optimal lot size model for deteriorating items with demand rate dependent on displayed stock level dsl and partial backordering in this paper we consider the problem of determining the lot size of a single deteriorating item with the demand rate dependent on displayed stock level selling price of an item and frequency of advertisement in the popular electronic and print media also through the sales representatives shortages if any are allowed and partially backlogged with a variable rate which depends on the duration of waiting time upto the arrival of next lot here the transportation cost for replenishing the goods is considered explicitly and the storage capacity of the showroom shop is assumed to be limited finite according to the relative size of the stock level dependency demand parameters and the storage capacity of the showroom shop different scenarios with sub scenarios have been mentioned and solved with the help of grg generalised reduced gradient method and the computational procedure the convexity analysis is done by showing the average profit function in each case as pseudo concave to illustrate the results and its significant features a numerical example is given finally to study the effect of changes of demand parameters deterioration backlogging parameters and mark up rate on the maximum initial stock level shortage level frequency of advertisement per cycle along with the maximum average profit are presented numerically

a deterministic inventory model for deteriorating items with stock dependent demand rate abstract a deterministic inventory model is developed by assuming that the demand rate is stock dependent and the items deteriorate at a constant rate the expression for the average net profit over one production run is derived and its optimization with respect to the decision variables q initial stock and t duration of a production cycle is carried out this leads to two highly nonlinear equations which are solved by using a subroutine neqnf in imsl math library in cyber 180 480a computer system the optimal solution so derived is compared with that for the no deterioration 0 case sensitivity of the optimal solution to changes in parameter values is examined several aspects of the functional form for the demand rate are considered in a separate section finally the salient features of the problem and its solution are discussed in brief

inventory policy with time dependent setup cost abstract assume a time interval t is given moreover assume that the setup cost is not constant but varies with the lapse of time our problem is to determine the inventory policy for the given t how often the order is placed during t and how much is ordered at each ordering time point are our main themes we solve these problems in the following ways if frequency of orders for t is given arbitrarily the ordering policy is to be planned by using the techniques of dp by choosing a proper frequency of orders so that it may minimize the total inventory cost required during t an optimal inventory policy for t is determined moreover by applying dp some mathematical properties of this policy are examined even if exact mathematical expressions for frequency of orders and inventory cost are determined their values are obtained these become the merit of applying dp

a note on eoq models for deteriorating items under stock dependent selling rate abstract in 1995 padmanabhan and vrat presented inventory models for deteriorating items with stock dependent selling rate and derived the profit functions without backlogging and with complete backlogging first this paper develops the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions of the profit per unit time functions without backlogging and with complete backlogging second this paper explains that it is appropriate to use the newton raphson method to find the optimal solutions of the profit functions per unit time in both situations modelled

optimal ordering and transfer policy for an inventory with stock dependent demand abstract this paper deals with an ordering transfer inventory model to determine the retailer s optimal order quantity and the number of transfers per order from the warehouse to the display area it is assumed that the amount of display space is limited and the demand rate depends on the display stock level the objective is to maximize the average profit per unit time yielded by the retailer the proposed models and algorithms are developed to find the optimal strategy by retailer numerical examples are presented to illustrate the models developed and the sensitivity analysis is also reported

an eoq model with stock dependent demand shortage inflation and time discounting abstract this paper develops a finite time horizon deterministic economic order quantity eoq inventory model with shortages where the demand rate at any instant depends on the on hand inventory stock level at that instant the effects of inflation and the time value of money are taken into account considering two separate inflation rates namely the internal company inflation rate and the external general economy inflation rate the results are discussed with a numerical example and particular case of the model is discussed in brief a sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

inventory model with stock level dependent demand rate and variable holding cost inventory models in which the demand rate depends on the inventory level are based on the common real life observation that greater product availability tends to stimulate more sales previous models incorporating inventory level dependent demand rate assume that the holding cost is constant for the entire inventory cycle this paper considers the inventory policy for an item with a stock level dependent demand rate and a storage time dependent holding cost the holding cost per unit of the item per unit time is assumed to be an increasing function of the time spent in storage two time dependent holding cost step functions are considered retroactive holding cost increase and incremental holding cost increase procedures are developed for determining the optimal order quantity and the optimal cycle time for both cost structures

inventory models with inventory level dependent demand a comprehensive review and unifying theory marketing researchers and practitioners have long recognized the demand of many retail items is proportional to the amount of inventory displayed recently two distinct types of inventory control models reflecting this relationship have appeared in the literature models in which the demand rate of an item is a function of the initial inventory level and those in which it is dependent on the instantaneous inventory level we present a comprehensive overview of this literature and demonstrate the equivalence of the two types of models through the use of a simple periodic review model an alternative approach to sensitivity analysis for inventory models with inventory level dependent demand is also presented

