Deterministic Inventory Model Research Articles

Deterministic inventory model for deteriorating items with trade credit financing and capacity constraints

This work presents an inventory model for optimizing the replenishment cycle time for a single deteriorating item under a permissible delay in payments and constraints on warehouse capacity (owned warehouse capacity, with excess inventory stored in rental warehouses). Rented warehouses are assumed to charge higher unit holding costs than owned warehouses. Furthermore, item deterioration rates are assumed to differ between warehouses. This study has two main purposes: First, the mathematical models of the inventory system are established under the above conditions. Second, this study demonstrates that the optimal solution not only exists but is unique, and two theorems are devised for determining the optimal replenishment cycle time. Finally, numerical examples are presented to illustrate the resulting theorems.

INTEGRATED DYNAMIC PRICING FOR SEASONAL PRODUCTS WITH PRICE AND TIME DEPENDENT DEMAND

In this paper, an inventory model for deteriorating items with ramp-type time and price dependent consumption rate over a finite planning horizon is considered. In contrast to the traditional deterministic inventory model with static price over the entire planning horizon or fixed number of price changes over the finite time horizon, an alternative model is derived in which prices and the number of price change are to be decision variables. We show that the total profit function is concave. With the concavity, a solution procedure is presented to determine optimal prices, optimal number of pricing cycles and optimal lot size and optimal profit. We illustrate the model with numerical examples. Sensitivity analysis of the model is also carried out.

Optimal replenishment policy for perishable items with stock-dependent selling rate and capacity constraint

In this paper, a deterministic inventory model is developed for deteriorating items with stock-dependent demand and finite shelf/display space. Furthermore, we allow for shortages and the unsatisfied demand is partially backlogged at the exponential rate with respect to the waiting time. We provide solution procedures for finding the maximum total profit per unit time. In a specific circumstance, the model will reduce to the case with no shortage. Further, we use numerical examples to illustrate the model.

Inventory and pricing strategies for deteriorating items with limited capacity and time-proportional backlogging rate

In the present study, a two-warehouse deterministic inventory model for deteriorating items with price-sensitive demand is developed. A rented warehouse (RW) is used to store the excess units over the fixed capacity of the own warehouse (OW). In addition, shortages are allowed in the OW and it is assumed that the backlogging demand rate is dependent on the duration of the stock-out. The objective is to find the optimal inventory and pricing strategies maximising the total average profit over the infinite planning horizon. For any given selling price, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total average profit is a concave function of price when the replenishment schedule is given. The optimal selling price and replenishment schedule is also calculated for the proposed model. Finally, the results have been validated with the help of a numerical example.

Optimal procurement and pricing policies for inventory models with price and time dependent seasonal demand

In day to day life, one observes that many commodities have a seasonal demand pattern, where demand rate depends upon both price and time. A common observation is that in the event of shortage, the proportion of customers who will wait to purchase the item decreases as the waiting time increases. In this paper, we consider a deterministic inventory model that incorporates these aspects when the product under consideration has general price and time dependent seasonal demand rate. Inventory once ordered can be used for more than one season. Order for replenishment is placed at the end of the season in which inventory depletes completely. The period of shortage cannot exceed one season. Backlog of shortages is time dependent. Conditions for optimality of the net profit function for pricing and procurement decisions are discussed. The solution procedure, numerical examples and sensitivity analysis are presented.

On reserve money for an EOQ model in an inflationary environment under supplier credits

We propose to derive a deterministic inventory model for a stock with time-varying deterioration rate with a linear trend in demand over a finite planning horizon in this study. We assume that the supplier offers a credit limit to the retailer during which there is no interest charged. However, the retailer has the reserve capital with him to make the payments at the beginning of the transaction, but he decides to take the benefit of the credit limit. Each cycle has shortages, which have been partially backlogged to suit present day competition in the market. Also, the whole study has been done in an inflationary environment using the Discounted Cash Flow (DCF) approach to impart economic feasibility to the model. Numerical examples have been presented to explain the theory, while sensitivity of the optimal solution of the system has been studied with respect to various system parameters.

Optimal lot size for an item with partial backlogging rate when demand is stimulated by inventory above a certain stock level

In this paper, a deterministic inventory model with time-dependent backlogging rate is developed. The demand rate is a power function of the on-hand inventory down to a certain stock level, at which the demand rate becomes a constant. We prove that the optimal replenishment policy not only exists but also is unique. Furthermore, we provide simple solution procedures for finding the maximum total profit per unit time. Numerical examples have also been given to illustrate the model and we conclude the paper with suggestions for possible future research.

