This review paper aims to provide review of current order and inventory models due to costs problems. A wide variety of previous studies reviewed the order man- agement or inventory control in supply chain problems such as inventory control problem of logistical systems but there are several studies that survey in service sys- tems for instance bank as case study. The remainder of this paper is organized as follows. Section 1 provides an overview of literature of current surveys in order and inventory. Section 2 several critical factors of the researches were highlighted. Sec- tion 3 of this paper attempted to discuss on the obtain findings and results and Section 4 provides some conclude remarks, limitations of this study, and suggestions for fu- ture researches.
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At the beginning of the 1990s, the Economic Order Quantity (EOQ) and the Economic Production Quantity (EPQ) models have been one of the most important subjects of production and operations management areas. Although there has been a significant effort by academicians and researchers to provide applicability of the inventory models, these models ignore many factors faced with real-world problems. For example, one of the basic assumptions of these models is that 100% of items produced or received are of perfect quality. However, in most of production processes, it is unavoidable that the items ordered or produced have defects. Recently, these models have been extended in many directions by relaxing the assumption. Salameh and Jaber (2000) extended the classical EOQ model by assuming that the ordered lot contains a random proportion of defective items and after the inspection of the whole lot, the identified defective items are sold in a single batch at a lower price. Chen (2003) considered the classical EOQ model under random demand. Chen used the cycle length 𝑇 as decision variable. Jamal et al. (2004) developed two production inventory models to determine the optimal production quantity in a single-stage production system where rework is done under two different cases to minimize the total inventory cost. In the first case, the defective items produced regular production process is reworked within the same cycle. In the second case, the defective items are accumulated until N cycles are completed, and then they are reworked. Later, Cárdenas-Barrón (2009) extended Jamal et al.’s (2004) model, where defective items are reworked within the same cycle, considering planned backorders. An extensive review of the models that deal with the classical inventory models can be found in Andriolo et al. (2014).
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At a broad level, inventory models based solely on minimizing costs need several types of costs as inputs. We should note at this point that the word “cost” is used in broad manner, to include monetary costs and difficult-to-quantify costs such as management burden. The first type is the cost related to placing an order. It is comprised of a fixed cost which is assessed anytime an order is made and a variable cost which is a function of the number of units purchased. The second type of cost reflects the downside of carrying and maintaining inventory and is typically referred to as holding cost. Holding costs are what keep a decision maker from ordering too many goods. They can represent opportunity costs to the firm, driven by investing in inventory rather than pursuing other investment opportunities, as well as the cost of having inventory left over after demand has ceased. Holding costs can be defined as the actual cost of maintaining inventory. Excess inventory at the end of the horizon often has a value (negative cost) associated with it, which is often referred to as the salvage value. Lastly there is a cost associated with not having enough inventory, a lost sales penalty. This factor is what drives a cost-minimizing firm to invest in at least some inventory. This cost is assessed when demand exceeds on-hand supply. It can have fixed and variable portions as well, but the fixed portion is typically ignored. We can now define our basic cost terms in their simplest form. Define:
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In this note, I have introduced a simple way to solve the four basic inventory models using Microsoft excel. This note can be used in courses like econom- ics, operations management, operations research, supply chain management. This note can be used in teaching basic inventory models to avoid the lengthy manual calculation involved in solving them. It can also be used as an inter- esting example for an advanced class in Excel. The user just needs to enter the data in the white cells and all the results are automatically calculated. We recommend showing students how to first solve the models by hand (not necessarily the example problem), so that they understand the procedure, and then show them how to do it using Excel. The four models considered here are EOQ model, Basic production model, Discount Model and Shortage Model. Using the excel managers would be able to compare the various sce- narios provided by the organization. They would find it very convenient to use these models.
This paper studies the environmentally responsible repair and waste disposal inventory models. The model is very helpful to reduce the cost of remanufacturing option provides inventory cost benefits for a wide range of system by giving the manufacturer the opportunity to balance the workload between two alternative ways to produce a product.
An order level inventory model for deteriorating items with inflation induced demand and shortage has been developed. Since most decision makers think that inflation does not have significant influence on the inventory policy, the effects of inflation are not considered in some inventory models. However, from a financial point of view, an inventory represents a capital investment and must compete with other assets for a firm’ s limited capital funds. Thus, it is
Lee and Yao (1998) developed an economic production quantity (EPQ) model in which the demand and the production quantity are assumed to be fuzzy. Lo et al. (2007) presented an EPQ model which includes uncertain factors like unreliability of the machineries, flaw of the products or shortage caused by reworked process. They used fuzzy analysis hierarchy procedure (AHP) to calculate the set-up, holding and internal failure costs which affect the optimum production quantity. Halim et al. (2010) addressed the lot sizing problem in an unreliable production system with stochastic machine breakdown and fuzzy repair time. They defuzzified the cost per unit time using the signed distance method. Mahata and Goswami (2006) developed a fuzzy production-inventory model with permissible delay in payment. They assumed the demand and the production rates as fuzzy numbers and defuzzified the associated cost in the fuzzy sense using extension principle. Hsieh (2002) considered two fuzzy production-inventory models: one for crisp production quantity with fuzzy parameters and the other one for fuzzy production quantity. He used the graded mean integration representation method for defuzzifying the fuzzy total cost.
