Multi-product Inventory Model Research Articles

Multi-warehouse, multi-product inventory control model for agri-fresh products – A case study

Warehouses that operate under controlled micro-climates are necessary to reduce the deterioration of fresh produce, but they are also costly to operate. Developing an efficient operation regime for these premises while considering energy costs, demand, and harvesting requirements is crucial to managing the food supply chain sustainably and profitably. This paper proposes a method to develop an operation regime by solving a multi-period, multi-product, multi-warehouse inventory control optimization problem that originates from the management of agri-fresh products from an Australian company. We propose a mixed-integer quadratic programming model for this problem. A significant challenge is that each product has a specific deterioration rate over storage, which differs in each warehouse mode. Our model allows for two different operational modes for warehouses, each with different electricity consumption, affecting the time the products remain fresh. The objective function of the model minimizes the total inventory costs. The model provides the optimal inventory flow of each product, the optimal number of active warehouses, the optimal operational length of warehouses, and the optimal mode of warehouses in each period. We solve the model using Gurobi and integrate three other solution approaches based on model properties, which reduce the computational time by half. The model is tested using real data from the case study, an Australian agri-fresh company. The results indicate a reduction in total cost by 8% and quantity of product deterioration by 20%. We also investigate the impacts of variations in demand and supply caused by growing or shrinking markets in our case study under different scenarios and instance sizes of the problem and analyze the impact in solution times that are observed in practice.

A robust optimization approach for multi-product inventory management in a dual-channel warehouse under demand uncertainties

This study explores the multi-product inventory problem of a dual-channel warehouse to determine the optimal continuous review inventory policies. The warehouse is divided into two areas, one for fulfilling online orders and the other for storing products and fulfilling offline orders. Uncertainties are involved in the demands of the products during lead time in the two areas with their means and variances as the only known demand information. Using a distributionally robust optimization approach, the problem is formulated as a multi-product inventory model with an individual chance constraint and a multi-product inventory model with a joint chance constraint for the warehouse capacity to minimize the annual total expected cost. Two types of service levels are considered to ensure an adequate customer satisfaction. Through mathematical manipulations, the developed distributionally robust multi-product inventory models are transformed into convex programming models which can be solved efficiently, and the corresponding solution algorithms are developed. In particular, the closed-form solution of the order quantities is derived for the model with the individual chance constraint. Numerical experiments are performed to verify the effectiveness and practicality of the proposed models and the solution approaches in dealing with demand uncertainties and to draw specific managerial insights. Effects of important problem parameters on inventory policies and cost performance are also analyzed through numerical studies. Recommendations on the warehouse structure are given for business firms engaged in both online and offline sales. The continuous review inventory policies obtained by the proposed approach are robust and are flexible in making decisions for the operations of dual-channel warehouses and supply chains with only limited demand information. The proposed algorithms are proved to be very efficient through computational experiments.

The Effect of Order Incentives in a Multi-product Dynamic Inventory Model

The Effect of Order Incentives in a Multi-product Dynamic Inventory Model

A Systematic Approach to the Purchase Dependence

Under the situation which customer orders are cancelled unless all products in the order are delivered all at once, this paper concentrates on the purchase dependent demands and explores the systematic approach to implant the purchase dependence into the multi-product inventory model. First, by acknowledging that it is a challenging task to formulate a suitable inventory model for the purchase dependence, we derive the optimal solution condition using an EOQ model and extend the optimal solution condition to periodic review models. Then, through the comparison simulation of four inventory policies regarding several degrees of purchase dependence, we demonstrate that the inventory models which consider the purchase dependence generate less total cost than the inventory models which ignore the purchase dependence. In general, the inventory models which consider the purchase dependence reduce the loss of sales by maintaining more inventories, which results in reducing the total cost. Consequently, the simulation result supports the effectiveness of this paper’s approach. In addition, this paper uses the individual order period and joint order period obtained from the EOQ model for the multi-product inventory model. Through the in-depth analysis of comparing the two models, we observe that the model of using the joint order period produces less total cost when the degree of purchase dependence is high, but the model of using the individual order period produces less total cost when the degree of purchase dependence is low.

