Stock-dependent Consumption Rate Research Articles

An Inventory Model for Non-instantaneous and Controlled Deterioration Rate with Stock and Time Dependent Consumption Rate

An Inventory Model for Non-instantaneous and Controlled Deterioration Rate with Stock and Time Dependent Consumption Rate

Inflationary Induced EOQ Model for Weibull Distribution Deterioration and Trade Credits

In any business transaction the constant unit price assumption is not true. The tendency in inflationary environment is to buy more in order to reduce the total system cost, which may be true in certain situations but it is not true when consumption rate of items is dependent on initial stock level since buying more quantity under inflationary environment leads to more consumption resulting in higher total system cost. The model developed in this paper helps to determine optimum ordering quantity for stock dependent consumption rate items under inflationary environment with infinite replenishment rate without permitting shortages. The effect of the inflation rate, deterioration rate, Initial-stock-dependent consumption rate and delay in payment are discussed. This study develops an inventory model for constant demand rate and time dependent deterioration rate with delay in payment is discussed. In this study mathematical model are also derived under two different cases. Case-I: The credit period is less then cycle time T; and Case-II: Credit period is greater than cycle time T. This study will proposes an inventory model under a situation in which the supplier provides the purchaser a permissible delay of payments if the purchaser orders a large quantity. Numerical example is given to support the purposed model. Mathematica 7.0 is used for numerical solutions.

Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages

In literature, many inventory studies have been developed by assuming deterioration of items as either a variable or constant. But in real life situation, deterioration of goods can be reduced by adding some extra effective capital investment in preservation technology. In this paper, a deteriorating inventory model with ramp-type demand under stock-dependent consumption rate by assuming preservation technology cost as a decision variable is formulated. Shortages are allowed and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. The objective of this study is to obtain the optimal replenishment and preservation technology investment strategies so that the total profit per unit time is maximum. Further, the necessary and sufficient conditions are considered to prove the existence and uniqueness of the optimal solution. Some numerical examples along with graphical representations are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed.

Fuzzy rough supply chain model under inflation and credit period with stock dependent consumption rate and partial backlogging shortages via genetic algorithm

In many inventory situations, purchasers are allowed a period to pay back for the goods bought without paying any interest. Depending on the length of that payment period, the purchaser can earn interest on the sales of the inventory. This paper develops a model to determine an optimal ordering policy for deteriorating items under inflation, stock dependent demand, permissible delay of payment, allowable shortage and unfinished demand is partially backlogged in fuzzy rough environments. The present value of total cost incurred in this inventory system is developed first, then an optimal order quantity and maximum allowable shortage are obtained by using a search procedure. The effect of inflation and time value of money was investigated under given sets of inflation and discount rates. This study shows that the optimal order quantity and maximum allowable shortage vary with the difference between inflation and time discount. Computational results provide some interesting policy implications. The genetic algorithm GA is used to make decision for above inventory model. The model is illustrated with some numerical data.

Mitigation of High-Tech Products with Probabilistic Deterioration and Inflations

This paper describes a deteriorating inventory model with ramp-type demand pattern under stock-dependent consumption rate. The deterioration of the product is considered as probabilistic to make the research a more realistic one. The proposed model assumes partially backorder rate which follows a negative exponential with the waiting time. The effect of inflation and time value of money are incorporated into the model. The purpose of this study is to develop an optimal replenishment policy so that the total profit is maximized. We provide a simple solution procedure to obtain the optimal solutions. Numerical examples along with graphical representations are provided to illustrate the model. Sensitivity analysis of the optimal solution with respect to key parameters of the model has been carried out and the implications are discussed.

A Complete Solution Procedure for a Replenishment Policy with Deteriorating Items, Stock-Dependent Consumption Rate and Shortages Under Infl ation and Time Discounting

Hou [European Journal of Operational Research 168 (2006) 463-474] developed an inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting. This paper will discuss the inventory model which is as same as that of Hou [7]. The main purpose of this note is to present a complete theorem and show the optimal solution k* exists and is unique. In addition, a few minor misprints in Hou [7] will also be corrected in this note. Finally, a numerical example is used to illustrate the application of this proposed model.

Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment

In this paper, some multi-item inventory models for deteriorating items are developed in a random planning horizon under inflation and time value money with space and budget constraints. The proposed models allow stock dependent consumption rate and partially backlogged shortages. Here the time horizon is a random variable with exponential distribution. The inventory parameters other than planning horizon are deterministic in one model and in the other, the deterioration and net value of the money are fuzzy, available budget and space are fuzzy and random fuzzy respectively. Fuzzy and random fuzzy constraints have been defuzzified using possibility and possibility–probability chance constraint techniques. The fuzzy objective function also has been defuzzified using possibility chance constraint against a goal. Both deterministic optimization problems are formulated for maximization of profit and solved using genetic algorithm (GA) and fuzzy simulation based genetic algorithm (FAGA). The models are illustrated with some numerical data. Results for different achievement levels are obtained and sensitivity analysis on expected profit function is also presented. Scope and purposeThe traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However for more sale, inventory should be maintained at a higher level. Of course, this would result in higher holding or procurement cost, etc. Also, in many real situations, during a shortage period, the longer the waiting time is, the smaller the backlogging rate would be. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging diminishes with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But at present, the economic situation of most of the countries has been much deteriorated due to large scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any further. The purpose of this article is to maximize the expected profit of two inventory control systems in the random planning horizon.

A Partial Backlogging Inventory Model for Deteriorating Item under Fuzzy Inflation and Discounting over Random Planning Horizon: A Fuzzy Genetic Algorithm Approach

An inventory model for deteriorating item is considered in a random planning horizon under inflation and time value money. The model is described in two different environments: random and fuzzy random. The proposed model allows stock-dependent consumption rate and shortages with partial backlogging. In the fuzzy stochastic model, possibility chance constraints are used for defuzzification of imprecise expected total profit. Finally, genetic algorithm (GA) and fuzzy simulation-based genetic algorithm (FSGA) are used to make decisions for the above inventory models. The models are illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented.Scope and Purpose. The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However, to keep sales higher, the inventory level would need to remain high. Of course, this would also result in higher holding or procurement cost. Also, in many real situations, during a longer-shortage period some of the customers may refuse the management. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging is diminishing with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But in the past, the economic situation of most of the countries has changed to such an extent due to large-scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any more. The purpose of this paper is to maximize the expected profit in the random planning horizon.

Improved solution process for inventory model with ramp-type demand under stock-dependent consumption rate

We use the smoothly connected property to simplify the solution process for inventory model with ramp-type demand under stock-dependent consumption rate. This article is a response to a complicated solution process of Wu et al. [“Retailer's optimal ordering policy for deteriorating items with ramp-type demand under stock-dependent consumption rate,” International Journal of Information and Management Sciences, 19, 245–262 (2008)]. They extended a minimum cost inventory model to a maximized profit problem and presented a detailed analysis for the solution procedure. However, their solution process may be too lengthy to involve many right but unnecessary results. In this article, we use the smooth connected property to dramatically simplify their solution structure. Our approach is also applied to minimum cost inventory models that were demonstrated by simplifying the paper of Deng et al. [“A note on the inventory models for deteriorating items with ramp type demand rate,” European Journal of Operational Research, 178, 112–120 (2007)]. Our findings will help ordinary readers to understand their important inventory models.

Supply chain coordination for a deteriorating product under stock-dependent consumption rate and unreliable production process

Article history: Received 1 July 2010 Received in revised form 2 October 2010 Accepted 4 October 2010 Available online 4 October 2010 This article develops a supply chain coordination model with a single-vendor and a singlebuyer. The vendor manufactures the product in lots and delivers to the buyer in equal shipments. The vendor’s production process is not perfectly reliable. During a production run, the process may shift from an in-control state to an out-of-control state at any random time and produces some defective items. The buyer whose demand is assumed to be a linear function of the on-hand inventory performs a screening process immediately after each replenishment. Moreover, the buyer’s inventory is deteriorated at a constant rate over time. The vendor-buyer coordination policy is determined by minimizing the average cost of the supply chain. It is observed from the numerical study that channel coordination earns significant cost savings over the non-coordinated policy. © 2011 Growing Science Ltd. All rights reserved.

Supply chain model for deteriorating items with stock-dependent consumption rate and shortages under inflation and permissible delay in payment

In today's world the financial decisions of any business/retail enterprise are very crucial, as from the financial standpoint, an inventory i.e., stock on display represents a capital investment and must compete with other assets for a firm's limited capital funds. Moreover, rising inflation rate directly affects the financial situation of an organization. On the contrary, the today's market is totally customer oriented which forces the retailer to invest more on stock in order to attract more and more customers. Further, this situation becomes more challenging when the retailer is dealing with deteriorating items. Apart from all this, the trade credit also plays a vital role in the financial decision making, as it helps in reducing the costs of holding stock. Keeping such a scenario in mind, this paper develops an inventory model for deteriorating items with stock-dependent consumption rate and allowable shortages under inflation and permissible delay in payments. Finally the model has been validated through numerical examples.

