Hardik N. Soni

Optimal strategy for an integrated inventory system involving variable production and defective items under retailer partial trade credit policy

This paper investigates an integrated inventory model with variable production rate and price-sensitive demand rate under two-level trade credit. The model considers two-level trade credit policy in which the retailer receives a full trade credit from its supplier, and offers partial trade credit to its customers. It is assumed that an arrival order lot may contain some defective items and the number of defective items is a random variable. This study attempts to offer a best policy for retail price, the replenishment cycle, and the number of shipment from the supplier to the retailer in one production run that aims at maximizing the joint expected total profit per unit time. An algorithm is designed to identify the optimum solution of the proposed model. Numerical examples are included to illustrate the algorithmic procedure and the effect of key parameters is studied to analyze the behavior of the model.

A fuzzy framework for coordinating pricing and inventory policies for deteriorating items under retailer partial trade credit financing

In this paper, we proposed a generalized economic order quantity (EOQ) - based inventory model using a trade credit policy in a fuzzy sense. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer, in turn, partially provides customers a permissible delay period N. This study considers fuzzy EOQ model to allow for: (1) selling price dependent demand rate which is imprecise in nature, (2) a profit maximization objective and (3) an imprecise holding cost, ordering cost, purchasing cost, interest earned and interest charged rate. Besides, the cases N==M are explored thoroughly. The objective function for the retailer in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method. For the defuzzified objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined.

An Eoq Model For Progressive Payment Scheme Under Dcf Approach

An attempt is made to formulate optimal ordering policies for the retailer when the supplier offers progressive credit periods to settle the account. We define progressive credit periods as follows: If the retailer settles the outstanding amount by M, the supplier does not charge any interest. If the retailer pays after M but before N(M Ic1). The objective function to be optimized is considered as present value of all future cash-out-flows. An algorithm is given to find the flow of optimal ordering policy. Analytic proofs are discussed to study the effect of various parameters on an objective function.

Joint pricing and replenishment policies for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint

This study develops an inventory model for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint. The model assumes price sensitive demand when the product has no deterioration and price and time dependent demand when the product has deterioration. Under these considerations, the study attempts to offer best policy for selling price and replenishment cycle for the retailer that aims at maximizing the total profit per unit time. Making use of nearest interval approximation and interval arithmetic, the single objective problem is transformed to multi objective problem. Employing Weighted Sum Method, an analytical approach along with simple algorithm is developed to identify Pareto optimal solution. Finally, the behavior of the model with varied parameters is illustrated in numerical examples.

Ordering policy for stock-dependent demand rate under progressive payment scheme

In this article, a mathematical model is developed to formulate optimal ordering policies for retailer when demand is practically constant and partially dependent on the stock, and the supplier offers progressive credit periods to settle the account. The notion of progressive credit period is as follows: If the retailer settles the outstanding amount by M, the supplier does not charge any interest. If the retailer pays after M but before second period N offered by the supplier, then the supplier charges the retailer on the unpaid balance at the rate Ic 1. If the retailer settles the account after N, then he will have to pay an interest rate Ic 2 on the unpaid balance (Ic 2 > Ic 1). The cost minimization is considered to be an objective function. An algorithm is given to find the flow of optimal ordering policy. A numerical illustration is given to study the effect of various parameters on ordering policy and total cost of an inventory system.

Optimal policies for vendor-buyer inventory system involving defective items with variable lead time and service level constraint

This paper investigates a single-vendor-single-buyer production inventory model involving defective items in both an individual and joint management system with service level constraint. In the system under study, the vendor produces a product in a batch with finite production rate and transfers the lot in equal size to the buyer facing stochastic demand, which is assumed to be normally distributed. The lead time can be reduced by added crashing cost. Moreover, the backorder rate is dependent on the length of lead time through the amount of shortages and the lead time and ordering cost reduction are interacted. A model has been formulated to minimise the joint total expected cost and individual total expected cost by simultaneously optimising order quantity, lead time, and the number of lots delivered from the vendor to the buyer for joint and individual management system respectively. For each model, an effective iterative procedure is developed to identify the optimal solutions. Numerical examples are provided to illustrate the algorithmic procedure and the effects of key parameters are studied for both systems.

Continuous review inventory model for fuzzy price dependent demand

In this paper, a continuous review inventory system has been analysed with an objective to determine an (r, Q) policy which minimises the cost function. The present study considers the demand rate, holding cost and shortage cost are sensitive to imprecise selling price. The proposed model assumes that shortages are allowed and completely backlogged and the lead time is fuzzy in nature. The arithmetical operations of fuzzy total cost are performed under function principle and the managers k-preference integration representation method is applied to defuzzify the fuzzy total cost. Trapezoidal distribution of fuzzy number is used to work out the shortages. Then the model is solved jointly for (r, Q) policy through generalised reduced gradient (GRG) technique. A rigorous numerical study has been carried out and explained as managerial view point.

Optimal policy for fuzzy expected value production inventory model with imprecise production preparation-time

A great deal of research has been done on economic production quantity (EPQ) model, which concern deterministic or stochastic or fuzzy demand and cost situations. In this paper, the EPQ model with imprecise demand and production preparation time is considered which are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Based on an expected value criterion or a credibility criterion, a fuzzy expected value model (EVM) is constructed. The purpose of the fuzzy EVM is to determine the optimal policy such that the fuzzy expected value of the total cost is minimal. In order to obtain the exact expected value directly, instead of relying on simulation procedure, the results for uncertain variables with uncertainty distribution are exploited by treating them as fuzzy variables with credibility distribution. The mathematical analysis is carried out to compute exact expected values. Numerical study is also provided to demonstrate the contribution of our model.

Periodic review inventory model with service level constraint in fuzzy environment

In the current world of high service levels and tight delivery schedules, companies need to adjust their actions to deal with smaller orders that are made more frequently. In this regard, a periodic review inventory system with service level constraint has been analysed in which (R, T) policy jointly minimises the cost function when single product having demand function of selling price which is imprecise in nature. The holding cost which is influenced by selling price comprises two components viz. holding cost for base stock and holding cost for critical stock, i.e., the amount of inventory reserved during stock out for high priority customers’ demand. Critical stock is maintained at high carrying rate as compared to carrying rate of base stock. The characteristic of the lead time is taken as fuzzy. The arithmetical operations of fuzzy total cost are performed under function principle and the manager’s k-preference integration representation method is applied to defuzzify the fuzzy total cost. Trapezoida...

A Periodic Review Inventory Model with Controllable Lead Time and Backorder Rate in Fuzzy-stochastic Environment

Abstract In this paper, an attempt has been made to develop a periodic review inventory model by considering lead-time and the backorder rate as control variables in fuzzy stochastic environment. Without loss of generality, we have assumed that all the observed values of the fuzzy random variable, representing the demand as triangular fuzzy numbers. The variance of fuzzy random demand is taken into consideration to give due attention to every fuzzy observations. The protection interval demand has also been assumed to be fuzzy stochastic. The expected shortages are calculated by using credibility criterion. For the proposed model, we provide a solution procedure incorporating numerical technique viz. Scan and zoom method to determine an optimal policy. A numerical example is taken up to illustrate the solution procedure and sensitivity analysis of the optimal solution with respect to the key parameters of the system is carried out.