Multi-item Inventory Control Research Articles

Multi objective optimization approach for multi-item inventory control: A case study in leather industry

PT ASA is a leather tanning company. Almost 65% of the company's assets are allocated for the procurement of raw leather, which consists of goat and sheepskin. In addition to being expensive, the availability of raw leather is also very limited. The company faces a trade-off where, on one hand, the raw material is easily decayed, but on the other hand, its availability is extremely limited, and if there is not enough inventory, the production process will be disrupted. In this research, a multi-objective optimization model is developed for controlling the inventory of raw leather using the Fuzzy Goal Programming approach. The objectives to be achieved are to minimize the total inventory cost, maximize the total quantity of raw leather that meets standards, and minimize the total cost of losses due to decayed raw leather. Based on the calculations, the fuzzy goal programming membership function value is obtained at 0.9155, with a total inventory cost over the planning horizon of IDR 10,341,630,000, a total of 1,279,542 sq ft of raw leather meeting standards, and a total loss cost due to decayed raw leather of IDR 142,911,691.

A machine learning approach to two-stage adaptive robust optimization

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote as the strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train machine learning models that predict high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. The models can be applied to problems with varying dimensions. We also introduce novel methods to expedite training data generation and reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy.

Multi-Item Inventory Control Using Economic Order Quantity (EOQ) Model with Safety Stock, Reorder Point, and Maximum Capacity in Retail Business

The presence of retail businesses in Indonesia has many positive impacts on the community, especially in improving the economy. The existence of buying and selling transactions involving suppliers, retailers, and the community as consumers can play a role in improving the national economy. Retail can be called a bridge for suppliers and consumers to meet their needs. The diversity of consumer needs requires retailers to provide a variety of products from many suppliers. Efforts that need to be made by retail businesses in order to minimize costs incurred are by controlling inventory. To prevent excessive expenditure, the inventory control method used is to apply the Economic Order Quantity (EOQ) model. The EOQ model can provide the optimum total inventory cost by adjusting the frequency of orders placed over a period of time. After obtaining the total inventory cost, the calculation of safety stock, reorder point, and maximum capacity can also be applied so that the inventory costs incurred can be minimal.

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.

예산제약이 존재하는 다기간, 다제품 재고관리문제에서 강화학습 기법의 효율성 개선 방안 연구

This paper considers the use of reinforcement learning for a multi-period, multi-item inventory control problem with a budget constraint. In the problem, we decide the order quantities of multiple items considering budget constraints so as to minimizes the total inventory cost including inventory holding cost and backlog cost. The previous literature proposed a modified Q-learning that include an optimization model in the Q-learning procedure to handle budget constrained actions, but it lacks the scalability. To address this issue, this paper proposed a two-stage method: the Q-learning learns actions without considering the budget constraint in the first stage, and an optimization model adjusts the learned actions so as to satisfy the budget constraint in the second stage. Numerical study compares the performance of the proposed two-stage method with others such as a conventional Q-learning without the budget constraint and the modified Q-learning in the literature. The numerical experiments reveal that the proposed method significantly reduces the computation time without increasing the total inventory cost.

A study of data-driven distributionally robust optimization with incomplete joint data under finite support

Missing data is a common issue for many practical data-driven stochastic programming problems. The state-of-the-art approaches first estimate the missing data values and then separately solve the corresponding stochastic programming. Accurate estimation of missing values is typically inaccessible as it requires enormous data and sophisticated statistical methods. Therefore, this paper proposes an integrated approach, a distributionally robust optimization (DRO) framework, that simultaneously tackles the missing data problem and data-driven stochastic optimization by hedging against the uncertainties of the missing values. This paper adds to the DRO literature by considering the practical scenario where the data can be incomplete and partially observable; it particularly focuses on data distributions with finite support. We construct several classes of ambiguity sets for our DRO model utilizing the incomplete data sets, maximum likelihood estimation method, and different metrics. We prove the statistical consistency and finite sample guarantees of the corresponding models and provide tractable reformulations of our model for different scenarios. We perform computational studies on the multi-item inventory control problem and portfolio optimization using synthetic and real-world data. We validate that our method outperforms the traditional estimate-then-optimized approaches.

