and the possibility of higher earning interest rate than interest payable. The components of demand function are assumed as triangular fuzzy number. The arithmetic operations are defined under the function principle and for defuzzification, signed distance method is employed to evaluate the optimal cycle length T, markup rate and payoff time which maximize the total profit in all possible cases. Finally, numerical examples are presented to show the validity of the model followed by the sensitivity analysis. Results have shown significant effect in real life.
In this paper, we develop a multi-period lot-sizing model for deteriorating itemswith varying demand patterns when the time horizon is unknown or unspecified. There are three main reasons for our assumptions. (i) The first reason is to present a multi-period inventorymodel for deteriorating items using a general ramp-type demand pattern with full backlogging of shortages. The general ramp-type demand function allows three-phase variation in demand, representing the growth, the steady and the decline phases of demand commonly experienced by many products. This will be more suitable for practical applications than single period models that assume a single replenishment to cover all phases of demand. (ii) The second reason is to make the developed model suitable for unknown time horizon by extending the Silver-Meal approach to a general ramp-type demand pattern. This makes the model to be suitable for situations, discussed earlier, when the time horizon is neither fixed nor infinite. (iii) Finally, the third reason is to examine various possible replenishment patterns when shortages and demand pattern variation occur in a multi-period inventorymodel. The replenishment intervals are allowed to vary from one period to another along the cycle and a replenishment policy to generate optimal replenishment schedules, order quantity and costs is proposed. An additional solution procedure based on trust region methods is also presented to complement the usual direct implementation of derivatives. This paper is organized as follows: Section 2 contains a brief literature review and the proposed model of this paper is presented in section 3. Solution procedure to obtain the optimal replenishment policy, numerical illustrations and conclusions are also presented in sections 4 to 6.
In real-life situations, exact data are often inadequate for a mathematical model. Inventory is a physical stock that a business keeps on hand in order to promote the smooth and efficient running of its affairs. But in practice, the effects of deterioration, shortages, holding cost, ordering cost etc. are important for inventory. Various types of uncertainties are involved in any inventory system. Historically, probability theory has been the primary test for representing uncertainty in mathematical models. Because of this, all the uncertainty was assumed to follow the characteristics of random uncertainty. A random process was one where the outcome of any particular realization of the process is strictly a matter of chance, and prediction of a sequence of events is not possible. Fuzzy set theory is an excellent tool for modeling the
Determining the optimal inventory control and selling price for deteriorating items is of great significance. In this paper, a joint pricing and inventory control model for deteriorating itemswith price- and time-dependentdemandrate and time-dependent deteriorating ratewith partial backlogging is considered. The objective is to determine the optimal price, the replenishment time, and economic order quantity such that the total profit per unit time is maximized. After modeling the problem, an algorithm is proposed to solve the resulted problem. We also prove that the problem statement is concave function and the optimal solution is indeed global.
The concept was also used on organizational communication (Castor, 2017) and in interpersonal communications studies to codify and analyze interaction between individuals at the relational level (Rogers & Escudero, 2004). In political studies, (Simons, 1994) metacommunication is a rhetorical tactic used in political debates e.g. politicians striving to cope with provocative questions by challenging the journalist’s legitimacy for asking them. In the international relations and political science domains (Rich & Craig, 2012), metacommunication is used as a key concept in Digital Media studies. Jensen (2016: 7), for instance, emphasizes, “the importance of meta-communication for contemporary communication theory, examines mediated presence as an instance of metacommunication, and addresses the implications of digitally mediated presence for current issues of surveillance”.
