Relevant Inventory Cost Research Articles

Optimal ordering policy in an economic order quantity (EOQ) model for non-instantaneous deteriorating items with defective quality and permissible delay in payments

Economic order quantity (EOQ) model has been used extensively over a century. Many studies have altered and modified the model in order to imitate the actual inventory problem. This article is concerned with the finding of the optimal replenishment cycle time for the inventory issues where items received are partly with imperfect quality and involve deterioration after the inspection time. Also, for financial safety, for the supplier, when the permissible delay in payments can promote their sales and reduce their on-hand stock level. For the retailer, he/she can sell the items and accumulate revenue and earn interest within the trade-credit period. At the end of the period, it is usually assumed that the retailer pays off all units bought, and starts to pay the capital opportunity cost for the items in stock. Different scenarios based on the combination of the inspection time, the certain period of time in which the item has no deterioration and the trade-credit period have been considered here. In order to minimize the total relevant inventory cost, mathematical theorems have been developed to determine the existence and the uniqueness of the optimal solution. Numerical calculations and illustrations demonstrate the application and the performance of the proposed theories.

Trade Credit Policy Between Supplier–Manufacturer–Retailer for Ameliorating/Deteriorating Items

This paper is related to the advancement of the inventory models for ameliorating items and focused on the real-life business situation as with the time the deterioration rate of ameliorating items is increased. In the global world, every supply chain entities as suppliers/manufacturers/retailers want to increase the consumption of their goods without any losses. For this, he/she tries to lure manufacturer/retailers by offering some discounts, i.e. credit period for settling the account. The problem states that the manufacturer purchases the ameliorating items from the supplier, where the supplier offers his/her credit period to settle the account. The manufacturer purchases ameliorating items (like pigs, fishes, ducklings, etc.) and take those items as raw material; when the livestock matures the manufacturer sells it to the retailer and offer credit time for settling the account. Reason to propose the model is when the quantities of livestock become larger, then the manufacturer faces difficulty in maintaining all the livestock. In such a situation, the traditional method (without offering credit period) fails to provide the maximum profit to the manufacturer. Therefore, in order to get maximum profit, the manufacturer needs some more realistic scientific outlook for making decisions. The proposed model provides a more realistic assumption of business markets, by offering credit policy. In the introduced model, manufacturer faces amelioration and deterioration rate simultaneously due to the growth and the death of livestock. The amelioration and deterioration rates are assumed as the Weibull distribution type. Shortages allowed only for the retailer, which is partially backlogged. The main goal of this paper is to minimize the total relevant inventory cost for both the manufacturer and the retailers, by finding the optimal replenishment policy. The mathematical formulation with optimal solutions for manufacturer and retailers are given. Convexity and existence of the proposed model via numerical examples and graphical representations are explained. Finally, the conclusions with some future research direction are discussed.

EOQ Model with Stock-Level Dependent Demand and Different Holding Cost Functions

This paper presents EOQ (Economic Order Quantity) model with stock- level dependent demand and different types of holding cost function. We show that the total relevant inventory cost per unit time is convex with respect to cycle time. Mathematical models are established to determine optimal order quantity and total relevant inventory cost. Numerical examples are provided for two different models i.e. (i): Instantaneous replenishment with inventory dependent holding cost and (ii) Instantaneous replenishment with quadratic time dependent carrying cost. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. The second order approximation is used for finding closed form optimal solution. Mathematica 5.2 software is used to find numerical results.

An Optimal Ordering Policy for Non-instantaneous Deteriorating Items with Conditionally Permissible Delay in Payment under Two Storage Management

In the present market scenario, trade credit financing has drawn much attention of various researchers. To increase sales, supplier/wholesalers offers some interest free period to their retailers. According to such consideration, in this paper a two warehouse inventory model for non-instantaneous deteriorating items with combination of different deterioration rate is developed. Shortages are not permissible. This paper mainly deals with non-instantaneous deteriorating items and trade credit financing with objective to derive the optimal replenishment policy that minimizes the average relevant inventory cost of the retailer. This model deals with single item only. Numerical examples are presented to validate the model. Sensitivity analysis has been performed by changing value of a parameter at a time and keeping value of rest parameters unchanged to study the effect on the inventory model.