an inventory model for deteriorating items with stock dependent demand rate abstract this paper discusses an inventory model with an inventory level dependent demand rate followed by a constant demand rate for items deteriorating at a constant rate where the terminal condition of zero inventory at the end of the scheduling period has been relaxed sensitivity of the decision variables to changes in the parameter values is examined and the effects of these changes on the optimal policy are discussed in brief

a production inventory model in an imperfect production process abstract the paper develops a model to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process the basic assumption of the classical economic manufacturing quantity emq model is that all manufacturing items are of perfect quality the assumption is not true in practice most of the production system produces perfect and imperfect quality items in some cases the imperfect quality non conforming items are reworked at a cost to restore its quality to the original one rework cost may be reduced by improvements in product reliability i e decreasing in product reliability parameter lower value of product reliability parameter results in increase development cost of production and also smaller quantity of nonconforming products the unit production cost is a function of product reliability parameter and production rate as a result higher development cost increases unit production cost the problem of optimal planning work and rework processes belongs to the broad field of production inventory model which deals with all kinds of reuse processes in supply chains these processes aim to recover defective product items in such a way that they meet the quality level of good item the benefits from imperfect quality items are regaining the material and value added on defective items and improving the environment protection in this point of view a model is introduced here to guide a firm industry in addressing variable product reliability factor variable unit production cost and dynamic production rate for time varying demand the paper provides an optimal control formulation of the problem and develops necessary and sufficient conditions for optimality of the dynamic variables in this purpose the euler lagrange method is used to obtain optimal solutions for product reliability parameter and dynamic production rate finally numerical examples are given to illustrate the proposed model

an inventory model with both stock dependent demand rate and stock dependent holding cost rate abstract in this paper we develop an inventory model under a stock dependent demand rate and stock dependent holding cost rate with relaxed terminal conditions shortages are allowed and partially backlogged in the model the purpose of this study is to determine the optimal order quantity and the ending inventory level such that the total profit per unit time is maximized for the retailer we first establish a proper model for a mathematical formulation then we develop several theoretical results and provide the decision maker with an algorithm to determine the optimal solution finally numerical examples are provided to illustrate the solution procedure and a sensitivity analysis of the optimal solution with respect to major parameters is carried out

the linkage between life insurer spread behaviour and credit swap transaction policyholder protection analysis the paper develops a contingent claim model to evaluate the equity of a life insurer when the insurer could act as a protection buyer or a protection seller in a credit swap transaction market the

an inventory model with deteriorating items under inflation when a delay in payment is permissible abstract this study develops an inventory model for initial stock dependent consumption rate when a delay in payment is permissible in the inventory model shortages are not allowed the effect of the inflation rate deterioration rate initial stock dependent consumption rate and delay in payment are discussed in the study mathematical models are also derived under two different circumstances i e case i the credit period is less than or equal to the cycle time for settling the account and case ii the credit period is greater than the cycle time for settling the account besides expressions for an inventory system s total cost are derived for these two cases moreover a computational procedure and gino lasdon et al acm transactions mathematical software 4 1978 34 50 are proposed to obtain the optimal order size and cycle time the results can help managers determine the optimal total cost finally a numerical example demonstrates the applicability of the proposed model

an inventory model for deteriorating items with time proportional demand and shortages under inflation and time discounting this paper proposes a generalized dynamic programming model for inventory items with weibull distributed deterioration in this model the demand rate is assumed to be time proportional shortages are allowed and completely backordered and the effects of inflation and time value of money are taken into consideration the solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of total cost associated with the inventory system is minimized the proposed model permits variation in both the replenishment intervals and the service levels between order cycles as a result it generates a better solution than other optimization models having fixed order intervals and or fixed service levels the solution procedure is illustrated by two numerical examples and comparison with an existing model is carried out

analysis of deteriorating inventory production systems using a linear quadratic regulator we consider an inventory production system where items deteriorate at a constant rate the objective is to develop an optimal production policy that minimizes the cost associated with inventory and production rate the inventory problem is first modeled as a linear optimal control problem then linear quadratic regulator lqr technique is applied to the control problem in order to determine the optimal production policy examples are solved for three different demand functions sensitivity analysis is then conducted to study the effect of changing the cost parameters on the objective function

production inventory models for a damageable item with variable demands and inventory costs in an imperfect production process in this paper economic production quantity epq models for breakable or deteriorating item are developed with variable demands being dependent on time or on hand stock here rate of production and holding cost are time dependent unit production cost is a function of both production reliability indicator and production rate set up cost is also partially production rate dependent the production process produces some imperfect quantities which are instantly reworked at a cost to bring back those units to the perfect ones the production process ultimately depends on both time and reliability indicator the models are formulated as optimal control problems and the total profit functions with effect of inflation and time value of money are expressed as finite integrals over the finite planning horizon the problems are solved using euler lagrange function based on variational calculus and newton raphson method to determine the optimal production reliability indicator r and then corresponding production rates and total profits in some cases results of the models for deteriorating item are obtained as particular cases from those of breakable item models similarly results of simple epq models without damageability are deduced as particular cases numerical experiments are performed to illustrate the models both numerically and graphically

an optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand and partial backlogging abstract in this study we consider a problem of determining the optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand in the model shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment the necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown as the special cases the results for the models with instantaneous or non instantaneous deterioration rate and with or without shortages are derived further we analytically identify the best circumstance among these special cases based on the minimum total relevant cost per unit time sensitivity analysis of the optimal solution with respect to major parameters is carried out finally four numerical examples are presented to demonstrate the developed model and the solution procedure

operations research in inventory management a review and critique the objectives of inventory management including the relevant related costs are examined in this paper a brief review of standard problems that have been effectively solved is presented however we point out that a serious gap exists between theory and practice in many organizations suggestions are made for bridging this gap finally a list is provided of a number of research problems whose implementable solution would have a major beneficial impact on the practice of inventory management

an eoq model with state dependent demand rate we present an eoq type model in which the demand rate is a function of the inventory level the demand functions and holding cost functions considered are quite general in particular we focus on two types of demand rate functions a piecewise constant function and a family of exponential functions the paper includes analysis of the problem optimization and sensitivity analysis we also extend the model by adding randomness to the order sizes

inventory models with the demand rate dependent on stock and shortage levels this paper investigates an inventory system in which the demand rate during stockout periods differs from that during the in stock period by a given amount the previous analysis conducted in this area formulated the model as a cost minimization model this type of formulation will intentionally try to decrease demand by increasing the stockout period in order to decrease costs this paper appropriately considers the model as a profit maximization model and develops a closed form solution the model is then further generalized to incorporate the effect of stock level dependent demand rates and considers initial stock dependent demand as well as instantaneous stock dependent demand rates

demand promotion by upgradation under stock dependent demand situation a model the idea of demand promotion by upgrading the existing system of the selling centre has been modelled in this article the consumption rate is assumed to be dependent on the stock level the problem has been reduced to a maximizing problem the algorithmic approach for solving this maximizing problem is also provided objective is to maximize the net profit over a prescribed time an increasing convex upgradation cost is considered exponential upgradation cost has been considered for the numerical examples

an optimal procurement policy for items with an inventory level dependent demand rate and fixed lifetime abstract this paper investigates an optimal procurement policy for items with an inventory level dependent demand rate and fixed lifetime the demand rate is assumed to be a function of current inventory level and each unit has its fixed expiry date so any units which remain unused by their expiry date are considered outdated and must be disposed of for the system presented a mathematical model and solution methodology were developed sensitivity of the decision variables to changes in the parameter values is examined and future research needs are discussed in brief

stack them high let em fly lot sizing policies when inventories stimulate demand in some retail contexts stocking large quantities of inventory may not only improve service levels but can also stimulate demand for products having demand rates that increase with inventory levels we analyze the effect of stocking decisions on firm profitability to develop managerial insights regarding the structure of the optimal inventory policy and to understand how this policy differs from traditional approaches when inventories stimulate demand iteratively applying the standard economic order quantity eoq model by setting the demand rate parameter equal to the observed average demand rate in prior cycles yields an equilibrium order quantity that is robust to demand parameter misestimation but is suboptimal the profit maximizing policy orders larger quantities and can replenish inventory even before on hand stock fully depletes using an extension of a standard inventory dependent demand model from the literature we first provide a convenient characterization of products that require early replenishment we demonstrate that the optimal cycle time is largely governed by the conventional trade off between ordering and holding costs whereas the reorder point relates to a promotions oriented cost benefit perspective we show that the optimal policy yields significantly higher profits than cost based inventory policies underscoring the importance of profit driven inventory management

an economic analysis of alternative grazing fee systems congress called for an evaluation of potential grazing fees and fee alternatives by 1985 this study contributes to that evaluation and constitutes an economic evaluation of the current and seven other fee systems fee systems are evaluated for total welfare income distribution future discrepancies between fees and forage values public administration cost usage potential administrative feasibility and data requirements these criteria are found to be mutually inconsistent particularly for welfare future discrepancies public administration cost and income distribution fee systems most consistent with these criteria involve ones based on private land lease rates government administration costs or competitive bidding

optimal replenishment policies for non instantaneous deteriorating items with stock dependent demand abstract wu et al 2006 an optimal replenishment policy for non instantaneous deteriorating items with stock dependent demand and partial backlogging international journal of production economics 101 369 384 established an inventory model for non instantaneous deteriorating items with stock dependent demand and obtained the optimal replenishment policy in this paper we first amend wu et al s model by changing the objective to maximizing the total profit secondly we set a maximum inventory level in the model to reflect the facts that most retail outlets have limited shelf space thirdly we relax the restriction of zero ending inventory when shortages are not desirable we then establish the theoretical results and provide an algorithm to find the optimal solution finally we present some numerical examples to illustrate the results