Multi-item Inventory Model Research Articles

Probabilistic Multi-Item Inventory Model for Chemicals in Regional Drinking Water Company

Inventory management of chemicals in The Regional Drinking Water Company (Perusahaan Daerah Air Minum, PDAM) is known to play an essential role in ensuring the smooth production of clean water and preventing shortages of chemicals that can affect production. At present, 2 primary models for multi-item inventory replenishment are under consideration by PDAM, namely individual and joint replenishment of items. Therefore, this study aims to evaluate the efficiency and effectiveness of individual and joint replenishment models based on uncertain demand with specific probability distribution. The results showed that a probabilistic inventory model (Q, r) with individual replenishment for chemicals in PDAM was recommended.

MULTI-ITEM PROBABILISTIC INVENTORY MODELS CONSIDERING DISCOUNT, EXPIRATION, WAREHOUSE CAPACITY, AND CAPITAL CONSTRAINTS

In general, companies have inventory stored in warehouses to be used or sold in the future. To optimize inventory, companies require a model to determine the appropriate order quantity and optimal reorder timing to minimize total inventory costs. To stay within the set capacity, several factors need to be considered in inventory management, such as a product's shelf life, warehouse capacity, and capital. On the other hand, suppliers may offer discounts, and companies tend to take advantage of them. However, they must consider the warehouse capacity and capital availability. This paper constructs two probabilistic multi-item inventory models, considering discounts, expiration, warehouse capacity, and capital constraint. The first model considers all-unit discounts, while the second deals with incremental discounts. We consider three items to be managed and examine three replenishment policies, namely individual order, joint order, and a combined policy of individual and joint order, to minimize the total inventory cost. Sensitivity analysis is performed on the joint order policy to determine the influence of parameter values' changes on the reorder time and total inventory cost.

A deterministic multi-item inventory model with quadratic demand under neutrosophic and pythagorean hesitant fuzzy programming approach

In this paper, a deterministic fuzzy inventory model with quadratic demand pattern, time-dependent holding cost, and time-dependent deterioration has been created. We have taken the rate of shortage as fully backlogged. In traditional inventory model, most of the cost parameters were taken as crisp. But in real world, fuzzy cost parameters are more realistic to appear instead of crisp parameters. Due to uncertainty we have considered all the cost parameters as hexagonal fuzzy number. We have regarded all of the cost parameters as hexagonal fuzzy numbers due to uncertainty. Our primary goal is to reduce the total average cost, and for that we've covered two optimization techniques: the Pythagorean Hesitant Fuzzy Programming Approach (PHFPA) and the Neutrosophic Hesitant Fuzzy Programming approach (NHFP).Through extensive numerical experiments and sensitivity analysis, the effectiveness and practicality of the proposed model are demonstrated. Comparative studies with traditional inventory models underscore the advantages of the Neutrosophic and Pythagorean Hesitant Fuzzy Programming Approach in managing multi-item inventory systems with quadratic demand patterns, highlighting its robustness in handling uncertain and ambiguous information.

Neutrosophic multi-item inventory control models with constraints

Inventory managers are expected to handle a large number of items in their inventory while adhering to budgetary and space limits, as well as the number of items bought from vendors. Multi-item inventory models with one or more resource constraints, such as budget, space, or number of orders. This paper talks about an EOQ model in neutrosophic multi-item inventory control models with constraints. The ordering costs, the holding costs, demands, storage area, investment amount, and the maximum average number of units are considered as triangular neutrosophic numbers, as opposed to crisp values, to make the inventory model more realistic. This idea is used to decide the neutrosophic optimal order quantities with the assistance of the Lagrange multiplier. Eventually, the proposed method is delineated with a numerical instance and the results are analysed briefly.

Development of a Multi-Item Inventory Model by Considering Perishable and Return of Goods in a Hospital Pharmacy

In determining an inventory's quantity, some factors need to be considered. The factors to be considered in the pharmaceutical industry are the fluctuating demand factor (diseases are unpredictable) and the perishable factors. The purpose of this paper is to propose a probabilistic inventory model by considering perishable and return of goods. Compared to the previous models, the developed model has lower inventory costs when compared to the model not considering the return of goods and higher inventory costs when compared to the model that considers deterministic demand patterns. The sensitivity analysis was done to see the behavior of the total cost, component costs, and time to order. The parameters to be changed for the sensitivity test were a fraction of good condition goods, holding costs per unit per period, and ordering cost per unit per period. The analysis showed that total cost, based on joint order, is sensitive to the fraction of good condition products. In general, the model was perceived as able to describe the behavior of the model components.