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.

Dynamic mixed-item inventory control with limited capital and short-term financing

For most companies, operational decisions and financing decisions jointly affect the earnings and efficiency. Although these effects have been studied in various contexts, there is little literature on the dynamic multi-item inventory control problem, especially the case of multi-item product firms which have limited capital and cannot get easy access to external financing. A serious problem is: What are the optimal procurement strategy and financing strategy for a company with a shortage of funds? In this article, we study a dynamic mixed-item inventory control problem where a capital-constrained firm periodically purchases items from suppliers and assembles some items to meet product orders from customers. In the single period, building the traditional model to obtain three inventory strategies. When the capital is sufficient, all items are purchased. When the capital is insufficient, perishable items are purchased. When the capital is appropriate, both perishable items and part of durable items are purchased. In the multi-period, by constructing new variable value to shape two types of functions and sequences, the procurement strategies of manufacturer at different levels of value are obtained. In the financing decision-making, the manufacturer limits the financing due to the limitation of the financing interest rate, so as to further define the concept of the joint bankruptcy point.

Inventory management in a closed-loop supply chain with advance demand information

We study inventory control for rental operations in a closed-loop supply chain. In such a system (e.g., Netflix), customers create online queues in a service provider’s website to indicate the items that they would like to rent. Leveraging this advance demand information, we propose effective forecast models and formulate a multi-item inventory control problem. We prove that the (L,U) policy is optimal in our multi-item setting. We also consider an aggregate service level constraint across all items and propose heuristics.

Inventory Management in a Closed-Loop Supply Chain with Advance Demand Information

We study forecast and inventory control problems for rental operations in a closed-loop supply chain. In such a system (e.g., Netflix for DVD rentals), customers create online queues in a service provider's website to indicate the next items that they would like to rent. Leveraging this advanced demand information, we propose effective forecast models for item-level returns and demands. Based on the forecast models, we formulate a multi-item inventory control problem. We prove that the (L;U) policy, which was shown to be optimal in single-item settings, remains to be optimal in our multi-item setting. Moreover, we show that the problem is separable in items, so the optimal solution can be computed by solving multiple single-item problems. In practice, the service provider would also like to impose a minimum aggregate service level across all items. This aggregate service level constraint complicates the problem significantly and the (L;U) policy is no longer optimal. In this case, we propose an inventory heuristic based on a single-period, multi-item formulation of our problem. This heuristic outperforms similar ones proposed in the literature and attains the optimal solution in all cases in a benchmark study.The online supplement is available at http://ssrn.com/abstract=2838885.

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.

Joint Replenishment Problem in Multi-Item Inventory Control with Carrier Capacity and Receiving Inspection Cost

In the present paper, a multi-item inventory problem with the capacity to replenish carriers is considered. In the present study, we propose a model that considers truck capacity, truck cost, and receiving inspection cost with inventories and shortages in inventory management simultaneously. A number of studies have examined the minimum total cost while considering the ordering cost as fixed and not considering the carrier capacity or receiving inspection cost. However, we consider the stepwise ordering cost, which changes in a stepwise manner according to the ordered quantity and the capacity of the carrier. In addition, we consider a receiving inspection cost that is defined not only by ordered quantity but also by ordered item variety. The problem considered herein was formulated as a mathematical programming problem in a finite planning period, and valid inequalities were considered. We could consider individual objective functions for ordering, holding, lost sales, and receiving inspection cost together. We can observe that the receiving inspection cost could be reduced by aggregating the order quantity.

