Multi-item Inventory Model Research Articles

Multi-warehouse partial backlogging inventory system with inflation for non-instantaneous deteriorating multi-item under imprecise environment

In this study, we explored a multi-item inventory model for non-instantaneous deteriorating items under inflation in fuzzy rough environment with multiple warehouse facilities, where one is an owned warehouse and others are rented warehouses with limited storage capacity. Due to a number of uncertainties in the environment, the various expenditures and coefficients are considered as a fuzzy rough type. The objective and constraints in fuzzy rough are made deterministic using Tr–Pos chance constrained technique. The demand of items is considered as stock dependent, and deterioration of items is assumed to be constant over time. The model allows shortages in owned warehouse subject to partial backlogging. The purpose of this study is to find the retailer’s optimal replenishment policies to maximize the total profit. To illustrate the proposed model and also test the validity of the same, a numerical example is solved using the Mathematica-8.0 software. Sensitivity analysis is also performed to study the impact of important parameters on system decision variables, and its implications are discussed.

Multi-item fuzzy inventory model for deteriorating items in multi-outlet under single management

Multi-item inventory model with stock-dependent demand is developed in fuzzy environment. Items are deteriorated in constant rate and are sold from different outlets in the city under single management. Due to the impreciseness of different parameters, objectives as well as constraints are imprecise in nature. As optimization of fuzzy objectives as well as fuzzy constraints are not well defined, the model is formulated as a multi-objective chance constrained programming problem where optimistic/pessimistic return of the objectives with some degree of possibility/necessity are optimized and constraints are satisfied with some degree of necessity. The model is solved via Multi-Objective Genetic Algorithm (MOGA) when crisp equivalent of the problem is available. In other cases, fuzzy simulation process is proposed to check the constraints as well as to determine the optimistic/pessimistic return of the objectives. The model is illustrated with some numerical examples.

Multi-item fuzzy inventory model by Kuhn-Tucker method

Multi-item fuzzy inventory model by Kuhn-Tucker method

A continuous review inventory model with complex correlations among components

Under a flexible mass-production system, a manufacturer may need to provide highly customized products to meet customer satisfaction. It is likely that components in a customized product are correlated in such a way that the demands of some components depend on those of others. In order to cope with dependence in the demands, we proposed a continuous review multi-item inventory (Q, r) model that included a general form of correlation and dependence in demands among components. We represented the proposed model by using a probabilistic graphical model under the assumption that the demands of all components and their correlations were represented by a multivariate Gaussian probability distribution. By taking an advantage of a directed acyclic graph and its topological order, we demonstrated that the correlated demands among components in the proposed model could be solved without any approximation and assumption. As an illustration of the proposed method, we solved an inventory (Q, r) model of eight correlated components and discussed the experimental results in terms of correlation and dependence in demand.

Adoption and Diffusion of Hi-Technology Product and Related Inventory Policies

The objective of this review article is to study the published research on the inventory modeling and optimization for substitutable technology products with a short product life cycle. This review explains the demand dynamics of technology generation products and how to administer supply chain management of this kind of products than any other functional products. The article does a review of the demand models proposed on the diffusion of innovation products, and then, moves on to the literature review of the multi-item inventory models, followed by the literature review of the inventory modeling of substitutable items. In order to ensure the quality, this study covers the review of the research papers mostly published in reputed SCI or ABDC rated journals. The study discovers that the research that has been done on the inventory optimization of multi generation technology products is not only rare but also very restrictive in its scope and assumptions. The study then proposes the directions for the future research.

An analysis of multi-item inventory model using particle swarm optimization under discrete delivery orders and limited storage space

This study explores an economic production quantity (EPQ) model designed with the assumptions of discrete delivery orders and storage capacity constraints for a multi-item production inventory system. The main purpose of this study is to determine the optimal order quantity, the optimal number of deliveries and the optimal delivery quantity. First, the developed model as part of this study was analyzed using Genetic Algorithm (GA). Numerical analysis results were compared with those of previous studies and it was found that it is possible to have better results with an increasing number of iteration. The same model was then analyzed using Particle Swarm Optimization (PSO) algorithm. A comparison of the optimization methods showed that PSO gives better results over the GA under the same number of iterations and using the same population. The effects of important model parameters such as number of iterations, population, crossover, mutation rate on the optimal solution were analyzed. The results showed that PSO performs better than the GA with respect to the total cost and the total runtime as the solution of the problem in question.

