Multi-item Inventory System Research Articles

Optimizing a Fuzzy Multi-Item Inventory System and Ordering Cost Depletion Contingent on Lead Time With Carbon Emission Cost

Optimizing a Fuzzy Multi-Item Inventory System and Ordering Cost Depletion Contingent on Lead Time With Carbon Emission 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.

A MULTI-ITEM INVENTORY MODEL WITH VARIOUS DEMAND FUNCTIONS CONSIDERING DETERIORATION AND PARTIAL BACKLOGGING

Inventory management is an important thing to be considered in order to run the activities of a company smoothly. By considering deterioration factor, partial backlogging policy and different type of demand functions, we develop a mathematical model for multi-item inventory system. In this paper, three inventory models with constant deterioration, partial backlogging, with various demand functions are developed. We consider inventory-dependent demand, time-dependent demand and exponential demand function in each model. In addition, we also consider the replenishment policies for those three items, viz. individual replenishment, joint replenishment and combination both individual and joint replenishments. Sensitivity analysis of the models is also performed, and we found that the ordering cost greatly affects the total inventory cost when comparing the available replenishment policies.

Multi-Item Inventory Systems with Joint Expected Value and Chance Constraints: Asymptotically Optimal Heuristics

Multi-Item Inventory Systems with Joint Expected Value and Chance Constraints: Asymptotically Optimal Heuristics

УПРАВЛЕНИЕ ПРЕДУПРЕДИТЕЛЬНЫМИ ЗАМЕНАМИ И ЗАПАСАМИ ДЕТАЛЕЙ И УЗЛОВ В АВТОБУСНОМ ПАРКЕ

The article deals with the problems of coordination of works on the maintenance of buses, their current repair and preventive replacements. The task was set to select a rational distribution criterion and the frequency of preventive replacements, which leads to coordination with the bus fleet stock management system. To model the inventory management system, the article proposes a factorial model for generating an interconnected series of spare parts supplies, which is included in a generalized analytical and simulation model of a multi-item inventory management system.

Constrained Stochastic Inventory Control Models for Multi-Item with Variable Demand

Constrained multi-item inventory system with variable demands are considered. The demand rates of five selected multi-item - Cowbell, Milo, SMA, Cerelac and Golden Morn were modeled as Weibull, Normal and Lognormal probability distributions respectively with the aid of chi-squared multinomial goodness-of-fit test. The respective probability distributions with estimated location parameters: 491.55, 536.92, 10.5, 2.1926 and 5.3103 were used as the basis of probabilistic inventory models to obtain dynamic EOQ for each item under each constraint subject to Kuhn, Karush and Tucker (KKT) conditions as against the use of simple averages in deterministic inventory models. The optimal values of these constraints: available warehouse space (124sq.ft), specified level of inventory (94 units), limited capital (76,671.52 naira) and number of orders (1/month) were obtained using the optimal EOQ values to establish optimal inventory level and constraints level/capacity for each item in order to avoid shortage or excess stock.

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.

Heuristics for setting reorder levels in periodic review inventory systems with an aggregate service constraint

Inventory managers are responsible for the trade-off between inventory holding costs and customer service. In this paper we consider a periodic review multi-item inventory system with exogenous lot-sizes and backordering. The objective is to minimize the total inventory holding costs subject to the constraint that the aggregate fill rate should be at least equal to a target level. The aggregate fill rate is a weighted average of the fill rates of all items in the assortment. We consider three ways of defining this aggregate fill rate: using generic weights, weights based on the average demand (volume) or weights based on the average (monetary) turnover. We show that the definition of the aggregate service can have huge effects on the performance of the system. So, inventory managers should be very careful on which definition to apply. We also derive four heuristics to determine the reorder levels for all items. One heuristic is very generic and can be applied to many problems including multi-item multi-echelon inventory systems and systems with a constrained aggregate ready rate. Since multiple assumptions made to derive the heuristics are common assumptions made in the literature, we first test the accuracy of these approximations using simulation. Next, we evaluate the heuristics based on data from a large international reseller. The heuristic based on the most accurate approximation performs best, is close to optimal and very efficient. Savings compared to no service level differentiation are large (up to 28.7%) and depend on the definition of the aggregate service.

