Traditional Inventory Models Research Articles

A Just-in-Time Inventory Model with Preventive Maintenance and Defect Rate

In competitive market environments, businesses employ Just-In-Time (JIT) systems not only to reduce costs, but also to enhance their business partnerships. Although product quality level is essential for maintaining competitiveness, traditional inventory models do not consider defect rate, which is the main determinant of product quality. Also, in real working environments, machines break down after long operating times, which increases product defect rate. Therefore, an effective preventive maintenance policy is needed to ensure that machinery is reliable. Reworking defective items is another important inventory problem. To answer the above questions regarding varying defect rate, preventive maintenance and rework, this study developed an integrated two-echelon inventory model to determine the best production quantity, delivery frequency and preventive maintenance schedule under JIT production and delivery policy. The model results can be used to minimize total cost.

Sustainable EOQ under Lead-Time Uncertainty and Multi-Modal Transport

In this paper, we examine a sustainable economic order quantity (S-EOQ) problem with a stochastic lead-time and multi-modal transportation options. With the S-EOQ, decisions of order quantities, as well as a reorder point could be influenced by various factors, including unit price, stock-out cost, lead-time variability and emission costs. For a better understanding, we present a mathematical model of the concomitant S-EOQ problem and, using numerical experiments, explore various scenarios to determine the effects of incorporating sustainability considerations into the traditional inventory model on operational decisions including the choice of transportation modal combination and the sourcing decisions

Model predictive control of cash balance in a cash concentration and disbursements system

This paper presents a Model Predictive Control (MPC) for a revenue account belonging to a cash concentration and disbursements system, based on the application of inventory policies to the cash balance. Dynamic Programming (DP) is used for the prediction model by including a standard forecasting model for uncertainty. Moreover, a band for the uncertainty is established to narrow the input of the DP model, together with a stabilizing regulator in cascade fashion using a linear feedback gain. This combination allows determining a range for the system stability regardless of the size of the prediction horizon. The reference signal used is a sawtooth function, which conveniently adapts to the inventory policy (s,S). Theoretically, and through simulation, it is shown that the proposed controller meets the control objective. Furthermore, the results achieved are equivalent to those obtained by using a traditional inventory control model by directly applying the (s,S) strategy with periodic review, which supports the conclusions in Lee and Wong [44], Wong and Lee [71] and Lee [42] regarding the limited effectiveness when ADP is applied together with MPC. However, the method leaves open the possibility of obtaining promising results if some complexity elements (e.g. delay) are added to model.

Comparisons of some improving strategies on NSGA-II for multi-objective inventory system

Different inventory control systems attempt to determine how much and when to order at the least relevant cost, while maintaining a desirable service level for customers. In this paper, a continuous review stochastic inventory system, with three objectives and certain resource constraints is studied. In the model for this system, contrary to the traditional inventory models, customer service is not considered a shortage cost in the objective function. Moreover, the frequency of stock-out occasions and the number of items stocked out annually are to be minimized. For determining the Pareto optimal set, Constrained Multi-Objective Evolutionary Algorithms are used. Constrained Reference-point-based Non-dominated Sorting Genetic Algorithm (C-R-NSGA-II) which integrates decision-makers’ preferences in the optimization process, is compared with the basic algorithm, constrained non-dominated sorting genetic algorithm (C-NSGA-II). Then, the best algorithms for each criterion are presented. Results show that C-R-NSGA-II has good scores for most criteria.

Internalisation strategies of external costs of transport for a sustainable logistics

Transport is a priority issue for a sustainable development. The European Commission planned to implement a full and mandatory internalisation of the transport external costs within the 2020 (EU, 2011). Traditional inventory models, however, minimise logistics costs neglecting externalities. The aim of this paper is to evaluate the social and environmental benefits of the internalisation of the external costs in the inventory management problem. The sustainable order quantity model (Digiesi et al., 2012) has been adopted here in order to identify the optimal lot-size and transportation mean minimising logistic and external costs of transport. A sensitivity analysis has been performed in order to investigate the effects of different internalisation strategies on the solution of the inventory problem. In order to evaluate the effectiveness of the proposed strategies, they have been tested on a real case study.

The replenishment policy of agri-products with stochastic demand in integrated agricultural supply chains

Market demand of agri-products is influenced by uncertain factors, such as weather, temperature, and customer preferences. In integrated agricultural supply chains, traditional inventory models are useless because of the stochastic demand and deteriorative characteristic of agri-products. This paper provides a method to determine the optimal replenishment policy of integrated agricultural supply chains with stochastic demand. In these EOQ/EPQ models, shortages are allowed and are backlogged if market demand is stochastic. The objective function is to minimize the total cost of the supply chain in the planning horizon. The total cost includes the ordering cost, the holding cost, the shortage cost and the purchasing cost. Thinking of the nonlinear relationship and dynamic forces in models, a system dynamic (SD) simulation model is constructed to find the optimal lot size and replenishment interval. Finally, an example is given to make a sensitivity analysis of the simulation model. Compared to traditional methods (such as equalize stochastic demand), the total cost decreases by 16.27% if the supply chains adopt the new replenishment policy. The results illustrated that the new replenishment policy (with intelligent method) is beneficial to help supply chain make decision scientifically. Moreover, the intelligent method can simulate stochastic demand perfectly, and it is effectively for solving the complicated and mathematically intractable replenishment problem.

