Economic Order Quantity Inventory Model Research Articles

Optimal Ordering Strategy of a Replenishment Policy for Deteriorating Items Under Retailer’s Partial Trade Credit Policy

This paper investigates the economic order quantity inventory model for a retailer under two levels of trade credit to reflect the supply chain management situation. It is assumed that the retailer maintains a powerful position and can obtain full trade credit offered by supplier, yet the retailer just offers the partial trade credit to customers. Under these conditions, the retailer can obtain the most benefits. This study also investigates the retailer’s inventory policy for deteriorating items in a supply chain management situation as a cost minimization problem. The present study shows that the annual total variable cost for the retailer is convex, that is, a unique solution exists. Mathematical theorems and algorithms are developed to efficiently determine the optimal inventory policy for the retailer. The results in this paper generalize some already published results. Finally, numerical examples are given to illustrate the theorems and obtain managerial phenomena.

Inventory models for breakable items with stock dependent demand and imprecise constraints

This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units with stock dependent demand under imprecise constraints. The units are damaged due to the accumulated stress of the stocked items kept in stacked form and the damaged function, i.e. rate of breakability per unit time may be linear or non-linear function of current stock level. Here shortages are not allowed. Both the crisp and fuzzy models have been formulated as profit maximization problems with crisp/imprecise space and budget constraints and solved by using a gradient based non-linear programming technique, Generalised Reduced Gradient (GRG) Method. The models are illustrated with a numerical example and some sensitivity analyses have been presented.

Robust optimization in simulation: Taguchi and Response Surface Methodology

Optimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a ‘robust’ methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Response Surface Methodology (RSM). George Box originated RSM, and Douglas Montgomery recently extended RSM to robust optimization of real (non-simulated) systems. We combine Taguchi's view with RSM for simulated systems. We illustrate the resulting methodology through classic Economic Order Quantity (EOQ) inventory models, which demonstrate that robust optimization may require order quantities that differ from the classic EOQ.

Robust Optimization in Simulation: Taguchi and Krige Combined

Optimization of simulated systems is the goal of many methods, but most methods assume known environments. We, however, develop a `robust' methodology that accounts for uncertain environments. Our methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Kriging. We illustrate the resulting methodology through classic Economic Order Quantity (EOQ) inventory models. Our results suggest that robust optimization requires order quantities that differ from the classic EOQ. We also compare our latest results with our previous results that do not use Kriging but Response Surface Methodology (RSM).

Robust Optimization in Simulation: Taguchi and Response Surface Methodology

Optimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a 'robust' methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Response Surface Methodology (RSM). George Box originated RSM, and Douglas Montgomery recently extended RSM to robust optimization of real (non-simulated) systems. We combine Taguchi's view with RSM for simulated systems, and apply the resulting methodology to classic Economic Order Quantity (EOQ) inventory models. Our results demonstrate that in general robust optimization requires order quantities that differ from the classic EOQ.

AN EOQ MODEL WITH LIMITED STORAGE CAPACITY UNDER TRADE CREDITS

In the classical economic order quantity (EOQ) inventory model, it was assumed that the retailer must pay for the received items immediately. However, in practice, the supplier not only allows retailer to settle the account after a certain fixed period but also may offer a cash discount to encourage the retailer to pay for his purchases as soon as possible. On the other hand, it is common practice in most inventory systems to hold excess stocks in a rented warehouse whenever the storage capacity of the owned warehouse is insufficient. Therefore, the purpose of this paper is to establish an EOQ model with limited storage capacity, in which the supplier provides cash discount and permissible delay in payments for the retailer. In the model, we develop some useful theorems to characterize the optimal solution and provide a simple method to find the optimal replenishment cycle time and payment time. Finally, several numerical examples are given to illustrate the theoretical results and some managerial insights are also obtained.

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.

Optimal replenishment policies for EOQ inventory model with limited storage capacity under permissible delay in payments

The main purpose of this paper wants to investigate the effect of trade credit policy with limited storage capacity within the economic order quantity (EOQ) framework. Goyal is frequently cited when the inventory systems under conditions of permissible delay in payments are discussed. But Goyal assumed that the retailer’s storage capacity is unlimited. This assumption is debatable. So, we want to extend Goyal’s model to the case that the retailer’s storage capacity is limited. Then, two theorems present solution procedures to locate the optimal cycle times of the annual total relevant cost function. In essence, the inventory model discussed in this paper generalizes that of Goyal. Finally, numerical examples are given to illustrate all theorems obtained in this paper.