Alignment between an ABC classification and results from an optimization approach

The paper analyzes a multi-item inventory system, using independent (R,Q) policies. The aim is to minimize the average stock level while keeping a weighted (across items) fill rate service level at a given target. The paper explores whether the optimal order sizes and the optimal safety factors are aligned with the ABC classification. Our results show that A items should be ordered more frequently followed by B items and C items. Concerning the optimal safety factors, our results depend on the weights applied in the specification of the weighted service level. If all items have equal weight, A items should have the lowest safety factors followed by B and C items. If the weights are the demand rates, the ranking of the safety factors follows the ratios between the demand rate and the unit purchase price, and the higher this ratio is, the higher is the optimal safety factor. However, this ranking is completely aligned with the ABC classification given that the demands are transformed into monetary units.

A fully polynomial time approximation scheme for the Replenishment Storage problem

The Replenishment Storage problem (RSP) is to minimize the storage capacity requirement for a deterministic demand, multi-item inventory system with specified individual reorder cycle lengths. The reorders can only take place at integer time units. This problem was shown to be weakly NP-hard for constant joint cycle length (the least common multiple of all individual cycle lengths). We devise here the first known FPTAS for the RSP with different individual cycle lengths and constant joint cycle length.

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.

Iventory policy for multi item products by short expiration period

Inventory planning is an importantpartin the industry. For industries that produces product with short expiration period, such as the food industry, product expiration period is an important factor that cannot be released in determining the inventory model. Small and Medium Enterprises (SMEs) in the food industry produce the product has a short expiration period of 3 days. Products that have exceeded the expiration period will be returned to the industry and will bear the product expiration costs. The SMEs obtain the expiration costs of IDR 1,518,800 with a total expired product of 600 units. SMEs have not considered multi-item inventory systems. Order policy conducted by single order system. Therefore, efforts should be made to reduce the quantity of expired products, and find out the optimal order quantity and time of ordering goods together (joint order). The optimal order quantity planned with the EOQ method. The result indicate thatoptimalquantity of orders on lapis legit as many as 60 units,30 units of Caramel, 54 units of Sponge cake, 6 units of Brownies and 108 units of Bika Ambon, frequency of delivery 28 times in a month with a total inventory cost of IDR 4,548,044.

The Replenishment Schedule to Minimize Peak Storage Problem: The Gap Between the Continuous and Discrete Versions of the Problem

The replenishment storage problem (RSP) is to minimize the storage capacity requirement for a multiitem inventory system, where each item has a given reorder size, uniform demand, and cycle length. The discrete RSP, which allows reorders to take place only at integer time units within the cycle, is NP hard for constant joint cycle length (the least common multiple of the length of all individual cycles). We show that discrete RSP is weakly NP hard for constant joint cycle length and strongly NP hard for nonconstant joint cycle length. For constant joint cycle-length discrete RSP, we present a pseudopolynomial time algorithm that solves the problem optimally and the first known fully polynomial time approximation scheme for the single-cycle RSP. The scheme is utilizing a newly introduced integer programming formulation of the problem. For the strongly NP-hard RSP with nonconstant joint cycle length, we devise a polynomial time approximation scheme, which runs in linear time for fixed $\epsilon$. This paper further explores the relationship of discrete RSP with the continuous RSP, where reorders can take place at any time within a cycle.

A two-stage heuristic approach for a multi-item inventory system with limited budgetary resource and all-units discount

Abstract This paper deals with a multi-item inventory system with a discrete stochastic demand stream under continuous review in which a limited resource and all-units quantity discount in purchasing are available. The resource is sharable and price-dependent which can be investments or budgetary. Most existing models focus on the resource restriction as a hard constraint, which is not always the common case since in some inventory systems resource shortage could be provided by renting extra resource and incurs the resource shortage cost to the system. In this case, as one of the recent extensions of (r, Q) inventory models, the resource constraint is treated as a soft constraint. By considering the discount opportunity besides the soft price-dependent resource constraint, the resource shortage cost will be dependent directly on quantity discount parameters. So, in the multi-item case the discounted price of each item is involved in determining other optimal policies. The problem is formulated as an integer nonlinear programming model. A heuristic method is presented to solve the model. According to this method, during the stages of the algorithm, the problem is separated into sub-problems which are solved by an exact method. A local search is used to improve the solutions during the algorithm procedure. In order to evaluate the efficiency of the solution approach, a lower bound on the minimum cost of the problem is proposed. Numerical evaluations based on the lower bound show that the proposed method with an average relative error equal to 3.91% performs well.

