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It is observed that large piles of consumer goods displayed in supermarkets lead consumers to buy more, which generates more profit to sellers. But a large number of on-hand display of stock leaves a negative impression on the buyer. Also, the amount of shelf or display space is limited. Due to this reason, we impose a restriction on the number of on-hand display of stock and also on initial and ending on-hand stock levels. We introduce an economic production lot size model, where production rate depends on stock and selling price per unit. A constant fraction deterioration rate is considered in this model. To illustrate the results of the model, four numerical examples are established. Sensitivity analysis of the changes of parameter values is also given.

In the present article, a production-inventory model is developed over a finite planning horizon where the demand varies linearly with time. The machine production rate is assumed to be finite and constant. Shortages in inventory are allowed and are completely backlogged. The associated constrained minimization problem is numerically solved. Sensitivity analysis is also presented for the given model.

In this paper, we consider the problem of simultaneous determination of retail price and lot-size (RPLS) under the assumption that the supplier offers a fixed credit period to the retailer. It is assumed that the item in stock deteriorates over time at a rate that follows a two-parameter Weibull distribution and that the price-dependent demand is represented by a constant-price-elasticity function of retail price. The RPLS decision model is developed and solved analytically. Results are illustrated with the help of a base example. Computational results show that the supplier earns more profits when the credit period is greater than the replenishment cycle length. Sensitivity analysis of the solution to changes in the value of input parameters of the base example is also discussed.

Single price discount in unit cost for bulk purchasing is quite common in reality as well as in inventory literature. However, in today's high-tech industries such as personal computers and mobile industries, continuous decrease in unit cost is a regular phenomenon. In the present paper, an attempt has been made to investigate the effects of continuous price decrease and time-value of money on optimal decisions for inventoried goods having time-dependent demand and production rates. The proposed models are developed over a finite time horizon considering both shortages and without shortages in inventory. Numerical examples are taken to illustrate the developed models and to examine the sensitivity of model parameters.

A finite time-horizon deterministic inventory model is developed, taking the demand rate at any instant to be a function of the on-hand inventory (stock-level) at that instant. Shortages in inventory are allowed. The effects of inflation and time value of money are considered. Two separate inflation rates: namely, the internal (company) and the external (general economy) are introduced. A numerical example of the model is discussed. A sensitivity analysis of the optimal solution with respect to the parameters of the model is examined.

This paper develops an infinite time-horizon deterministic economic order quantity (EOQ) inventory model with deterioration based on discounted cash flows (DCF) approach where demand rate is assumed to be non-linear over time. The effects of inflation and time-value of money are also taken into account under a trade-credit policy of type "α/T1 net T". The results are illustrated with a numerical example. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2004.08.041 Byline: S.K. Manna (a), K.S. Chaudhuri (b) Keywords: Ramp type demand; Time-dependent deterioration; Unit production cost; With shortage; Without shortage Abstract: An order level inventory system for deteriorating items has been developed with demand rate as a ramp type function of time. The finite production rate is proportional to the demand rate and deterioration rate is time proportional. The unit production cost is inversely proportional to the demand rate. The model with no shortage case in inventory is first solved. The inventory shortage is discussed next. Results are illustrated with two numerical examples for two models along with its sensitivity. Author Affiliation: (a) Department of Mathematics, Sovarani Memorial College, Jagatballavpur, Howrah 711 408, WB, India (b) Department of Mathematics, Jadavpur University, Kolkata 700 032, India Article History: Received 25 June 2003; Accepted 16 August 2004

A production-inventory model for a deteriorating item having a linear time-dependent demand and a uniform production rate is presented. The optimal number of production cycles that minimizes the average cost is determined and the sensitivity analysis of the optimal solution is carried out.

An extended EOQ-type inventory model was developed as an extension of the existing models, such as Goh (1994), to account for the deterioration of items in an inventory where the amount of deterioration is dependent on the on-hand-inventory. Results reveal that an optimal solution is produced by the terminal circumstances in the stock-dependent demand-rate model when holding costs are nonlinear.