Perishable Inventory Management Using GA-ANN and ICA-ANN

We have developed a multi-objective multi-product inventory management model for perishable products, focusing on the inventory management of veterinary drugs. This model minimises holding, shortage, and expired costs and also demand forecast error simultaneously. The number of expired and shortage drugs can be calculated for each period using this model. Data from three types of veterinary drugs have been collected from a distribution centre (DC). In this research, multi-layer perceptron (MLP) neural network is used to forecast the demand and genetic algorithm (GA) and imperialist competitive algorithm (ICA) are used to solve and find satisfactory solutions. In this research, artificial neural network (ANN) is combined with the two above-mentioned algorithms to solve the problem. The results show that the proposed model can find high-quality solutions because it reduces inventory costs and forecast errors in the DC. Finally, the results of combining ANN with each of the algorithms were compared and it was concluded that the combination of ANN and ICA produced better solutions.

An Integrated Multi-Product Inventory Model for a Two-Echelon Supply Chain under Cap-and-Trade Mechanism

Currently many companies are interested in reduction of the carbon emissions associated with their supply chain activities such as transportation and operations. Operational decisions, such as modifications in order quantities could an effective way in reducing carbon emissions in the supply chain. Cap-and-trade regulation, sometimes called emissions trading, is a market-based tool to limit greenhouse gas emissions. Under cap-and-trade regulation, emission credits are allocated to the firms and the firms trades emissions under cap-and-trade schemes. In this paper, we propose a single-manufacturer single-buyer two-echelon supply chain problem under the cap-and-trade mechanism incorporating the carbon emissions caused by transportation and warehousing activities where a single manufacturer produces a family of items in order to deliver a family of items to a single buyer at a fixed interval of time for effective implementation of Just-In-Time (JIT) Purchasing. An integrated multi-product lot-splitting model of facilitating multiple shipments in small lots between buyer and manufacturer is developed in a JIT Purchasing environment. Also, an iterative heuristic algorithm is developed to derive the common order interval, the number of intervals for each product and the number of shipments between the buyer and the manufacturer during the common interval. A numerical example is given to illustrate the savings in reduction of total cost and carbon emissions by the inventory model incorporating cap-and-trade mechanism compared to the classical inventory model. The proposed inventory model could be useful for the practical solution of two-echelon supply chain inventory problem under cap-and-trade mechanism.

Implementing Green Supply Chain Management for Online Pharmacies through a VADD Inventory Model.

Online pharmacies are an important part of the modern healthcare system. They interact with customers through well-designed web interfaces to deliver the healthcare customers need. In addition to well-designed web interfaces, online pharmacies rely on an effective supply chain system to provide medical supplies and services, and especially effective inventory management for supply systems. As green supply chain management (GSCM) becomes increasingly considered by countries, how to develop a sustainable inventory model that takes into account the revenue growth of an online pharmacy while preventing waste and reducing energy costs has become very important. In line with this trend, the study develops a sustainable inventory model that focuses on both economic aspect (profit) and environmental aspect (losses from excessive inventory) within a framework of a single period multi-product inventory model. Specifically, the sustainable inventory model applies the visual-attention-dependent demand (VADD) rate to characterize customer demand in an online trading environment, thereby seeking a profitable marketing strategy and reducing losses due to excessive inventory. Since the complexity of model optimization will drastically increase due to the inclusion of many products in the problem, a Genetic Algorithm (GA) based solution procedure is proposed to increase the feasibility of the proposed model in solving real problems. The sustainable inventory model and the solution procedure are illustrated, compared, and discussed with an online pharmacy example. Additionally, a sensitivity analysis is formulated to study the influence of model parameters on the model solution, the loss of unsold inventory that results in a waste of resources and energy, and the profit of online pharmacies.