The backroom effect in retail operations

Traditional inventory models fail to take into account the dynamics between the retail sales floor and the backroom, commonly used by retailers for extra storage. When a replenishment order for a given item arrives at a retail store, it may not fit on the allocated shelf space, making backroom storage necessary. In this article, we introduce the backroom effect (BRE) as a consequence of misalignment of case pack size, shelf space, and reorder point. This misalignment results from the fragmented nature of inventory policy decision making in the retail industry and affects basic trade-offs in inventory models. We specify conditions under which the BRE exists, quantify the expected amount of backroom inventory, derive an optimal short-term inventory policy, and assess the impact of the BRE on the optimal inventory policy and total costs. Our results indicate that ignoring the BRE leads to artificially high reorder points and higher total costs. The paper concludes with a discussion of theoretical and managerial implications.

A sustainable lot-sizing model with partial backordering

Due to the competitive nature of business, accompanied by social and environmental awareness, a great necessity to incorporate additional non-classical criteria into traditional inventory models is comprehended. Sustainable lot-sizing model is considered to be a powerful response to this necessity. In this paper a novel sustainable lot-sizing model is developed which converts all emission types of inventory management life-cycle into tangible economic metrics. In order to develop the model in a more practical manner, partial backordering consideration is embedded into the model. A pretty simple procedure is developed to determine the optimal solutions of the proposed model. Finally the formulated model is illustrated with a numerical example. A comprehensive sensitivity analysis has been accomplished on model parameters as well. According to the sensitivity analysis the results show that the decision variables are highly sensitive respect to the selling price and purchasing cost and are moderately sensitive to the demand rate, fixed ordering cost, annual average inventory obsolescence rate, weight of an obsolete unit stored and also partial backordering rate. In the other hand the changes of other parameters have slight effects on the decision variables.

The Application of Functions of Several Variables Analysis in an Optimal Replenishment Policy for Deteriorating Items

Abstract Very often must be taken into account the gradual deterioration of goods in inventory management. This fact is not taken into account in multiple management systems. Traditional inventory models at the same time assume that a retailer pays for the goods the moment they are received. Nowadays, however, it is becoming a common practice that a supplier offers a retailer the option to pay for the goods with a certain delay. If the retailer is not able to meet his obligations within the deadline, he is charges an interest.In this study we introduce a newly constructed suitable model which enables a retailer to set an optimal price of deteriorating goods under permissible delay in payments, and to determine the maximum repayment term. We considered a deterministic inventory model with time-dependent demand, holding costs variable in time where deterioration is directly proportional to the time. The model is based on the assumption of time-dependent demand and has been developed for deteriorating goods. The paper further analyses a situation in which the retailer sell all the goods in time, and a situation in which the deadline was not met. Further assumption is that the inventory is depleted only by demand. The scientific aim is to verify if such an optimizing problem can be solved. Theoretical results are illustrated with numerical example for the model. Results show that the developer model is capable of solving the theoretical problem illustrated by an example. It helps to the retailer to set the selling price and the replenishment interval in order to maximize profit. The authors of the paper used methods of analysis and synthesis, and the method of mathematical analysis (differential calculus of multivariable functions, solution of ordinary differential equations, Taylor series).The model suggested in the paper can be expanded in the future. One option is generalization of the model, allowing for the lack of goods, bulk discounts, time value of money, inflation etc.

Research on life cycle CO2 emissions of energy carriers in China

The purpose of this study is to determine the life cycle CO2 emissions for the production and distribution of energy carriers in China. The mathematical method of input–output analysis was used to model the complicated materials flows between different energy industries. The results show that, for providing 1 GJ fuels, coking products have the largest CO2 emission, followed by oil products, middling coal, cleaned coal, natural gas and crude oil, and raw coal. The results also show that the theory and mathematical model of input–output analysis are more proper for energy carriers than traditional inventory calculation models. The comparison between China and Japan indicates that the life cycle CO2 emissions of energy carriers produced in China are higher than developed level; therefore there is CO2 mitigation potential for China’s energy industries.

Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment

In this paper, some multi-item inventory models for deteriorating items are developed in a random planning horizon under inflation and time value money with space and budget constraints. The proposed models allow stock dependent consumption rate and partially backlogged shortages. Here the time horizon is a random variable with exponential distribution. The inventory parameters other than planning horizon are deterministic in one model and in the other, the deterioration and net value of the money are fuzzy, available budget and space are fuzzy and random fuzzy respectively. Fuzzy and random fuzzy constraints have been defuzzified using possibility and possibility–probability chance constraint techniques. The fuzzy objective function also has been defuzzified using possibility chance constraint against a goal. Both deterministic optimization problems are formulated for maximization of profit and solved using genetic algorithm (GA) and fuzzy simulation based genetic algorithm (FAGA). The models are illustrated with some numerical data. Results for different achievement levels are obtained and sensitivity analysis on expected profit function is also presented. Scope and purposeThe traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However for more sale, inventory should be maintained at a higher level. Of course, this would result in higher holding or procurement cost, etc. Also, in many real situations, during a shortage period, the longer the waiting time is, the smaller the backlogging rate would be. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging diminishes with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But at present, the economic situation of most of the countries has been much deteriorated due to large scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any further. The purpose of this article is to maximize the expected profit of two inventory control systems in the random planning horizon.

Production inventory model with reworking of imperfect production, scrap and shortages

In traditional inventory models such as the economic order quantity and the economic production quantity models, the sole objective is to minimize the total inventory-related costs, typically the holding cost and the ordering cost. These models do not consider the presence of defective products in the lot or reworking them. In an imperfect manufacturing process, the defective items are produced with the finished goods. The rework process is necessary to convert those defective items into finished goods. This paper develops a production inventory model with planned backorders for determining the optimum quantity for a single product manufactured in a single stage manufacturing system that generates imperfect quality products where a proportion of the defective products are reworked in the same cycle. Additionally, a range of real values for the proportion of defective products for which there is an optimal solution is established, and a closed form for the total cost of the inventory system is obtained. To achieve this objective, a suitable mathematical model is developed and the optimal production lot size that minimises the total cost is derived. The relevant model is built and solved, and necessary and sufficient conditions for a unique and globally optimal solution are derived. Illustrative examples are provided and numerically verified. For validation of the results, this model was coded in Microsoft® Visual Basic 6.0.

A sustainable EOQ model: Theoretical formulation and applications

Traditional inventory models involve different decisions that attempt to optimize material lot sizes by minimizing total annual supply chain costs. However, the increasing concern on environmental issues stresses the need to treat inventory management decisions as a whole, by integrating economic and environmental objectives. Recent studies have underlined the need to incorporate additional criteria in traditional inventory models in order to design “responsible inventory systems”. This paper explores the integration of factors affecting the environmental impact within the traditional EOQ model and proposes a “Sustainable EOQ Model”. All sustainability factors linked to the material lot size are analyzed from the beginning of the purchasing order to the end of its life inside the buyer plant. Thus, the environmental impact of transportation and inventory is incorporated in the model and investigated by an economic point of view. In particular internal and external transportation costs, vendor and supplier location and the different freight vehicle utilization ratio are considered in order to provide an easy-to-use methodology. The optimization approach is applied to representative data from industrial problems to assess the impact of sustainability considerations on purchasing decisions if compared with the traditional approaches. Finally, an illustration of the effect of using the new “Sustainable EOQ model” is presented and discussed.

Optimizing inventory decisions in a two-level supply chain with order quantity constraints

A fundamental assumption in traditional inventory models is that all of the ordered items are of perfect quality. A two-level supply chain is considered consists of one retailer and a collection of suppliers that operate within a finite planning horizon, including multiple periods, and a model is formulated that simultaneously determines both supplier selection and inventory allocation problems in the supply chain. It is supposed that the ordered products dependent on the suppliers include a certain percentage of imperfect quality products and have different prices. In this paper, we study the impact of the retailer’s financial constraint. On the other hand, suppliers have restricted capacities and set minimum order quantity (MOQ) policy for the retailer’s order amount happened in each period. So, the problem is modeled as a mixed integer nonlinear programming. The purpose of this model is to maximize the total profit. The nutrients, fishery and fruitage industries give good examples for the proposed model. A numerical example is presented to indicate the efficiency of the proposed model. Considering the complexity of the model, a genetic algorithm (GA) is presented to solve the model. We demonstrate analytically that the proposed genetic algorithm is suitable in the feasible situations.

The Backroom Effect in Retail Operations

Traditional inventory models fail to take into account the dynamics between the retail sales floor and the backroom, commonly used by retailers for extra storage. When a replenishment order for a given item arrives at a retail store, it may not fit on the allocated shelf space, making backroom storage necessary. In this article, we introduce the backroom effect (BRE) as a consequence of misalignment of case pack size, shelf space, and reorder point. This misalignment results from the fragmented nature of inventory policy decision making in the retail industry and affects basic trade‐offs in inventory models. We specify conditions under which the BRE exists, quantify the expected amount of backroom inventory, derive an optimal short‐term inventory policy, and assess the impact of the BRE on the optimal inventory policy and total costs. Our results indicate that ignoring the BRE leads to artificially high reorder points and higher total costs. The paper concludes with a discussion of theoretical and managerial implications.