A cost analysis on Multi-item Inventory model for Factory Outlets with investment constraint under ranking Asteroid Fuzzy Set

Purpose of the study: A multi-item inventory model for factory outlets in crisp and fuzzy sense are formulated in the fuzzy environment with investment under one constraint has been considered. In this model, demand is constant and is related to the price per unit item. The asteroid fuzzy set is defined and is properties are given.
 Methodology: The parameters involved in this model represented by asteroid fuzzy set. The average total cost is defuzzify by ranking method.
 Main Findings: The analytical expressions for maximum inventory level and average total cost are derived for the proposed model by using nonlinear programming technique. A numerical example is presented to illustrate the results.
 Applications of this study: Ranking Asteroid fuzzy set is considered profitable in small businesses. Here we considered the factory outlet .Also its use is considered to help the small scale entrepreneurs during festival period and pandemic situation.
 Novelty/Originality of this study: In this paper, a novel approach to handle the asteroid fuzzy set is proposed. It uses ranking the cost parameters of the asteroid fuzzy set with the best approximation level. The parameters involved are asteroid fuzzy set and are all ill-defined in nature.

Inventory Policy for Retail Stores: A Multi-Item EOQ Model Considering Permissible Delay in Payment and Limited Warehouse Capacity

The retail industry such as minimarkets has many products consisting of several types of products that have expiration dates. Their warehouses have limited capacity, making it difficult to make decision about optimum inventory. Most of the suppliers will give permissible delay in payment, that can be used to increase income potential through earned by considering the risk of fines imposed if payments are exceeded and help companies raise capital before generating sales. These three factors must be considered when developing the inventory model. The purpose of this study is to develop a multi-item inventory model by considering perishable or damaged products, permissible delay in payment in limited warehouse. Model development is carried out in 2 stages. The first stage was the development of a multi-item EOQ model by considering product defects and permissible delay in payment. The second stage model is by adding a capacity constraint factor to the model. The results obtained are getting the optimal order quantity by considering the number of product types, product damage factors, late payments in limited warehouses, the best ordering policy can be found, and it is known that the total inventory costs to changes in parameters are good and sensitive to changes in percentage, interest percentage, payment allowances, and warehouse capacity through sensitivity tests.

Optimal Pricing, Ordering, and Replenishment Policies in a Multi-Item Inventory System for Deteriorating Items Under Time-Varying Backlogging Rate

In today’s advanced society, customers are influenced by products full of choices. For more sales, the retailer should maintain an inventory of each variety of items. These varieties have been seen in most food shops, fruit shops, fashion shops, electronic shops, etc., where the products deteriorate with time elapse. Depending on the customer’s demand, the stock out time of different deteriorating items is different. Assimilating all these varieties, in this paper, we have developed a multi-item inventory model for deteriorating items where demands depend on the sales price of the product. Shortages are allowed and partially backlogged with a time-dependent backlogging rate. The multi-item mechanism’s prime objective is to find the optimal sales price, order quantity, time length up to zero inventory, and cycle length to maximize the retailer’s overall profit. Finally, numerical examples are provided to illustrate the model with some managerial insights.

Timing intermittent demand with time-varying order-up-to levels

Current intermittent demand inventory control models assume that the demand interval is memoryless: the probability of observing a positive demand does not depend on the time since the last demand occurred. Contrarily, several forecasting contributions suggest that demand intervals contain more distributional information. We find that the data of the M5 forecasting competition confirms this. Therefore, we propose an inventory control model that explicitly uses the full distributions of the demand sizes and intervals and thereby acknowledges that the probability of a demand occurrence may vary throughout the interval. To exploit this information, we also allow for time-varying order-up-to levels that flexibly adjust inventories according to the dynamic requirements. We derive the long-run average holding costs, non-stockout probability, order fill rate, and volume fill rate. Inspired by an analogy with multi-item inventory control models, we propose a greedy marginal-analysis heuristic to optimize the order-up-to levels, which we benchmark against the optimal solution on theoretical instances. In a simulation study on the M5 competition data we demonstrate this method’s improved on-target service performance compared to that of traditional solutions. We furthermore show that target service levels can be achieved at significantly lower costs with time-varying than with fixed order-up-to levels.