Single Manufacturer and Multiple Retailers Multi-Product Inventory Model under Cap-and-Trade Mechanism

Single Manufacturer and Multiple Retailers Multi-Product Inventory Model under Cap-and-Trade Mechanism

Simultaneous pricing and inventory decisions for substitute and complementary items with nonlinear holding cost

In practice, the holding cost in inventory models can be considered as linear or nonlinear functions. Nevertheless, nonlinear holding cost rarely attracted the attention of the researchers, and to our knowledge, it is novel in the presence of complementary or substitute items. It can also be interpreted as a way to include the perishability of products. Except for the perishability, nonlinear holding cost can be employed for other purposes like cold supply chain. In this paper, a new pricing method based on a multi-product inventory model is presented for complementary and substitute items. This paper aims to find the optimum value of the replenishment cycle and prices for the products supplied together (complementary) or interchangeable (substitute), such that the total cost of the inventory system is minimized. Demand is assumed as a price sensitive function while the proposed model is trying to obtain the optimal values of prices and the replenishment cycle simultaneously.

A multi-product inventory management model in a three-level supply chain with multiple members at each level

A multi-product inventory management model in a three-level supply chain with multiple members at each level

A single-retailer multi-supplier multi-product inventory model with destructive testing acceptance sampling and inflation

ABSTRACTIn this paper, a multi-product inventory problem is investigated in which a retailer buys items from different suppliers based on their purchasing costs and defective rates. Due to the warehouse and staff constraints involved, the inventory cycle consists of two parts. The first part corresponds to a screening period in which a destructive testing acceptance-sampling plan is used to accept or reject a lot. The other part is for selling the items. In the screening period, a lot that is rejected is returned to the suppliers where another lot is claimed for substitution at no cost. Shortage occurs during the screening period and the defective items are sold at a lower price at the end of the second part of the cycle. As we show that the problem belongs to the class of NP-hard problems, a particle swarm optimization (PSO) and a genetic algorithm (GA) is used to solve it.

A multiproduct inventory control model for supply of two types of goods at random interval between deliveries

A multiproduct inventory control model for supply of two types of goods at random interval between deliveries

Modelo de inventario multi-producto, con pronósticos de demanda y optimización Bayesiana

La complejidad de las cadenas de suministro exige mejores métodos para programar los inventarios de una empresa. En este trabajo se presenta una comparación entre modelos de pronósticos de demanda de múltiples productos, eligiendo el mejor entre: ARIMA, Suavización exponencial, Regresión Lineal Bayesiana y un Modelo Lineal Dinámico Bayesiano. Para ello, primero se realiza una simulación de casos donde no hay una Distribución Normal en las series de tiempo, segundo, se estiman las predicciones de ventas de tres productos de una estación de servicios de gasolina con los cuatro modelos, encontrando los mejores resultados para la Regresión Lineal Bayesiana. Seguido a esto, se presenta la optimización de un Modelo de Inventarios Multi-Producto. Para definir la política de pedidos, inventarios, costos y ganancias, se utiliza una búsqueda bayesiana, que integra elementos de búsqueda Tabú para mejorar la solución. Dicha Optimización del Modelo de Inventarios se aplica a un caso de una estación de combustibles en Colombia.

Multi-product inventory model for cold items with cost and emission consideration

While sharing storage and transportation units is common for many product types, cold items usually have different temperature requirements and as a result, not all items can share a holding/transportation unit. Consequently, the type of products and their compatibility with other products needs to be considered in the inventory model. In this paper, we propose multi-product inventory models for cold items. The models determine the inventory levels that minimize either the cost or carbon-equivalent emissions. We model the compatibility of items as a constraint in the inventory model. To solve the model, we first find an appropriate “family of products” that can share a storage/transportation unit. Then, for each family of products we develop an approximate solution method to determine the order quantity of each product within a family. Numerical experiments demonstrate the solution procedure, and provide managerial insights into cold item inventory policies.