Optimizing of Multi-objective Inventory Model by Different Fuzzy Techniques

A multi-objective, multi item inventory model is constructed for deteriorating items where the demand is considered as exponential time function under limited storage space as well as budget. By using Fuzzy non linear programming (FNLP) and Intutionistic fuzz optimization (IFO) techniques results are obtained and then compared. The objective of this work is to use FNLP and IFO techniques for multi-objective inventory model and to compare these techniques through numerical results. The major goal of the paper is to find optimal quantity to be replenished and identify time point when shortages will occur. In this paper FNLP and IFO are applied to multi item multi-objective inventory model with budget and warehouse space constraint and investigating for multi-objective inventory model which method either FNLP or IFO gives efficient solution. In case of maximization objective IFO works well than FNLP while in case of minimization FNLP works better. By observing objectives, the above methods can apply to various inventory problems. All these results along with relation of profit and shortage cost with budget, warehouse space is studied through sensitivity analysis. The result shows that the IFO better results for maximizing profit while FNLP works better in case of minimizing shortage cost.

Optimal replenishment policy for multi-item probabilistic inventory model with all-units discount

In this paper, we develop a multi item inventory model for the retailer by considering all-units discount offered by the supplier. Demands in this model are assumed to be probabilistic following a Gamma distribution with certain values of shape and scale parameters. The aim of the model is to determine the optimal replenishment policy that minimize the total inventory cost. The total inventory cost was composed from the purchasing, ordering, handling or storing and shortage costs. All shortages are handled by backorder. We compare the individual and joint replenishment policies for the model and develop an algorithm to find the optimal replenishment policy. Numerical examples are given to give a better understanding of the model in comparing the individual and joint replenishment policies. We also perform sensitivity analysis by changing values of shape and scale parameters of the demand distribution to analyse the effects on the optimal solution.

Optimal payment time and replenishment decisions for retailer’s inventory system under trade credit and carbon emission constraints

This study presents a multi-item inventory and pricing model by considering marketing, service activities, trade credit, carbon emissions, and the restrictions of production cost and storage space. In the proposed model, shortages are allowed and demand rate is a power function of service and marketing costs, and selling price. The main objective of this study is to optimize retailer’s payments time, service and marketing expenditure, and replenishment decisions in order to maximize retailer’s total profit and minimize carbon emissions, simultaneously. Model is developed in a fuzzy environment under carbon tax regulation when the length of credit period provided by supplier is less than or equal to the length of time in which no shortage happens. To solve the proposed model, we first transform the original problem into a multi-objective Signomial Geometric Programming (SGP) problem using fuzzy and hybrid parameters, which minimizes both the mean value and the total dispersion value of the objective function. Then a global optimization problem method has been used to solve the SGP problem. Efficiency of this algorithm is tested and compared with multi-objective genetic algorithm, multi-objective genetic algorithm with varying population, and hybrid heuristic algorithm. At the end, several numerical examples and sensitivity analysis are performed to demonstrate the application of the proposed model and solution procedure to obtain managerial insights.

Analysis of Optimal Inventory Management for Dual Blood Products with Dual Sources

We study inventory management for a blood center that periodically collects whole blood and processes it into multiple blood products such as red blood cells and platelets. The blood center may also be able to collect a single blood product by apheresis. With limited lifetimes, blood products are stored to satisfy random demands or sold in clearance sales before becoming outdated. We formulate a multi-item inventory model and characterize the optimal replenishment and salvage policies. Applying the concept of multimodularity, we show the substitutable properties between the inventories of the same product in different ages, as well as the complementary properties between inventories of distinct products. We demonstrate that the replenishment and salvage decisions can be coordinated to optimize the inventory system and discuss the value of implementing the alternative.

Determination of Multi-Item Inventory Model with Limitations of Warehouse Capacity and Unit Discount in Leading Garment Industry in Indonesia

Determination of Multi-Item Inventory Model with Limitations of Warehouse Capacity and Unit Discount in Leading Garment Industry in Indonesia

A multi-item inventory model for small business - a perspective from India

Micro, small and medium enterprises (MSMEs) in India are focused on improving their inventory management function as part of government's program to increase their contribution to the gross domestic product (GDP). A plethora of inventory models are available in literature; these models are either very complex, or need reliable inventory cost data, or are not applicable to all classes of items and are, therefore, rendered ineffective. In this paper we have developed and presented a simple, yet effective, model that combines the characteristics of selective inventory control (SIC) and an exchange curve (EC). Combination of these techniques not only allows determination of ordering policy for all items, but also involves managers in decision making, thus providing MSMEs with a solution that is robust and practical. We also describe application of this model to a sample of 30 items in an auto components manufacturing firm. The case study demonstrates ease of implementation of the proposed model as well as solution completeness.