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A standard return of investment can be a result for having excess of current assets. However, firms may have shortages and difficulties for managing operations if they have a few current assets . The management of the working capital is the essential part, companies demand to maintain its liquidity in functioning from day to day to assure smooth running and respect its obligation. However, it is not simple task because the administrators have to arrange companies operation is in the course of execution in an effective and profitable way . The operations of working capital requirement includes all operations with financial need beginning with the reception of orders, procurement, manufacturing, product inventory and finally distribution. The solution for many firms is to produce just what they forecast to sell and assign all the assets to optimize supply chain. But, as the customer demand is not stable the firm must follow that demand .
A simple computational method (SCM) to analyze a class of (s, S) type inventory problem is developed. Under this (s, S) policy, (i) the number of units demanded where d = 1, 2… a ( s) at successive demand epochs form a Markov chain (MC) with one step transition probability matrix (TPM) P and (ii) the replenishments are instantaneous. This method gives the algorithm for computation of stationary probabilities of inventory process, joint probability function of number of transitions and quantities of replenishments per cycle, conditional and unconditional average costs. Illustrative example for a few special cases are provided, which strengthen the applicability of the SCM to practical problems.
One alternative to the traditional penalty cost model is the perturbed demand (PD) model. The perturbed demand model was first introduced by Schwartz (1966), where stock-outs alter future demand as a consequence of unsatisfied consumers not returning for future purchases (or convincing others to shop elsewhere). Perturbed demand models are founded on the idea that customers who are faced with a stock-out are less likely to return in the future because they will get their needs satisfied elsewhere. This claim is supported by consumer behavior literature (Verbeke et al., 1998; Campo et al. 2004). We assume loss of future demand is directly proportional to the number of stock-outs that occur. It is commonly assumed that customers will eventually forgive/forget that they were disappointed and return to their previous ordering behavior (Schwartz, 1966). This assumption enables the system to find a steady state balance between customers leaving due to stock-outs and customers returning. Without the ability to gain demand back over time, demand would monotonically decrease. Schwartz’s model is only concerned with the long term state of the system after demand has reached a steady state rate. The assumptions made concerning the order policy and state space limits the applicability of the model. Our model relaxes some of his assumptions, thereby allowing demand loss to be updated periodically and enabling the model to be more realistic.
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Many of the classic inventory models and strategies tend to establish a static horizon of time and given the conditions when a cycle is created making the inventory management a more standardized and efficient process. In a disaster relief situation, inventories cannot be designed like a repetitive model . This is caused due to the nature of the sudden onset disasters, the time, place, impact and needs are unknown before and even short time after the disaster strikes; the uncertainty in the disaster setting makes it problematic to make decisions such as what and when to send or purchase.
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In the present competitive market, the effect of marketing policies and conditions such as the price variations and the advertisement of an item change its demand pattern amongst the public. The propaganda and canvassing of an item by advertisement in the well-known media such as Newspaper, Magazine, Radio, T. V., Cinema, etc. and also through the sales representatives have a motivational effect on the people to buy more. Also, the selling price of an item is one of the decisive factors in selecting an item for use. It is commonly observed that lower selling price causes increase in demand whereas higher selling price has the reverse effect. Hence, it can be concluded that the demand of an item is a function of displayed inventory in a show-room, selling price of an item and the advertisement expenditures frequency of advertisement, Very few OR researchers and practitioners studied the effects of price variations and the advertisement on the demand rate of items. Kotler (1971) incorporated marketing policies into inventory decisions and discussed the relationship between economic order quantity and pricing decision. Ladany and Sternleib (1974) studied the effect of price variation on selling and consequently on EOQ. However, they did not consider the effect of advertisement. Subramanyam and Kumaraswamy (1971), Urban (1992), Goyal and Gunasekaran (1995), Abad (1996) and Luo (1998), Pal et al. (2007), Bhunia and Shaikh (2011) developed inventory models incorporating the effects of price variations and advertisement on demand rate of an item.