Production and shipment policy under dynamic demand in the supply chain environments

This paper considers an integrated multi-product (1:N) inventory model where a manufacturer produces multiple products via a cyclic production and supplies them to N buyers. The objective is to establish a production and delivery planning under the sequence of dynamic demands at the minimum total cost of the entire system (manufacturer and multiple buyers) subject to some constraints of the range on the product delivery interval between each buyer and the manufacturer. Some solution properties are characterised, with which a heuristic solution algorithm is derived. Computational experiments with numerical problems show that the heuristic algorithm finds good solutions within a reasonable time.

A bi-objective continuous review inventory control model: Pareto-based meta-heuristic algorithms

In this paper, a bi-objective multi-product (r,Q) inventory model in which the inventory level is reviewed continuously is proposed. The aim of this work is to find the optimal value for both order quantity and reorder point through minimizing the total cost and maximizing the service level of the proposed model simultaneously. It is assumed that shortage could occur and unsatisfied demand could be backordered, too. There is a budget limitation and storage space constraint in the model. With regard to complexity of the proposed model, several Pareto-based meta-heuristic approaches such as multi-objective vibration damping optimization (MOVDO), multi-objective imperialist competitive algorithm (MOICA), multi-objective particle swarm optimization (MOPSO), non-dominated ranked genetic algorithm (NRGA), and non-dominated sorting genetic algorithm (NSGA-II) are applied to solve the model. In order to compare the results, several numerical examples are generated and then the algorithms were analyzed statistically and graphically.

Multi-objective linear fractional inventory model of multi-products with price-dependant demand rate in fuzzy environment

In this paper, we propose a multi-criteria decision making approach for the solution of a multi-product inventory model without shortages. The model is considered over infinite horizon with price-dependant demand rate. The proposed model is formulated as a fractional multi-objective optimisation problem along with four constraints: budget constraint, space constraint, number of order constraint, and budgetary constraint on ordering cost of each item. The proposed inventory model becomes a multiple criteria decision making (MCDM) problem in fuzzy environment. This model is solved by multi-objective fuzzy goal programming (MOFGP) approach. Two numerical examples are given to illustrate the proposed model.

Inventory Control and Replenishment of Multi-Product Multi-Echelon Based on Time Cost Under JMI Environment

Joint managed inventory is an advanced supply chain inventory management tool, which will effectively tackle the complicated problem between the inventory cost of supply chain and service level. The research on inventory model and its’ control under JMI environment is a hot issue at present. In this paper, the authors deeply discuss the question of the inventory time costs about the multi-product and multi-echelon control model and its’ replenishment strategy under JMI environment. With considering the foundation of JMI and time cost, the authors propose the multi-product multi-echelon inventory cost control model under time cost. Then formulate corresponding replenishment strategy. At last, through a numerical example, the authors discover that the multi-product multi-echelon joint inventory management based on time cost can effectively reduce the total inventory costs and improve the competitiveness of the entire supply chain.

Stochastic Multiproduct Inventory Models with Limited Storage

This paper studies multiproduct inventory models with stochastic demands and a warehousing constraint. Finite horizon as well as stationary and nonstationary discounted-cost infinite-horizon problems are addressed. Existence of optimal feedback policies is established under fairly general assumptions. Furthermore, the structure of the optimal policies is analyzed when the ordering cost is linear and the inventory/backlog cost is convex. The optimal policies generalize the base-stock policies in the single-product case. Finally, in the stationary infinite-horizon case, a myopic policy is proved to be optimal if the product demands are independent and the cost functions are separable.

Optimality of (σS)-type policies for a stationary multi-product inventory model with a canonical diffusion process as demand process

The presented multi-product inventory problem is a special impulse-control problem of canonical diffusion processes and is considered within a general, time-discrete, Markovian decision model. A proof of the optimality of a (σS) type policy is given by using a policy iteration method