Deterministic Economic Order Quantity Research Articles

Innovation of Economic Order Quantity (EOQ) Model for Deteriorating Items with Time-Linked Quadratic Demand Under Non-decreasing Shortages

Demand for several variety of commodity depends on its nature like; price, corrosion and time. In most inventory models demand is considered constant or time-dependent. In this study, we set up a deterministic EOQ for weakening stuffs when demand is quadratic time linked. Shortages are permitted and totally backlogged. Mathematical representation is derived and then some constructive outcomes is framed to demonstrate most favorable answers. Numerical illustrations are incorporated to demonstrate the optimal clarification. Sensitivity analysis with effects of system constraints is provided to scrutinize the nature of representation. Mathematica 7.1 software is employed to get arithmetical results.

Deterministic EOQ models for non linear time induced demand and different holding cost functions

This paper presents an Economic order quantity (EOQ) model for deteriorating items. The demand rate is non-linear function of time. In this paper two models have been derived for different holding costs (i) The holding cost is linear function of the on hand inventory level. (ii). A non-linear function of time for which the item is kept in the stock. Optimization is done for both the models and numerical examples are presented to check the feasibility of the optimal solutions. Sensitivity analysis is also presented with respect to the various parameters used in the numerical example.

Multi-item EOQ model while demand is sales price and price break sensitive

In this paper, the authors study a multi-item deterministic EOQ (economic order quantity) model for a vendor when the demand rate of the essential commodities decreases quadratically with increasing sales price and increase exponentially with increasing level of price breaks. A price discount is offered to the customers when the revenue of the vendor crosses the level of price break. The main aim of the present article is to find out the optimal order quantities, optimal selling prices and optimal level of price break in order to maximize the average profit of the whole products. Numerical examples are also illustrated to test of our proposed model.

A finite horizon deteriorating inventory model with two-phase pricing and time-varying demand and cost under trade credit financing using particle swarm optimization

In this paper, we consider a deterministic economic order quantity model with generalized type demand, deterioration and unit purchase cost functions under two levels of trade credit policy. Our objective is to find the optimal values of selling prices, replenishment number and replenishment scheme which maximize the total profit over the finite planning horizon. We establish the inventory system and provide structural properties of the optimal solution that facilitate computation. A particle swarm optimization with constriction factor is coded and used to solve the mixed-integer nonlinear programming problem by employing the properties derived from this paper. At the end, some numerical examples are used to illustrate the features of the proposed model.

Optimal payment time for a retailer under permitted delay of payment by the wholesaler with dynamic demand and hybrid number cost parameters

In many inventory situations, purchasers are allowed an interest-free credit period to pay for the goods bought. Depending on the length of that period, the purchaser can earn interest on the sales of the inventory. In this paper, a deterministic economic order quantity (EOQ) inventory model is developed with time dependent demand under permissible delay in payment. The cost parameters are taken as hybrid numbers (parameters are fuzzy number as well as random variables). This study shows that the optimal values of order quantity and number of cycles for this inventory model. Numerical example is presented to illustrate the model and sensitivity analysis has been done with the variation of demand parameters on optimal cost.

On Optimal Inventory Model for Obsolescence Perishable Products under Unpermitted-Stockout

With the advancement of science and technology and the fast change of buyer requirements, the short-life products have been shortened at large, some formerly long-life products gradually turn to value deterioration products. The ratio of value deterioration products to modern products is getting higher and higher. This paper develops a deterministic economic order quantity EOQ inventory model, where the demand rate depends on the on-hand inventory when inventory level exceeds certain quantity , otherwise the demand rate is constant. The effects of obsolescence are taken into account, for it is related to the demand rate. The results are discussed through two numerical examples. A sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.