A multi-item inventory model for small business - a perspective from India

A multi-item inventory model for small business - a perspective from India

Probabilistic Inventory Model Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment

This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions).
 The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. Finally, a numerical example is applied.

Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand

In this paper, a two echelon supply chain with one manufacturer and one retailer is developed for multi products. The retailer faced with the uncertain demand for all products which follows a normal distribution. The production process is assumed to be imperfect, and the defectiveness is assumed to follow a beta distribution. The manufacturer produces and delivers the products in a number of equal-sized batches to the manufacturer's warehouse, and thereby it is delivers in a number of equal batches to the retailer's warehouse. Shortages are allowed to occur, at the retailer side, and it is backordered partially. The retailer offers a price discount for backordered items to his customers. Both the lead time crashing cost and the partial backorder ratio are considered as the inverse function of lead time. Under these assumptions, there are three inventory models proposed in this paper, one with non-integrated approach, the other with an integrated approach without trade credit and finally an integrated approach with trade credit. A new iterative algorithmic procedure has been developed to minimise the total cost. Finally, numerical examples are given to illustrate the models and the sensitivity analysis is conducted over various model parameters.

Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy

This article is concerned with a multi-item inventory model for deteriorating items. The model is formed on the basis of a two-level supply chain policy, i.e., based on manufacturer's and retailer's perspective. The deterioration rate is considered as constant. The demand factor of any items suffer from a large amount of stock level; so, we consider stock-dependent demand function. The demand of any item is also dependent on its selling price; thus, a price-dependent demand function is introduced here. The retailer adopts the trade-credit policy for his customers in order to promote market competitiveness. He can earn revenue and interest after the customer pays the amount of purchasing cost to the retailer until the end of the trade-credit period, offered by the supplier. Shortages are allowed in the retailer's model as it is a very realistic item, too. A price discount on backordered commodities is offered for those customers who are willing to backorder their demand. Thereafter, we present an easy analytical solution procedure to find the total profit for both manufacturer and retailer. We also use the classical game theory and Nash equilibrium approach to find an optimal solution of the joint profit. The results are discussed with several numerical examples to illustrate our model and to provide some managerial insights related to the model. Furthermore, a parametric sensitivity analysis of the optimal solutions is provided and a concavity figure of our profit function is supplied to stabilize our model. The paper ends with a conclusion and an outlook to future research projects.

Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment

This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions).The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. Finally, a numerical example is applied.

A fuzzy rough multi-objective multi-item inventory model with both stock-dependent demand and holding cost rate

In this paper, we developed a multi-objective multi-item inventory model with fuzzy rough coefficients. Here, we have considered both demand and holding cost which is a non-linear function of the instantaneous stock level. Chance-constrained fuzzy rough multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. By examining the various definitions and theoretical results of fuzzy rough variables, we have designed a Tr-Pos chance constrained technique to determine the optimal solutions of a fuzzy rough multi-objective inventory problem. Finally, a numerical example is provided to illustrate the present model, and a sensitivity analysis of the optimal solution with respect to the major parameters is carried out.

Dual-channel warehouse and inventory management with stochastic demand

This study examines the inventory policy for the emerging dual-channel warehouse, which has a unique structure where the warehouse is divided into two areas: one for fulfilling online orders and the other for storing products and fulfilling offline orders. A multi-item inventory model was developed considering the warehouse capacity constraint, demand, and lead time uncertainty. Solution methods are provided for both uniform and normal distributions. Adopting the proposed inventory policy for a dual warehouse is cost effective and adds flexibility to the warehouse and supply chain. The study also offers managerial insights on some critical issues faced by companies operating in a dual-channel context.

Development and simulation analysis of a new perishable inventory model with a closing days constraint under non-stationary stochastic demand

Abstract The food waste in grocery retail is a worldwide problem. Many mathematical inventory models for perishable items do not have a closing days constraint, although the age of perishable items also increases on closing days in grocery stores. We develop a new age-based inventory model with a closing days constraint. This stochastic multi-item inventory model includes total stock capacity constraints, a positive lead time, a periodic inventory control, a target customer service level and mixed FIFO and LIFO issuing policies for perishable items with a fixed lifetime under a non-stationary random demand. We show in a comparative simulation study under a rolling planning that the closing days constraint improves order decisions and reduces waste quantities and costs in grocery stores.