An Asymptotically Optimal Heuristic for Multi-Item Inventory Models with Joint Inventory Constraints

An Asymptotically Optimal Heuristic for Multi-Item Inventory Models with Joint Inventory Constraints

Deterioration Item Inventory Policy with Sales Discount under Order Quantitiy Discount and Permissible Delay in Payments

Most of the items sold at supermarkets have an expiration date. While many suppliers offer discounts and allow non-cash payments during certain time intervals. Supermarkets has the opportunity to take this offer so that profits can be increased, but they are faced with the nature of goods that have a shelf life. The greater the number of items stored, the greater the risk of expiration. Therefore, it is necessary to regulate the right inventory control policy so that the total costs incurred can be minimized. In this paper, it will be developed a multi-item inventory model of deteriorating item with sales discounts, all unit quantity discount from supplier and permissible delay in payments. The aim is to determine the right policy for controlling the inventory of items that have an expiration date in order to minimize losses and total inventory costs. This model is expected to help supermarkets in determining the optimal number of orders and when to place orders so as to minimize total inventory costs. The model solution is carried out with an optimization approach based on the parameters that affect the model. A numerical example is given at the end of this paper for model validation and illustrates the model solving algorithm.

A Multi-Item Probabilistic Inventory Model that Considers Expiration Factor, All Unit Discount Policy and Warehouse Capacity Constraints

The characteristics considered in this study are probabilistic demand, perishable products, and warehouse constraints for multi-item inventory models. This condition occurs in several industries that consider perishable factors and warehouse constraints, namely companies that produce food, food sales agents, and retail that sell goods to end customers. The Karush-Kuhn-Tucker Condition approach was used to solve the warehouse capacity problem to find the optimum point of a constrained function. The results of the developed inventory model provide two optimal ordering times, namely ordering time-based on warehouse capacity and joint order time, and the two ordering time values ​​will be compared to determine which ordering time is optimal. In addition, the sensitivity analysis to the model was done to analyse the total inventory costs in a planning horizon, the time between goods ordering from one cycle to the next cycle, and the number of items that will expire. The parameters to be changed for the sensitivity test were warehouse constraint, a fraction of good condition goods, holding costs per unit per period, and all unit discount factors. The sensitivity analysis was done to see the behaviour of the total cost, time to order changes, and the quantity of perished products. The result of model testing and sensitivity analysis showed that total cost, based on joint order, is sensitive to the fraction of good condition products, discount, and holding cost. The joint order was not sensitive to the warehouse capacity. In general, the model was perceived as able to describe the behaviour of the model components.

Multi-item inventory policy with time-dependent pricing and rework cost

The price of broiler chickens at the consumer level varies daily. The price can be very low or otherwise. The price has resulted from the imbalance between the availability of chicken from suppliers and the market demand. As a result, demand will also fluctuate because it is influenced by consumer purchasing power. When the price of live chickens is low, the carcass company will usually buy in large quantities and expect to sell them at a higher price. The problem arises when the chicken overstock company will risk product damage due to product buildup in the refrigerated warehouse, so rework is necessary. In this paper, we will be developed a multi-item inventory model that considers material prices that vary to time, probabilistic demand, and rework costs. The aim is to determine the right policy for controlling frozen chicken products' inventory to minimize losses and total inventory costs. This model can evaluate the best time to order broiler chickens, how much to order, how long the interval between orders, and the optimal number of orders, resulting in minimum total inventory cost per period. The model solution is carried out with an optimization approach based on the parameters that affect the model. A numerical example is given at the end of this paper for model validation and illustrates the model solving algorithm.

Possibilistic mean of generalized non-linear intuitionistic fuzzy number to solve a price and quality dependent demand multi-item inventory model

In real-life problems, there is always a situation where a decision maker is engrossed in detecting multi aspiration levels for the purposes that cannot be explained in specific way. To address this, the paper aims to consider a new generalized non-linear intuitionistic fuzzy number and, hence, defined the possibilistic mean of it with possibility measures. In addition, we have proposed the arithmetic operations of different generalized non-linear intuitionistic fuzzy number using $$(\alpha , \beta )$$ -cut method. The applicability of the developed operations are explained with a case study from the multi-item inventory model in which the price and quality dependent demand are modeled under the generalized non-linear intuitionistic fuzzy environment. A new defuzzification method has been developed to solve the developed multi-item inventory model. Finally, numerical and graphical representation of the proposed model has been discussed to highlight the superiority of the presented work.

Optimization of the lubricating oil inventory policy applied in a mining company

ABSTRACT The mining industry should sustain mass and continuous production with an essential contribution of high-capacity machinery. Therefore, spare parts inventory management is vital in ensuring the intended mining production rate as an integral part of maintenance policies. In this paper, a mixed-integer model is presented to solve a multi-item and multi-supplier spare parts inventory model. This model is addressed to a lubricating oil inventory problem in one of the biggest multi-process mining companies in Turkey. The optimisation results show that the company’s current lubricating oil inventory policy can be improved financially by yielding an annual saving up to ₺18,566.