Two Warehouse Inventory Model with Ramp Type Demand and Partial Backordering for Weibull Distribution Deterioration

In the recent years, the effect of deterioration of physical goods has drawn much attention of various researchers. The more the deteriorationis, the more order quantity would be. According to such consideration, taking the deterioration rate into account is necessary. Thus in this paper, we develop the two ware-house inventory model with partial backlogging and two parameter weibull distribution deterioration. In the present market scenario the demand of certain items does not remain constant with time and may increase/decrease for a fixed time interval. The objective of this paper is to derive the optimal replenishment policy considering varying demand rate and deterioration that minimize the present worth of total relevant inventory cost per unit of time. In addition to this single ware-house system is also developed and the results have been compared with the help of numerical example.

AN INVENTORY MODEL FOR NON-INSTANTANEOUS DETERIORATING ITEMS WITH QUADRATIC DEMAND RATE AND SHORTAGES UNDER TRADE CREDIT POLICY

In this paper, we propose an appropriate inventory model for noninstantaneous deteriorating items over quadratic demand rate with permissible delay in payments and time dependent deterioration rate. In this model, the completely backlogged shortages are allowed. In several existing results, the authors discussed that the deterioration rate is constant in each cycle. However, the deterioration rate of items are not constant in real world applications. Motivated by this fact, we consider that the items are deteriorated with respect to time. To minimize the total relevant inventory cost, we prove some useful theorems to illustrate the optimal solutions by finding an optimal cycle time with the necessary and enough conditions for the existence and uniqueness of the optimal solutions. Finally, we discuss the numerical instance and sensitivity of the proposed model.

A Novel Continuous KNN Prediction Algorithm to Improve Manufacturing Policies in a VMI Supply Chain

This paper examines and compares various manufacturing policies which manufacturer may adopt so as to improve the performance of a vendor managed inventory (VMI) partnership. The goal is to maximize the combined cumulative profit of supply chain while minimizing relevant inventory management costs. The supply chain is a two-level system with a single manufacturer and single retailer at each level, in which the manufacturer takes the responsibility of overall inventories of supply chain. A base system dynamics (SD) simulation model is first employed to describe the dynamic interactions between the variables and parameters of manufacturer and retailer under VMI. Then, the mentioned policies are constructed using the base SD model that lead us to differentiate the behavior supply chain for each policies within a same duration of time. In this paper, we use continuous K-nearest neighbor (CKNN) as one of the instance-based learning methodologies to predict the best manufacturing rates. This algorithm effectively increases the combined profit of supply chain in comparison with other two policies. Accordingly, a numerical example along with a number of sensitivity analyses is conducted to evaluate the performance of mentioned policies.

A two-warehouse inventory model for deteriorating items with linear demand under conditionally permissible delay in payment

An inventory model for deteriorating items having two separate warehouses, one being the firm’s own warehouse (OW) of finite dimension and the other being a rented warehouse (RW) for storing units in excess of the fixed capacity of the OW in practice. The RW is assumed to offer better preserving facilities than the OW, resulting in a lower rate of deterioration, and it is assumed that higher holding costs will be charged for the RW than for the OW. In this study, a two-warehouse inventory model for deteriorating items is considered with a linear demand rate under conditionally permissible delay in payment. The purpose of this study is to find the optimal replenishment policies for minimizing the total relevant inventory costs. The results are illustrated with the help of a numerical example. A sensitivity analysis of the optimal solutions to changes in the values of the major parameters associated with the model is discussed.

A vendor managed inventory model under contractual storage agreement

Vendor managed inventory (VMI) is a supply chain partnership strategy that allows a supplier to place orders on behalf of its customers. This paper considers a supply chain composed of a single vendor and multiple retailers operating under a VMI contract that specifies limits on retailers' stock levels. We address the problem of synchronizing the vendor's cycle time with the buyers' unequal ordering cycles by developing a mixed integer non-linear program that minimizes the joint relevant inventory costs under storage restrictions. We also propose a cost efficient heuristic to solve the developed optimization problem. We conducted computational experiments to assess the reduction in the total supply chain costs resulting from relaxing the restriction of equal ordering cycles. It is found that the heuristic generates greater cost savings in cases of increased variability in retailers' demand and cost parameters.