Fair no-unnecessary-waiting-time-FCFS allocation rule in multi-item inventory systems

ABSTRACTThe average customer waiting time is an important measure of service quality in systems in which customers may order multiple items. In this article, we introduce a new allocation discipline that not only eliminates the unnecessary waiting time of new customers by reallocating reserved items but also retains the fairness of the First-Come-First-Serve allocation rule. We develop analytic expressions for the average customer waiting time in the system with two items and unit demands under the new allocation rule, and our numerical experiments demonstrate a reduction in waiting time. We also provide an algorithm to evaluate the average customer waiting time when a system is with multiple items and batch ordering; simulation results show that the average customer waiting time of some demands can be significantly reduced up to 99.97%.

An efficient method for solving a correlated multi-item inventory system

We propose an efficient method of finding an optimal solution for a multi-item continuous review inventory model in which a bivariate Gaussian probability distribution represents a correlation between the demands of different items. By utilizing appropriate normalizations of the demands, we show that the normalized demands are uncorrelated. Furthermore, the set of equations coupled with different items can be decoupled in such a way that the order quantity and reorder point for each item can be evaluated independently from those of the other. As a result, in contrast to conventional methods, the solution procedure for the proposed method can be much simpler and more accurate without any approximation. To demonstrate the advantage of the proposed method, we present a solution scheme for a multi-item continuous review inventory model in which the demand of optional components depend on that of a “vanilla box,” representing the customer’s stochastic demand, under stochastic payment and budget constraints. We also perform a sensitivity analysis to investigate the dependence of order quantities and reorder points on the correlation coefficient.

Demand fulfillment probability in a multi-item inventory system with limited historical data

ABSTRACTIn a budget-constrained multi-item inventory system with independent demands, we consider the case of unknown demand parameters that are estimated from limited amounts of historical demand data. In this situation, the probability of satisfying all item demands, as a measure of demand fulfillment, is a function of the finite-sample estimates of the unknown demand parameters; thus, the demand fulfillment probability is a random variable. First, we characterize the properties of an asymptotical approximation to the mean and variance of this random variable due to the use of limited data for demand parameter estimation. Second, we use the characterization of the variance of the demand fulfillment probability for quantifying the impact of demand parameter uncertainty on demand fulfillment via numerical experiments. Third, we propose an inventory optimization problem that minimizes the variance of the demand fulfillment probability due to demand parameter uncertainty subject to a budget constraint on the total inventory investment. Our numerical experiments demonstrate that, despite the availability of limited amounts of historical demand data, it is possible to manage inventory with significantly reduced variance in the demand fulfillment probability.

An inventory model of three-layer supply chain of wood and furniture industry in the Caribbean region of Colombia

ABSTRACTThis article deals with a mathematical model for multi-item inventory system under a collaborative scheme in a three-level supply chain consisting of multiple raw material suppliers, multiple manufacturers and multiple retailers in which different cycle lengths and stochastic demand and production rates are considered for the purpose of evaluating the optimal solution. The model is also validated in the supply chain of wood and furniture industry in the Caribbean region of Colombia. In the process, suppliers of raw wood (sawmills), manufacturers of home furnishings and major retailers are participated. Results include a comparison between three-level and two-level supply chains using the collaborative scheme as well as for the non-collaborative scheme among the participating members of the chain.

Economic and environmental comparison of grouping strategies in coordinated multi-item inventory systems

The increasing concerns for sustainability throughout supply chains are enforcing managers to plan their operations considering not only economic but also environmental performance. Inventory management is one of the main determinants of the costs incurred and emissions generated throughout supply chains as it defines the level of logistical operations, freight transportation, and warehousing activities. In this study, we analyze a multi-item inventory control system with coordinated shipments. In particular, we revisit the well-known deterministic joint replenishment problem (JRP) with economic and environmental objectives under indirect and direct grouping strategies. We formulate and develop solution methods for each bi-objective JRP and compare direct and indirect grouping strategies with respect to their economic as well as environmental performance. A set of numerical studies is presented to examine the settings where a specific grouping strategy can be economically and environmentally better than the other.

A coordinated multi-item inventory system for perishables with random lifetime

This paper considers the continuous review can-order (s,c,S) policy for coordinating the replenishment of multiple perishable items with random lifetimes. For zero lead time, we model this inventory system as a Markov process. An iterative procedure is proposed to solve the joint replenishment problem for perishable items under positive lead time. We investigate the impact of perishability and cost parameters on the performance of the can-order policy and compare it to the optimal periodic review (s,S) policy.