The impact of RFID on management of returnable containers

Inventory shrinkage is a common problem in the management of returnable containers. RFID-based container tracking systems have been proposed as a possible solution. Benefits of RFID-based tracking of returnable transport items such as pallets, kegs and boxes are documented in several case studies, but have so far hardly been analyzed from a theoretical perspective. In this article, we analyze the impact of RFID on container management using a deterministic inventory model. The analysis focuses firstly on inventory control for which we deduce changes due to RFID for the optimum policy. We then turn to the profitability of the RFID system and determine relevant relations of costs and benefits. Finally we analyze alternatives of implementing an RFID-based container tracking system. These alternatives are analyzed with respect to diffusion speed and profitability.

An inventory model with quadratic demand rate for decaying items with trade credits and inflation

We propose to derive a deterministic inventory model for a stock with random deterioration rate and a quadratic trend in demand. In this study we assume that the supplier offers a credit limit to the customer during whom there is no interest charged, but upon the expiry of the prescribed time limit, the supplier will charge some interest. The whole study has been done in an inflationary environment. Numerical examples have been presented to explain the theory and the sensitivity of the optimal solution of the system has been studied with respect to various system parameters.

A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint

This article develops a deterministic inventory model for perishable items with stock-dependent selling rate. In the model, the unsatisfied demand is partial backlogged and the backlogged demand rate is dependent on the negative inventory level during the stock-out period. Furthermore, a ceiling is imposed on the number of on-display stocks because too much inventory leaves a negative impression on the buyer and the amount of shelf space is limited. Next, the existence and uniqueness of the solution to the problem under two cases are examined, respectively. Then a solution procedure is shown to find the optimal replenishment policy of the considered problem. At last, two numerical examples and a real case study are presented to illustrate the application of the developed model.

Financial Innovation and the Transactions Demand for Cash

We document cash management patterns for households that are at odds with the predictions of deterministic inventory models that abstract from precautionary motives. We extend the Baumol–Tobin cash inventory model to a dynamic environment that allows for the possibility of withdrawing cash at random times at a low cost. This modification introduces a precautionary motive for holding cash and naturally captures developments in withdrawal technology, such as the increasing diffusion of bank branches and ATM terminals. We characterize the solution of the model, which qualitatively reproduces several empirical patterns. We estimate the structural parameters using micro data and show that quantitatively the model captures important economic patterns. The estimates are used to quantify the expenditure and interest rate elasticity of money demand, the impact of financial innovation on money demand, the welfare cost of inflation, and the benefit of ATM ownership.

Understanding supplier credits in an inflationary environment when reserve money is available

A deterministic inventory model for a deteriorating item is explored in an inflation-induced environment for a finite planning horizon. The supplier, as a policy, offers credit limit to his retailers and charges no interest during this period. The retailer has the reserve money to pay off the supplier in the beginning, but takes advantage of his credit policy. Inflationary effects have been studied using the Discounted Cash Flow (DCF) approach. Numerical examples have been presented to explain the theory while sensitivity analysis with respect to inflation rate and credit limit has been done.

Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation

In this paper, the traditional inventory lot-size model is extended to allow not only for general partial backlogging rate but also for inflation. The assumptions of equal cycle length and constant shortage length imposed in the model developed by Moon et al. [Moon, I., Giri, B.C., Ko, B., 2005. Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting, European Journal of Operational Research 162(3), 773–785] are also relaxed. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule is proved and further the convexity of the total cost function of the inventory system in the number of replenishments is established. The theoretical results here amend those in Yang et al. [Yang, H.L., Teng, J.T., Chern, M.S., 2001. Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand, Naval Research Logistics 48(2), 144–158] and provide the solution to those two counterexamples by Skouri and Papachristos [Skouri, K., Papachristos, S., 2002. Note on “deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand” by Yang et al. Naval Research Logistics 49(5), 527–529.]. Finally we propose an algorithm to find the solution, and obtain some managerial results by using sensitivity analyses.

An ordering policy with a cost minimization procedure for deteriorating items under trade credit and time discounting

This paper follows the discounted cashflow (DCF) approach to investigate the inventory replenishment problem for deteriorating items taking account of inflation over a finite planning horizon. A deterministic inventory model with deterioration is developed when a delay in payments is permissible. In addition, an algorithm is developed to find the optimal number of replenishment, cycle time, and order quantity so that the total present value of costs is minimized. Finally, a numerical example is given to illustrate the results and the sensitivity analysis of parameters on the optimal solutions is carried out.

Determining optimal lot size for a two-warehouse system with deterioration and shortages using net present value

Abstract In this paper, we develop a deterministic inventory model for deteriorating items with two warehouses by minimizing the net present value of the total cost. Deterioration rates of items in the two warehouses may be different. In addition, we allow for shortages and complete backlogging. We then prove that the optimal replenishment policy not only exists but also is unique under some condition. Further, the result reveals that the reorder interval based on the average total cost, if it exists, must be longer than that derived using net present value. Finally, we use Yang’s [H.L. Yang, European Journal of Operational Research 157 (2004) 344–356] numerical example to illustrate the model and conclude the paper with suggestions for possible future research.