Utilizing a Simulation Exercise to Illustrate Critical Inventory Management Concepts

ABSTRACTMost undergraduate business students simply do not appreciate the elegant mathematical beauty of inventory models. So how does an instructor capture students’ interest and keep them engaged in the learning process when teaching inventory management concepts? This paper describes a competitive and energizing in‐class simulation game that introduces students to basic inventory management concepts. This hands‐on, active‐learning exercise presents students with a simulated single‐product inventory environment that requires them to make ordering decisions in an attempt to minimize the total relevant inventory costs in the face of variable demand.

An Inventory Replenishment Model under Purchase Dependency in Retail Sale

multi-item inventory with very large number of items in retail sale stores, purchase dependency in demand amongst the items can be described by association rules mined from sale transaction data. With the knowledge of association rules, inventory replenishment policy can be designed which will result in low inventory cost and better profitability. The relevant inventory costs include the cost of lost sale along with other conventional inventory costs. Various inventory replenishment policies can be simulated on synthetic data for a particular purchase pattern. Using sequence of random numbers, future demand data can be generated to depict purchase dependency in demand given by an association rule observed in the past sale transaction data. To learn the cost effectiveness of different inventory replenishment policies, simulation is conducted on the generated future demand data. Based on cost-benefit analysis of all the applicable inventory replenishment policies, the best one can be selected for implementation.

A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment

For the capacity of any warehouse is limited, it has to rent warehouse (RW) for storing the excess units over the fixed capacity W of the own warehouse (OW) in practice. The RW is assumed to offer better preserving facilities than the OW resulting in a lower rate of deterioration and is assumed to charge higher holding cost than the OW. In this paper, a two-warehouse inventory model for deteriorating items is considered with constant demand under conditionally permissible delay in payment. The purpose of this study is to find the optimal replenishment policies for minimizing the total relevant inventory costs. Useful theorems to characterize the optimal solutions have been derived. Furthermore, numerical examples are provided to illustrate the proposed model, sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.

A Fuzzy Inventory System with Deteriorating Items under Supplier Credits Linked to Ordering Quantity

The inventory problem associated with trade credit is a popular topic in which interest income and interest payments are important issues. Most studies related to trade credit assume that the interest rate is both fixed and predetermined. However, in the real market, many factors such as financial policy, monetary policy and inflation, may affect the interest rate. Moreover, within the environment of merchandise storage, some distinctive factors arise which ultimately affect the quality of products such as temperature, humidity, and storage equipment. Thus, the rate of interest charges, the rate of interest earned, and the deterioration rate in a real inventory problem may be fuzzy. In this paper, we deal with these three imprecise parameters in inventory modeling by utilizing the fuzzy set theory. We develop the fuzzy inventory model based on Chang et al.'s [1] model by fuzzifying the rate of interest charges, the rate of interest earned, and the deterioration rate into the triangular fuzzy number. Subsequently, we discuss how to determine the optimal ordering policy so that the total relevant inventory cost, in the fuzzy sense, is minimal. Furthermore, we show that Chang et al.'s [1] model (the crisp model) is a special case of our model (the fuzzy model). Finally, numerical examples are provided to illustrate these results.

Optimal Inventory Control Policy for Items with Time-Dependent Demand

SYNOPTIC ABSTRACTIn today's time based competition, the demand for a product may grow or decline with time. In this paper, we assume that the demand depends on time. Shortages are allowed. The unsatisfied demand is partially backlogged with a time-proportional backlogging rate. We formulate an inventory model over a finite planning horizon, to minimize the total cost for non instantaneous deteriorating items. Further the necessary and sufficient conditions for the existence and uniqueness of the optimal solutions are derived. Numerical examples are presented to demonstrate the developed model. The impact of various parameters of the system on the optimal solution is analyzed by carrying out sensitivity analysis and their effects are discussed in detail. According to the results of sensitivity analysis, we provide several ways for the retailer to effectively reduce the total annual relevant inventory cost.