On the Accuracy of Fluid Approximations to a Class of Inventory-Level-Dependent EOQ and EPQ Models

Deterministic Economic Order Quantity (EOQ) models have been studied intensively in the literature, where the demand process is described by an ordinary differential equation, and the objective is to obtain an EOQ, which minimizes the total cost per unit time. The total cost per unit time consists of a “discrete” part, the setup cost, which is incurred at the time of ordering, and a “continuous” part, the holding cost, which is continuously accumulated over time. Quite formally, such deterministic EOQ models can be viewed as fluid approximations to the corresponding stochastic EOQ models, where the demand process is taken as a stochastic jump process. Suppose now an EOQ is obtained from a deterministic model. The question is how well does this quantity work in the corresponding stochastic model. In the present paper we justify a translation of EOQs obtained from deterministic models, under which the resulting order quantities are asymptotically optimal for the stochastic models, by showing that the difference between the performance measures and the optimal values converges to zero with respect to a scaling parameter. Moreover, we provide an estimate for the rate of convergence. The same issue regarding specific Economic Production Quantity (EPQ) models is studied, too.

Price-sensitive demand for perishable items – an EOQ model

This paper develops a finite time-horizon deterministic EOQ ( Economic Order Quantity) model where the rate of demand decreases quadratically with selling price. Prices at different periods are considered as decision variables. The objective is to find the optimal ordering quantity and optimal sales prices that maximizes the vendor’s total profit. The results are discussed with numerical examples. Sensitivity analysis of the optimal solution with respect to the key parameters of the system is carried out.

A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and trade credit financing

Pricing is a major strategy for a retailer to obtain its maximum profit. Furthermore, under most market behaviors, one can easily find that a vendor provides a credit period (for example 30 days) for buyers to stimulate the demand, boost market share or decrease inventories of certain items. Therefore, in this paper, we establish a deterministic economic order quantity model for a retailer to determine its optimal selling price, replenishment number and replenishment schedule with fluctuating demand under two levels of trade credit policy. A particle swarm optimization is coded and used to solve the mixed-integer nonlinear programming problem by employing the properties derived in this paper. Some numerical examples are used to illustrate the features of the proposed model.

Price discounts for increased profitability under partial backordering

If some, but not all, customers are willing to wait for an out-of-stock product to become available, sellers may be able to increase their profits by offering a price discount to increase the number of backordered demands rather than losing those sales. We modify an existing model for the deterministic economic order quantity with partial backordering by making the backordering percentage a function of the size of the discount. We combine results about the optimal solution for a partial backordering model with a fixed backorder percentage and a search procedure to determine whether offering a discount is optimal and, if so, how large the discount should be to maximize profit.

A general model for EOQ inventory systems with partial backlogging and linear shortage costs

We present a mathematical model which generalises several known deterministic Economic Order Quantity (EOQ) inventory systems with partial backlogging. This inventory model considers purchasing cost, holding cost, shortage costs and replenishment cost. Shortage costs (backorder cost and lost sales cost) are both made up of a fixed cost and a variable cost which depends on the length of the waiting time for the next replenishment. The optimal policy is characterised through a sequential optimisation procedure. To illustrate the model, numerical examples and sensitivity results are given.

Contracting Under Vendor Managed Inventory Systems Using Holding Cost Subsidies

Vendor managed inventory systems are becoming increasingly popular. An important issue in implementing a vendor managed inventory scheme is the contracting terms that dictate the ownership of the inventory and the responsibility of inventory replenishment decisions. Thus the performance of a vendor managed system crucially depends on these terms and on how inventory‐related costs are shared in a supply chain. We consider a system where a manufacturer supplies a single product to a retailer who faces random demand in a competitive market. The retailer incurs a fixed cost per order, inventory holding cost, and a penalty cost for a stockout (unsatisfied demand is back‐ordered). Further, the manufacturer incurs a penalty cost when there is a stockout at the retailer and a fixed replenishment cost. We assume that the players are rational and act noncooperatively. We compare the performance of retailer managed inventory systems, where the retailer places orders and makes replenishment decisions, with vendor managed inventory systems, wherein the vendor or manufacturer makes inventory and replenishment decisions. Specifically, in the vendor managed inventory system, we propose and evaluate holding cost subsidy‐type contracts on inventories offered by the retailer to improve system performance. We evaluate this contract in the context of three widely used inventory systems—deterministic economic order quantity, continuous review ( Q, r) policies, and periodic review policies—and show when such contracts may improve channel performance.