구매가격 변동 하에서 초기재고 재분배를 통한 위험회피 재고모형의 효율화

In traditional inventory models, purchase prices of raw materials are assumed to be fixed and have no effect on the optimal choice of inventory policies. However, when purchase prices fluctuate continuously over time, inventory costs are heavily affected by purchasing prices. Risk-averse inventory model decides order quantity and ordering time by considering not just purchase prices but also the risk from the discrepancy between estimated prices and realized prices. In this paper, we propose a myopic inventory policy which incorporates price risk into deciding ordering time and quantities. While the existing risk-averse model has no mechanism to reallocate inventories already purchased for a specific future period, the revised one reallocates initial inventories of each period to other future periods so that it can avoid purchasing raw materials at high prices. Experimental results demonstrate that the revised model outperforms the existing one in respect of total cost and variability.

A Partial Backlogging Inventory Model for Deteriorating Item under Fuzzy Inflation and Discounting over Random Planning Horizon: A Fuzzy Genetic Algorithm Approach

An inventory model for deteriorating item is considered in a random planning horizon under inflation and time value money. The model is described in two different environments: random and fuzzy random. The proposed model allows stock-dependent consumption rate and shortages with partial backlogging. In the fuzzy stochastic model, possibility chance constraints are used for defuzzification of imprecise expected total profit. Finally, genetic algorithm (GA) and fuzzy simulation-based genetic algorithm (FSGA) are used to make decisions for the above inventory models. The models are illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented.Scope and Purpose. The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However, to keep sales higher, the inventory level would need to remain high. Of course, this would also result in higher holding or procurement cost. Also, in many real situations, during a longer-shortage period some of the customers may refuse the management. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging is diminishing with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But in the past, the economic situation of most of the countries has changed to such an extent due to large-scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any more. The purpose of this paper is to maximize the expected profit in the random planning horizon.

Loss-Averse Inventory and Borrowing Decisions with Constraints on Working Capital in Fashion and Textiles Industry

Traditional inventory models focus on operational decisions and inventory control. Quite few models consider the financial constraint and decision bias such as loss aversion, which are the reality in today's business environment, especially for the fashion and textiles industry. In this paper we study the inventory control problem for a loss-averse retailer with financial constraint for operations in a periodic review setting in a finite horizon. We characterize the optimal inventory control policies with self-financing or with borrowing as capital-dependent base-stock policies. We demonstrate with numerical examples that the optimal base-stock level is nonincreasing in the accumulated wealth and the loss-aversion indicator.

Managing Inventory for Entrepreneurial Firms with Trade Credit and Payment Defaults

This paper considers an entrepreneurial firm that periodically orders inventory to satisfy demand in a finite horizon. The firm offers trade credit to its customer while receiving one from its supplier. In addition to standard inventory-related costs, cash-related costs are incurred in each period. The cash-related cost is composed of a default penalty cost due to a cash shortage and an interest gain (negative cost) due to excess cash after inventory payments. The objective is to obtain an inventory policy that maximizes the working capital at the end of the horizon. We show that this problem is equivalent to that of minimizing the total inventory related cost and the cash-related cost in the horizon. The model with ample cash reduces to the traditional inventory model. For the general model, we prove that a state-dependent policy is optimal. To facilitate implementation and reveal insights, we consider a simplified model in which a myopic policy is optimal. A numerical study suggests that the myopic policy is effective for the original system. The myopic policy generalizes the classic base-stock policy and resembles practical working capital management under which firms make inventory decisions according to their working capital status. The policy parameters have closed-form expressions, which show the impact of demand and cost parameters on the inventory decision. Our study assesses the value of considering financial flows when the firm makes the inventory decision and reveals insights that are consistent with empirical findings in the literature.

A note on ‘a replenishment policy for items with price-dependent demand, time-proportional deterioration and no shortages’

In a recent paper, Begum et al. (2012, International Journal of Systems Science, 43, 903–910) established pricing and replenishment policy for an inventory system with price-sensitive demand rate, time-proportional deterioration rate which follows three parameters, Weibull distribution and no shortages. In their model formulation, it is observed that the retailer's stock level reaches zero before the deterioration occurs. Consequently, the model resulted in traditional inventory model with price sensitive demand rate and no shortages. Hence, the main purpose of this note is to modify and present complete model formulation for Begum et al. (2012). The proposed model is validated by a numerical example and the sensitivity analysis of parameters is carried out.