RETAILER'S ORDERING POLICY FOR NON-INSTANTANEOUS DETERIORATING ITEMS WITH QUANTITY DISCOUNT, STOCK-DEPENDENT DEMAND AND STOCHASTIC BACKORDER RATE

ABSTRACT This article deals with an inventory problem for non-instantaneous deteriorating items with stock-dependent demand when supplier offers an all-unit quantity discount. In the model, shortages are allowed and the backorder rate is a random variable. The purpose of this study is to determine an optimal ordering policy for minimizing the expected total relevant inventory cost for the retailer. We have developed some useful theorems to characterize the optimal solution and provide an easy and useful algorithm to find the optimal order quantity and replenishment time. Furthermore, several numerical examples are given to illustrate the solution procedure for the mathematical model developed. Finally, we also implement sensitivity analysis of the optimal solution with respect to major parameters.

Integrated inventory and transportation mode selection: A service parts logistics system

We present an optimization-based model to gain insights into the integrated inventory and transportation problem for a single-echelon, multi-facility service parts logistics system with time-based service level constraints. As an optimization goal we minimize the relevant inventory and transportation costs while ensuring that service constraints are met. The model builds on stochastic base-stock inventory model and integrates it with transportation options and service responsiveness that can be achieved using alternate modes (namely slow, medium and fast). The results obtained through different networks show that significant benefits can be obtained from transportation mode and inventory integration.

A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments

In this study, an appropriate inventory model for non-instantaneous deteriorating items with permissible delay in payments is considered. The purpose of this study is to find an optimal replenishment policy for minimizing the total relevant inventory cost. This mathematical model is a general framework that comprises numerous previous models such as in Ghare and Schrader [Ghare, P. M., & Schrader, G. H. (1963). A model for exponentially decaying inventory system. International Journal of Production Research, 21, 449-460], Goyal [Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 36, 335-338], and Teng [Teng, J. T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 53, 915-918] as special cases. We have developed some useful theorems to characterize the optimal solutions and provide an easy-to-use method to find the optimal replenishment cycle time and order quantity under various circumstances. Several numerical examples are given to test and verify the theoretical results. Finally, a sensitivity analysis of the optimal solution with respect to major parameters is also included. According to the results of numerical analysis, we provided several ways for the retailer to effectively reduce total annual relevant inventory cost.

Supplier management for manufacturer ? a case study of flexible PCB

The purpose of this study is to provide a guideline for manufacturer with multiple products on supplier’s selection. The proposed approach has been constructed based on the total cost, given that each supplier possesses different unit prices, purchasing lead time, and variability. A case study of a Taiwanese company manufacturing flexible printed circuit boards (PCBs) is used to illustrate the proposed model, from which the following can be concluded: supplier selection does affect expected raw material cost, expected relevant inventory cost, setup cost, expected capacity cost, transportation cost, and eventually the total cost. Instead of unit price, total cost should be the criterion for supplier selection. In addition, there exists a relationship of trade-off between expected capacity cost and transportation cost.

(Q, R) inventory control involving a variable backorder rate

This study considers a (Q, R) continuous review inventory model with a partial backorder rate, and analyzes the effects of backorder rate as a control variable on the inventory system. Through running the optimal backorder policy, we can have the relevant inventory cost minimized to increase the competitive edge in business. We discuss two models that are complete and partial information about the lead time demand distribution, that is, we first assume that the lead time demand follows a normal distribution, and then remove this assumption and only assume that the first and second moments of the probability distribution of lead time demand are known. For each case, we develop a procedure to find the optimal ordering policy.

Simple Models and Insights for Warehouse Sizing

This study is concerned with minimizing the total discounted cost of operating an inventory system and providing the warehouse space necessary to accommodate the replenishment lots, under the assumption of constant product demand. The use of an approximation objective function for the single-item case allows the optimal warehouse size as well as the ratio of relevant investment costs to relevant inventory costs to be written in closed-form. Based upon the value of this ratio, circumstances are identified under which an integrated approach is justified, and others under which the inventory policy and storage capacity can be determined sequentially. The multi-item version of the problem under study is solved by the Lagrangian multiplier method, given that no coordination takes place between the items. Finding the optimal Lagrange multiplier can be accomplished efficiently by the Newton–Raphson method.