The Replenishment Decision for EOQ Inventory Model under Permissible Delay in Payments

This paper discusses the economic order quantity (EOQ) under conditions of permissible delay in payments. In 1985, Goyal assumed that: (1) The unit selling price and the unit purchasing price are equal. (2) At the end of the credit period, the account is settled. The retailer starts paying for higher interest charges on the items in stock and returns money of the remaining balance immediately when the items are sold. The main purpose of this paper is to modify Goyal’s model to presume that the unit selling price and the unit purchasing price are not necessarily equal to reflect the real-life situations. Furthermore, this paper will propose that at the end of the credit period, the retailer will borrow 100% purchasing cost from the bank to pay off the account. Comparing with Goyal’s model, it is also shown that the optimal cycle times in this paper are not longer than those of Goyal’s model. Three theorems are developed to determine the optimal cycle time and the optimal order quantity. Numerical examples are given to illustrate these theorems.

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.

The resource constrained single-item inventory problem with demand-dependent unit cost

In this paper, we present an economic order quantity (EOQ) with both demand-dependent unit cost and restrictions. An analytical solution of the EQO is derived using a recent and simple method, which isthe geometric programming approach. The EOQ inventory model with demand-dependent unit cost without any restriction and the classical EOQ inventory model are obtained.

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.

Time-limited free back-orders EOQ model

This paper presents the classical economic order quantity (EOQ) inventory model under the effect of time-limited free back-orders. That is, during a stockout period, customers will be willing to wait for a limited time until their orders are filled at no extra charge. However, if the delay time is too long, a fraction of the customers will be lost, while the orders of the rest will be back-ordered and will incur a time-weighted penalty cost. Keeping this in mind, our objective is to find the optimal ordering quantity and back-ordering level such that the total average cost per unit time is minimized.

An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting

An economic order quantity (EOQ) inventory model for deteriorating goods is developed with a linear, positive trend in demand allowing inventory shortages and backlogging. The effects of inflation and the time-value of money are incorporated into the model, considering two separate inflation rates: namely, the internal (company) inflation rate and the external (general economy) inflation rate. It is assumed that the goods in the inventory deteriorate over time at a constant rate θ. The inventory policy is discussed over a finite time-horizon with several reorder points. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. Several particular cases of the model are discussed in brief.

System to Maximize Inventory Performance in a Small Hospital

A computerized system to maximize inventory performance in a small hospital is described. An inventory control system, which integrates economic order quantity (EOQ) and ABC inventory models was implemented in a 146-bed hospital. The perpetual inventory control data base, supported by the hospital's mainframe computer, generates monthly inventory statistics that are segregated into A, B, and C reports. Using a hand-held computer that interfaces with the perpetual inventory system, a series of inventory management reports were developed. These reports, which are based on the EOQ model, provide the following information for each drug line item: EOQ, EOQ proposed carrying cost, actual inventory carrying costs, safety stock, order point, average inventory, and the "on hand/on order" point. Several supplemental inventory management reports were also developed. While implementing the computerized inventory system, the pharmacy also changed its purchasing strategy from predominantly direct accounts to a progressive prime-vendor wholesaler. From December 1980 to December 1981, the ABC/EOQ system with progressive prime-vendor involvement essentially doubled total aggregate inventory turnover. A 46.5% reduction in standing inventory levels occurred. The drug cost per line item dispersed remained relatively constant over the one-year period, despite price increases. The application of the computerized ABC/EOQ inventory model to an online perpetual inventory control data base effectively reduced the inventory operation costs.

The Effects of Non‐Constant Purchase and Replenishment Costs on the EOQ Model

This paper examines the sensitivity of the Economic Order Quantity (EOQ) inventory model to lot size errors when the purchase cost per unit, C, and the replenishment cost per order, A, are both dependent on the amount ordered, Q. A formula for the percentage increase in average annual variable costs due to using a Q‐value different from Q is derived, and is shown to be the same as that for the simple EOQ and backorders model.

Credit Policy and Inventory Control

Credit policies are shown to be important in the basic economic order quantity inventory model. An economic order quantity model is derived which explicitly considers possible credit periods allowed by suppliers. This model is shown to be very sensitive to the length of the credit period, and to the relationship between the credit period and inventory level. It is also shown to be more sensitive to estimates of demand for inventory items and less sensitive to order costs than the basic economic order quantity model. A practical example illustrates this sensitivity, shows how inventory costs may be considerably reduced by taking the existence of a credit period into account, and demonstrates the implications for inventory and credit policies.

Order Quantity, Product Popularity, and The Location of Stock in a Warehouse

Abstract In the assignment of warehouse space to inventory items, the amount of space allocated to each item is traditionally determined on the basis of inventory or production cost considerations. Actual assignment of items to storage locations within the warehouse is then carried out independently, with the space requirements taken as given. Assuming an out-and-back order picking procedure and the simple economic order quantity inventory model, it is demonstrated that the quantity and location problems must be considered simultaneously in order to achieve a minimum total cost (order picking cost plus inventory cost). An iterative solution procedure, based on a gradient search, is developed and applied to a test problem.