Managing Operations of a Hog Farm Facing Volatile Markets: Inventory and Selling Strategies

Problem Definition: We study a dynamic finishing stage planning problem of a pork producer who gets to see how many market-ready hogs she has available for sale at the beginning of each week and the current market prices. Then, she must decide how many hogs to sell to a meatpacker and on the open market. The producer has a contract to deliver a fixed quantity to the meatpacker each week priced according to a predetermined formula that depends on market commodity indices. She pays a penalty if she fails to deliver. The numbers of hogs that become market-ready every week, all costs, and all prices fluctuate over time. Academic/Practical Relevance: We solve the finishing stage planning problem as a dynamic, multi-item (hogs of different weight fetch different prices) inventory model with uncertain supply and stochastic prices. Methodology: We use a dynamic programming approach to derive an optimal policy and a one-period look-ahead heuristic informing the farmer on what hogs to sell at the beginning of each week. Results: We show there are sell/hold thresholds that depend on the available hogs' weights, quantities, and prices. Unfortunately, identifying the thresholds requires messy computations. So, we propose an approximate dynamic programming approach that preserves the optimal policy structure and produces a sharp heuristic that is easy to implement. Managerial Implications: Numerical experiments calibrated to a pork producer's data (The Maschhoffs) reveal the optimal policy is a substantial improvement over the existing practice (around 25% on average), and the one-period look-ahead policy is as close as 1.76% from the optimal. The majority of the improvement value over the current practice is recognizing and exploiting the ``real option'' value of under-weight hogs in hedging supply uncertainty and stochastic prices.

WITHDRAWN: Optimization of unconstrained multi-item (EPQ) model using fuzzy geometric programming with varying fuzzification and defuzzification methods by applying python

In this paper, an unconstrained multi item inventory model for a single vendor and single buyer with constant demand is considered. Fuzzification was done by using five different types of fuzzy numbers, which are triangular, trapezoidal, pentagonal, hexagonal, and octagonal. To minimize the total cost of the (EOQ) Economic order quantity, is solved by using geometric programming, it gives maximize the optimal Shipment order quantity and optimal Shipment and The optimal policy for the developed model is determined using the geometric programming after the defuzzification of the cost function with the Robust ranking and singed distance method. We acquainted a substitute arrangement with the manual figuring’s, supplanted by python program which lessens the endeavours and blunders. Mathematical models and an affectability investigation study are given to feature the contrasts among crisp and the fuzzy cases.

Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming

<p style='text-indent:20px;'>In recent years, numerous studies have been conducted regarding inventory control of deteriorating items. However, due to the complexity of the solution methods, various real assumptions such as discrete variables and capacity constraints were neglected. In this study, we presented a multi-item inventory model for deteriorating items with limited carrier capacity. The proposed research considered the carrier, which transports the order has limited capacity and the quantity of orders cannot be infinite. Dynamic programming is used for problem optimization. The results show that the proposed solution method can solve the mixed-integer problem, and it can provide the global optimum solution.</p>

Effect of reliability on multi-item inventory system with shortages and partial backlog incorporating time dependent demand and deterioration

This study presents a new model of multi-item economic order quantity where deterioration is time and reliability dependent. The demand rate of this system is an advertisement, time, and reliability dependent, and also the ordering cost is reliability dependent. The paper develops a cost-effective ordering inventory model where the increase in reliability of the item leads to a rise in demand and decreases the rate of deterioration. The cycle lengths for each item of the system are constant and the same. The shortages are allowed in this economic order quantity model, which are partially lost in sales and partially backlogged. Numerical examples and graphical representation are provided to illustrate the proposed model and the significant features of the results are discussed. The proposed multi-item inventory model is solved using MATLAB, and the effects of different parameters on the inventory model are presented through sensitivity analysis.

Multi objective fuzzy inventory model with deterioration, price and time dependent demand and time dependent holding cost

In this paper, we have formulated an inventory model with time dependent holding cost, selling price as well as time dependent demand. Multi-item inventory model has been considered under limitation on storage space. Due to uncertainty all the require cost parameters are taken as generalized trapezoidal fuzzy number. Our proposed multi-objective inventory model has been solved by using fuzzy programming techniques which are FNLP, FAGP, WFNLP and WFAGP methods. A numerical example is provided to demonstrate the application of the model. Finally to illustrate the model and sensitivity analysis and graphical representation have been shown.