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In recent years there has been increased attention in integrating return flows in traditional production processes. The return flows have gained significant attention because of two main reasons: Environmental concern and modern technology making recovery of used products economically more attractive. While the reuse of products and materials is not new to industries; metal scrap reuse, waste paper recycling, P.E.T bottle recycling have been around a long time; the increase in re-manufacturable inventory as a percentage of serviceable inventory in recent times has made the need for traditional models to adapt to these changes. Various academicians have grasped this stark change in inventory models cutting across all sectors of industries and developed new models with various underlying mathematical assumptions. These assumptions have been dealt with in different research papers.
uch work has been reported regarding inventory models for deteriorating items in recent years. In many of the inventory systems the major consideration is regarding the pattern of demand and supply. Goyal and Giri  have reviewed inventory models for deteriorating items. They also developed on the basis of demand variations and various other conditions or constraints. Various functional forms are considered for describing the demand pattern. Aggarwal and Goel  have developed an inventory model with the weibull rate of decay having selling price dependent demand. In reality, the demand rate of any product may vary with time or with price or with the instantaneous level of inventory displayed in a supermarket. Mathew  Roy and Chaudhuri , Sana , Tripathy and Mishra  have studied inventory models with demand rates depending on selling price of the item. Inventory problems involving time dependent demand patterns have received the attention of several researchers in recent years. Mathew  Chun, et al. , Giri, et al. , Manna, et al. , Mahata and Goswami  and Skouri, et al.  are among those who studied inventory models for deteriorating items having time dependent demand.
Purpose: The aims of this article are to develop an integrated production-inventory-marketing model for a two-stage supply chain, and to study the effect of coordination on the performance of the system. The demand rate of the end customer is assumed to be sensitive to the selling price. The inventory models are developed, and then optimal values of the selling price, order quantity and number of shipments for the independent and also joint supply chain are determined. In addition, the effects of coordination and the parameters of the model on the optimal solution and the performance of the supply chain are investigated.
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Let the production of ith product starts at time t=0 and reaches stock level Q i at time when the deterioration of the items starts. At this stage the production of the product is stopped. The stock level reduces due to demand as well as due to deterioration upto time T 1 i when stock level reduces to zero. After this shortage starts and goes upto level S i . Then production of the product restarts and shortage is backlogged upto time T 2 i . This inventory model has been shown in figure 1. Our objective is to obtain the optimal values of different variables to maximize the profit.
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Inventory can be defined as stock of goods kept in a warehouse for future scale or using it in common day to day activities they may include raw materials, work in process goods, finished goods, packing material and general supplies. In order to meet the time, companies must keep on hand a stock of goods that is awaiting sale. The purpose of inventory theory is to determine rules that management can use to minimize the cost associated with maintaining inventory and meeting customer demand. Inventory control is the supervision of supply, storage and accessibility of items in order to ensure an adequate supply without excessive over supply. It can be referred to as internal control. It is always good to maintain an optimal inventory. There are two basic inventory questions generally taken by managers those are when to replenish the inventory of an item? And how must of an item to order when the inventory of that item is to be replenished? If one places frequent orders, the cost of ordering will be more, but the inventory carrying cost will be less. On the other hand if one places less frequent orders the ordering cost will be less but the carrying cost will be more.
In Vendor managed inventory a supplier of good ,usually the manufacturer, is responsible for optimizing the inventory held by a distributor.VMI requires a communication link-typically electronic data interchange or the internet –that provide the supplier with the distributor sales and inventory data it needs to plan inventory and place order. in contrast ,under the traditional arrangement the distributor handle those tasks The inventory can be owned by the distributor, or by the supplier . In this paper survey of 20 industries was carried out. On the basis of the mean calculated for different elements of VMI on 0-80 scale, all the elements were analyzed and plotted on a scatter chart, from where most important and less difficult elements were found out. Analysis of the data has done with the help of the XY Scatter Chart which is drawn between importance as abscissa and difficulty as . . After identifying the elements from XY scatter chart, apply the ANOVA analysis on those elements. From the result of the ANOVA analysis, we have checked the value is significant. This study help in finding VMI element which are most important and easy to implement
reliability consideration. Singhal and Singh (2015) discussed a modelling of an inventory system with multi variate demand under volume flexibility and learning. Singhal et al. (2016) developed a stochastic partial backlogging inventory models for deteriorating items with time dependent demand and volume elasticity.
anthropogenic sources in Europe, North America and Asia have been shown to contribute substantially to Arctic tropo- spheric burdens of SLCPs (e.g., Fisher et al., 2010; Sharma et al., 2013; Monks et al., 2014; Law et al., 2014). The Arc- tic troposphere is more polluted in winter and spring as a re- sult of long-range transport from northern mid-latitude con- tinents and the lack of efficient photochemical activity or wet scavenging needed to cleanse the atmosphere (Barrie, 1986). Large forest fires in boreal Eurasia and North America also impact the Arctic in the spring and summer seasons (Sode- mann et al., 2011). Our understanding of contributions from SLCP sources to present-day Arctic heating is sensitive to the ability of models to simulate the transport and processing of SLCPs en route to the Arctic from lower latitude sources. This model skill has implications for our confidence in pre- dictions of Arctic climate response to future changes in mid- latitude anthropogenic and wildfire emissions.
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