An EOQ model for deteriorating items with price- and stock-dependent selling rates under inflation and time value of money

This study applies the discounted cash flow (DCF) approach for the analysis of a replenishment problem over a finite planning horizon. Thus, a deterministic economic order quantity (EOQ) inventory model taking into account inflation and time value of money is developed for deteriorating items with price- and stock-dependent selling rates. An efficient solution procedure is presented to determine the optimal number of replenishment, the cycle time and selling price. Then the optimal order quantity and the total present value of profits are obtained. Numerical examples are presented to illustrate the proposed model and particular cases of the model are also discussed.

An EOQ model for a deteriorating item with non-linear demand under inflation and a trade credit policy

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 "?/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.

Deterministic economic order quantity models with partial backlogging when demand and cost are fluctuating with time

In today's time-based competition, the unit cost of a high-tech product declines significantly over its short life cycle while its demand increases. In this paper, we extend the classical economic order quantity model to allow for not only time-varying demand but also fluctuating unit cost. In addition, we also allow for shortages and partial backlogging. We then prove that the optimal replenishment schedule not only exists but also is unique. In addition, we also show that the total cost is a convex function of the number of replenishments, which simplifies the search for the optimal number of replenishments to find a local minimum. Moreover, we further simplify the search process by providing an intuitively good starting search point.

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

This paper develops a finite time-horizon deterministic economic order quantity (EOQ) inventory model for deteriorating items. The items deteriorating at a constant rate and the demand at any instant depends on the on-hand inventory (stock-level) at that instant, shortages are allowed and completely backordered and the effects of inflation and time-value of money are taken into consideration. The proposed model facilitates managers in determining the optimal number of replenishments and optimal reorder time point. The results are discussed with two numerical examples and a sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.

An EOQ model with stock-dependent demand, shortage, inflation and time discounting

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.

Economic Inventory/Transport Lot, Sizing with Quantity and Freight Rate Discounts

ABSTRACTDiscounts are a primary marketing mechanism for inducing customers to increase the size of their purchases. Quantity discounts from suppliers and freight discounts from shippers are commonly encountered by organizations. This paper structures quantity and freight discounts into the order size decision in a deterministic economic order quantity system. Optimum lot‐sizing algorithms are derived for the dual discount situations of all‐units or incremental quantity discounts and all‐weight or incremental freight discounts.

All‐Units Discounts for Standard Container Sizes

ABSTRACTSome vendors offer their products to a purchaser in various container sizes. Normally, vendors will offer larger all‐units discounts on larger container sizes. Two algorithms have been developed in this paper to solve for the optimal number of each container size and the order quantity for the deterministic economic order quantity (EOQ) situation. The first algorithm, based in part on the dynamic programming solution to knapsack problems, solves the general case. The second algorithm, based in part on the dominance relations inherent in the pricing schedule, solves the more restricted case in which the purchaser is forced to accept the discount in the following manner. An order must be filled with containers of successively smaller sizes, beginning with the largest size. The purchaser is forced to accept the largest discount first, then the next largest, and so on.

A PRESENT VALUE FORMULATION OF THE CLASSICAL EOQ PROBLEM*

ABSTRACTThe usual analysis of the deterministic economic order quantity problem seeks to minimize the average cost of inventory ordering and holding costs per unit time. An alternative approach described in this paper examines the present value of discounted costs over an infinite horizon. Differences in the solutions and implications of errors using the two methodologies are discussed.