A note on “Two-warehouse inventory model with deterioration under FIFO dispatch policy”

A recently published paper by Lee [C.C. Lee, Two-warehouse inventory model with deterioration under FIFO dispatching policy, European Journal of Operational Research 174 (2006) 861–873] considers different dispatching models for the two-warehouse inventory system with deteriorating items, in which Pakkala and Achary’s LIFO (last-in–first-out) model [T.P.M. Pakkala, K.K. Achary, A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate, European Journal of Operational Research 57 (1992) 71–76] is first modified, and then the author concludes that the modified LIFO model always has a lower cost than Pakkala and Achary’s LIFO model under a particular condition specified by him. The present note points out that this conclusion is incorrect and misleading. Alternatively, we provide a new sufficient condition such that the modified LIFO model always has a lower cost than Pakkala and Achary’s model. Besides, we also compare Pakkala and Achary’s original LIFO model with Lee’s FIFO (first-in–first-out) model for the special case where the two warehouses have the same deteriorating rates. Finally, numerical examples are provided to investigate and examine the impact of corresponding parameters on policy choice. The results in this note give a much clearer picture than those at Lee’s paper about the relationships between the different dispatching policies for the two-warehouse inventory system with deterioration items.

Multi-criteria decision making on total inventory cost and technical readiness

XYZ Company spends millions of dollars in the procurement of spare parts and tools every year. The maintenance part plays the role of sustaining the technical readiness of the equipment and vehicles. This research will try to find ways to reduce total inventory cost while maintaining the targeted level of technical readiness. The research consists of two phases of multi-criteria decision making on total inventory cost and technical readiness. First phase is to apply a 2-dimentional material classification technique to the selected data. Thus, a combination of ABC- and 123-analysis is used to simplify the problem by focusing on costly items only. The second phase is to apply a deterministic inventory model to the results of the material classification. A detailed analysis of the technical readiness and total inventory cost is covered for the deterministic inventory model. The objective of this research is to design a new system to balance readiness and the associated total inventory cost by finding the relationship between the desired level of technical readiness and cost. Finally, a comparison between the current inventory system and the proposed one shows around 42% savings in the total inventory cost over a period of 3 years, (Adi in Optimizing total inventory cost and enhancing technical readiness level. Master’s thesis, ESM at AUS, Sharjah, UAE, 2005).

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

Deterministic inventory theory provides streamlined optimization models that attempt to capture trade-offs in managing the flow of goods through a supply chain. We will consider two well-studied deterministic inventory models, called the one-warehouse multiretailer (OWMR) problem and its special case the joint replenishment problem (JRP), and give approximation algorithms with worst-case performance guarantees. That is, for each instance of the problem, our algorithm produces a solution with cost that is guaranteed to be at most 1.8 times the optimal cost; this is called a 1.8-approximation algorithm. Our results are based on an LP-rounding approach; we provide the first constant approximation algorithm for the OWMR problem and improve the previous results for the JRP.

A note on the deterministic inventory models with shortage and defective items derived without derivatives

Huang [Journal of Statistics and Management Systems, Vol. 6(2) (2003), pp. 171–180] considers the deterministic inventory models with shortage and defective items derived without derivatives. Huang’s paper involves the logical problem such that his inventory models are questionable. Numerical examples illustrate the above observations.

Technical note: A use of the complete squares method to solve and analyze a quadratic objective function with two decision variables exemplified via a deterministic inventory model with a mixture of backorders and lost sales

Several researchers have recently derived formulae for economic-order quantities (EOQs) with some variants without reference to the use of derivatives, neither for first-order necessary conditions nor for second-order sufficient conditions. In addition, this algebraic derivation immediately produces an individual formula for evaluating the minimum average annual cost. The purpose of this paper is twofold. Exemplifying a use of the complete squares method through solving and analyzing Montgomery et al.'s [Montgomery, D.C., Bazaraa, M.S., Keswani, A.C., 1973. Inventory models with a mixture of backorders and lost sales. Naval Research Logistics Quarterly 20, 255–263] model, i.e. the EOQ model taking into account the case of partial backordering first we can readily derive global optimal expressions from a non-convex quadratic cost function with two decision variables in an algebraic manner, second we can straightforwardly identify some analytic cases in a way that is not as easy to do this using calculus. A numerical example has been solved to illustrate the solution procedure. Finally, some special cases can be deduced from the EOQ model under study, and concluding remarks are drawn.