An inventory policy for items which deteriorate at a constant rate is introduced. The model, which is based on T.L. Urban's 1992 model, relaxes the condition of zero inventory at the end of the inventory cycle. It controls replenishment of the items by assuming an inventory-level-dependent demand pattern followed by a constant demand rate for the items. The sensitivity of its decision variables to modifications in the parameter values is likewise examined.

Byline: K.A. Halim, B.C. Giri, K.S. Chaudhuri The paper deals with lot sizing in an unreliable production system which is subjected to machine breakdown and repair in an uncertain and imprecise mixed environment. The machine failure time is random and is assumed to follow an exponential probability distribution whereas the repair time is imprecise and is characterised by a triangular fuzzy number. Two mathematical models are proposed for the production system – one with crisp demand and fuzzy repair time and the other one with fuzzy demand and repair time. In each model, the expected cost per unit time is derived in the fuzzy sense and defuzzified by using signed distance method. The optimal lot sizing decisions are obtained numerically and a comparison with those of the crisp models is made.

Byline: T. Roy, K.S. Chaudhuri The present article develops an inventory model for a perishable item assuming that the demand rate depends not only on time, but also on selling price of the item. The deterioration rate of the item is taken to be constant and time-value of money is also considered. Shortages in inventory are allowed in all cycles and are completely backlogged. Planning horizon in the inventory problem is considered to be finite. The solution of the model determines the optimal number of replenishments, order quantity and price over finite planning horizon so that time-value of total profit associated with the inventory system is maximised. A heuristic approach is presented to determine the optimal solution of the proposed problem. The solution procedure is illustrated by four numerical examples. Sensitivity analysis of each example is carried out to study the effect of changes in the input parameters. All the results are graphically illustrated.

Byline: K.A. Halim, B.C. Giri, K.S. Chaudhuri Most of the perishable inventory models in the literature assume that the rate of deterioration is a known constant. But in many practical situations, deterioration rate cannot be prescribed in advance; it may vary in a certain interval and hence can preferably be considered as a fuzzy number. The purpose of the paper is to develop and investigate an Economic Order Quantity (EOQ) model in the fuzzy sense by considering stochastic demand, partial backlogging and fuzzy deterioration rate. The proposed model is also extended to the case where the partial backlogging factor is assumed to be a fuzzy number. The minimum total cost and optimal order quantity are derived by defuzzifying the total cost through the signed distance method. Numerical examples are taken to demonstrate the developed models and compare the optimal results with those of the crisp models.

Byline: S.K. Manna, K.S. Chaudhuri, C. Chiang In this paper, we develop two Economic Order Quantity (EOQ) models for quadratic time-varying demand. It is assumed that successive replenishment cycle lengths are in arithmetic progression and I[sup.3] is the rate of reduction of successive cycle lengths. The model with shortages is studied first. The corresponding results for the model without shortages are derived next. Decision variables are determined numerically for given input parameters. Optimum costs for both the models are also calculated. Computational results show that the model with shortages allowed is economically beneficial. Finally, sensitivity analysis is performed to study the effect of changes in input parameters on the optimal cost.

Byline: T. Roy, K.S. Chaudhuri Strategy of pricing is a major one for a manager of any economic sector to obtain its maximum profit. Therefore, in this article, we introduce here an order-level inventory model for a deteriorating item, taking the demand to be dependent on the sale price of the item to determine its optimal selling price and net profit. Also the concept of the special sale campaign for a festive season or for the purpose of clearance sale by way of price reduction is incorporated into the model. It is seen that the economic sector runs on a net loss without price reduction and special sale campaign. This is proved in theory and should be followed in practice. We compare two models of without special sale (Model I) and with special sale (Model II). The model is solved analytically and a numerical simulation of the results is carried out for a given data set. Sensitivity of the model for different values of G to changes in the parameter values is also examined.