In a wide variety of practical applications, the characteristics of the plant dynamics are changing through time due to aging of components or the variation of the reference. When the dynamics of the system is changing at a slow pace, the least squares algorithm (with and without forgetting factor) is quite effective when it is used to follow this type of behavior. Nevertheless, the efficiency of the algorithm diminishes when the dynamics is changing rapidly. In the past years, systems with fast changing dynamics are being used more often in modern engineering applications; in particular, linear periodic time varying systems (LPTVS) have appeared in different areas such as Control, Power Electronics, Aeronautics, Communications and Signal Processing . For example, in aeronautics, the equations that describe the flight dynamics in aircrafts have coefficients that are functions of time. Recently, the high speeds and accelerations that modern aircrafts can handle, have contributed to show that the parameters of the system that depend on speed will change in the same fashion. For instance, the dynamic of a main rotor in a helicopter, which can be modeled by a linear periodic system, is important from the control perspective due to the fact that a precise control of certain variables in the system can help to attenuate vibrations in the rotor components, that eventually may cause high levels of stress and fatigue . Thus, there
The PGIS-II factors had stronger relations with the presence of meaning in life than with the other variables. The presence of meaning in life refers to the extent to which people comprehend and see significance in their lives, as well as the degree to which they perceive themselves to have a purpose or overarching goal in life (Steger, Shin, Shim, & Fitch-Martin, 2013). Theoretically, it is a future- oriented, cognitive, and motivation-based construct. PGI, in turn, refers to active and intentional engagement in the process of self-improvement (Robitschek et al., 2012). People will use their PGI skills in life domains of greatest importance to them (Freitas, Damásio, Tobo, Kamei, & Koller, 2016). Growth and development that are personally important should lead to an increased sense of purpose in life. Although not tested in this study, it is possible that better developed PGI skills promote a greater sense of meaning in life.
Note that Alice and Bob need a strategy which must include some communication during its execu- tion, which would help each of them to know who is assigned which task during the day, and hence who cannot do the shopping. Note also that the model incorporates some timing information, such that the two agents need a strategy with perfect recall in order to reach their goal: after working tx time units both Alice and Bob must use their observable past to remember if they have finished working. Finally, note that, if we consider that strategies for coalitions are tuples of strategies for individual members, as in [AHK98, Sch04] then the formula φ is false: whatever decision Alice and Bob take together, in the morning, about who is to pick the child, who is to do shopping, and in what observable circumstances (but without exchanging any information), can be countered by the task assignment, which would bring Alice and Bob at the end of the day either with an empty fridge or the child spending his night at the nursery.
rate for the newly launched deteriorating item. Joglekar (2003) used a linear demand function with price sensitiveness and allowed retailers to use a continuous increasing price strategy in an inventory cycle. He derived the retailer’s optimal profit by ignoring all the inventory costs. His findings are restricted to growing market only, which is neither for stable market nor for a declining market.
I published in 1951 a study of the geographic vari- ation of Amphisbaena fuliginosa Linnaeus, 1758, concluding that five subspecies could be recognized, based mainly on color pattern, but with substantial support from scale counts. The paper was writ- ten in the flush and heat of the Mayrian paradigm (Mayr 1942): if two taxa are similar and allopatric, they should be considered as geographical races or subspecies. I have since come to question the un- qualified application of the paradigm. The concept of subspecies involves more than likeness and al- lopatry; it entails too the presence of broad areas of morphological stability connected by relatively nar- row belts of integradation (Vanzolini and Williams 1970). Additionally, I came to worry about the sta- tistical tools: the methods then available in text- books within my reach were not ideally suited to the
SAGE II version 6.3 to more confidently avoid the introduc- tion of systematic error. We have retained the cutoff for two reasons. Firstly, although the error function is defined as the deviation between the calculated and true transmission, in practice the “true” transmission must be approximated. Specifically, we use a “best guess” profile, constructed by smoothing the data using a boxcar average and a running median, the same algorithm that is used to generate the fi- nal profile from the transmission scatter data. It is possible that errors in the best guess transmission profile could lead to errors in the timedependent correction, and these errors are more likely where the atmosphere has a high degree of natural variability. There is also some risk of falsely “cor- recting” or attempting to correct real atmospheric variability by the method described here. It is possible that future de- velopments will allow the algorithm to distinguish between real atmospheric variability and timedependent calibration errors.
Abstract: This study considered reorder point on the continuous review inventorymodel under controllable lead timewith mixture of backorder price discounts and partial lost sales. We developed a continuous review inventorymodel where the lead time, the order quantity, backorder discount and safety factor were considered as the decision variables of a mixture of backorders and lost sales inventorymodel. The objective was to minimize the expected total annual cost with respect to related decision variables. The purpose modelwith lead timedemand distribution was unknown. The author applies a minimax distribution free procedure to find the optimal solution and numerical example was included to illustrate the solution procedure of the proposed algorithms.