A partial backlogging inventory model for non-instantaneous deteriorating items with stock-dependent consumption rate under inflation

In this paper, we derive a partial backlogging inventory model for noninstantaneous deteriorating items with stock-dependent demand rate under inflation over a finite planning horizon. We propose a mathematical model and theorem to find minimum total relevant cost and optimal order quantity. Numerical examples are used to illustrate the developed model and the solution process. Finally, a sensitivity analysis of the optimal solution with respect to system parameters is carried out.

Replenishment policy for single item inventory model with money inflation

Finding out the replenishment policy is a hot topic of research in inventory management. In this article, we propose an optimal replenishment policy by considering stock dependent consumption rate for non instantaneous deteriorating items with money inflation and time discounting. In this model shortages are allowed and backlogging is partial. Solution procedure is given and explained with examples. The impact of various parameters of the system on the optimal solution is analyzed by carrying out sensitivity analysis with perturbations in various parameters.

An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages

In this paper, we extend Teng, J.T., Chang, H.J., Dye, C.Y., Hung, C.H. [2002. An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging. Operations Research Letters 30(6), 387–393.] and Hou, K.L. [2006. An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting. European Journal of Operational Research 168(2), 463–474.] by considering an inventory lot-size model under inflation for deteriorating items with stock-dependent consumption rate when shortages are partial backlogging. The proposed model allows for (1) partial backlogging, (2) time-varying replenishment cycles, and (3) time-varying shortage intervals. Consequently, the proposed model is in a general framework that includes numerous previous models as special cases. We then prove that the optimal replenishment schedule exists uniquely, and provide a good estimate for finding the optimal replenishment number. Furthermore, we briefly discuss some special cases of the proposed model related to previous models. Finally, numerical examples to illustrate the solution process and some managerial implications are provided.

An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting

This paper derives an inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting over a finite planning horizon. We show that the total cost function is convex. With the convexity, a simple solution algorithm is presented to determine the optimal order quantity and the optimal interval of the total cost function. The results are discussed with a numerical example and particular cases of the model are discussed in brief. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.

Optimal payment time for retailer's inventory system

A retailer's inventory control system for the optimal delay in payment time for initial stock-dependent consumption rate when a wholesaler permits delay in payment is developed. Shortages are not allowed in the inventory system. The effect of inflation rate, deterioration rate, initial stock-dependent consumption rate and a wholesaler's permissible delay in payment is discussed. A mathematical model is derived when a wholesaler permits that the credit period is less than or equal to the retailer's optimal payment time, and that the retailer's optimal payment time is less than or equal to the cycle time for settling the account. Besides, an expression for a retailer's inventory system's total cost derived for this case and five special cases will be discussed. Moreover, a computational procedure is proposed to obtain the optimal cycle time, retailer's payment time and order size. The results could help retailer's managers to determine the optimal total cost and strive for the wholesaler's permission to delay the payment period. Thus, a retailer can attempt to gain two very big advantages: (1) that the retailer will have more money to run in that period because of the extension of the optimal payment time and (2) that extra interest will be earned in that period. Finally, a numerical example demonstrates the applicability of the proposed model and a sensitivity analysis is also discussed.

An inventory model under inflation for stock dependent consumption rate items

Under inflation the assumption of constant unit price is not valid. The tendency in inflationary environment is to buy more in order to reduce the total system cost, which may be true in certain situations but it is not true when consumption rate of items is dependent on initial stock level since buying more quantity under inflationary environment leads to more consumption resulting in higher total system cost. The model developed in this paper helps to determine optimum ordering quantity for stock dependent consumption rate items under inflationary environment with infinite replenishment rate without permitting shortages. The results are illustrated with a numerical example.

An EOQ model for items with stock dependent consumption rate and exponential decay

In this paper an inventory model is developed for Initial Stock Dependent Consumption Rate and Exponential Decay Items, considering cost of the material lost due to deterioration in addition to ordering cost, carrying cost and material cost. Infinite replenishment rate is assumed and backlogging is not permitted. Expression for optimum ordering quantity has been obtained. The model is illustrated with a numerical example and the effects of various parameters on economic ordering quantity and total system cost have been analysed through sensitivity analysis.

An Inventory Model for Deteriorating Items and Stock-Dependent Consumption Rate

An Inventory Model for Deteriorating Items and Stock-Dependent Consumption Rate

An Inventory Model for Deteriorating Items and Stock-dependent Consumption Rate

An Inventory Model for Deteriorating Items and Stock-dependent Consumption Rate