Improving DVD-by-Mail Operations for In-Circulation Items with Accurate Forecasts

In this paper we study forecast and inventory control problems for DVD-by-mail operations. Specifically, we focus on inventory management for in-circulation items after the new release rental peak. For such items, the demand volume is usually low and unpredictable. Leveraging on the unique operational feature of DVD-by-mail services, we propose effective forecast models for item-level returns and demands. Based on the forecast models, we formulate a service-constrained multi-item inventory control problem. Unlike previous studies in the literature, which rely on approximated service levels, we develop an algorithm for computing the exact service level. The resulting inventory optimization problem is a nonlinear integer program. To tackle the computational challenge, we propose an effective solution based on a dynamic program. Our benchmark study shows that the dynamic program solution is superior to the heuristics used for similar problems in the literature, and it achieves the minimum cost in all numerical scenarios. To evaluate the performance of our forecast and inventory control methods, we conduct an extensive simulation study. Our simulation results suggest that our forecast models play a crucial role in improving the cost performance. In addition, we find that the combined value of our forecast and inventory control methods increases with service level requirements, but is relatively insensitive to customers’ return speed; these features are all desirable for practical implementations.

Genetic Algorithm-Based Coordinated Replenishment in Multi-Item Inventory Control

We herein consider a stochastic multi-item inventory management problem in which a warehouse sells multiple items with stochastic demand and periodic replenishment from a supplier. Inventory management requires the timing and amounts of orders to be determined. For inventory replenishment, trucks of finite capacity are available. Most inventory management models consider either a single item or assume that multiple items are ordered independently, and whether there is sufficient space in trucks. The order cost is commonly calculated based on the number of carriers and the usage fees of carriers. In this situation, we can reduce future shipments by supplementing items to an order, even if the item is not scheduled to be ordered. On the other hand, we can reduce the average number of items in storage by reducing the order volume and at the risk of running out of stock. The primary variables of interest in the present research are the average number of items in storage, the stock-out volume, and the number of carriers used. We formulate this problem as a multi-objective optimization problem. In a numerical experiment based on actual shipment data, we consider the item shipping characteristics and simulate the warehouse replenishing items coordinately. The results of the simulation indicate that applying a conventional ordering policy individually will not provide effective inventory management.

Multi-Item Inventory Control under Uncertainty and Non-Stationarity

Abstract This paper addresses the problem of multi-item inventory control under uncertainty and non-stationarity. Under uncertainty and in the absence of credible data on statistics of the demand the real-life management of a multi-item inventory must rely on a multi-stage procedure outlined in the paper. At the fist stage trends are identified that incorporate seasonal components of the demand and at later stages a deterministic problem of inventory control is solved. At subsequent stages a solution is analyzed of obtaining additional orders aimed at replenishing stores (safety stocks) in order to offset random deflections of the demand from the trends identified.

Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering

In this paper, we consider the stochastic joint replenishment problem in an environment where transportation costs are dominant and full truckloads or full container loads are required. One replenishment policy, taking into account capacity restrictions of the total order volume, is the so-called QS policy, where replenishment orders are placed to raise the individual inventory positions of all items to their order-up-to levels, whenever the aggregate inventory position drops below the reorder level. We first provide a method to compute the policy parameters of a QS policy such that item target service levels can be met, under the assumption that demand can be modeled as a compound renewal process. The approximation formulas are based on renewal theory and are tested in a simulation study which reveals good performance. Second, we compare the QS policy with a simple allocation policy where replenishment orders are triggered by the individual inventory positions of the items. At the moment when an individual inventory position drops below its item reorder level, a replenishment order is triggered and the total vehicle capacity is allocated to all items such that the expected elapsed time before the next replenishment order is maximized. In an extensive simulation study it is illustrated that the QS policy outperforms this allocation policy since it results in lower inventory levels for the same service level. Although both policies lead to similar performance if items are identical, it can differ substantially if the item characteristics vary.

An association clustering algorithm for can-order policies in the joint replenishment problem

Many studies have shown that the total cost of employing joint replenishment for correlated items is less than the total cost of using single-item replenishment. Savings increase dramatically when the demand between items is closely related. Although the benefits of joint replenishment are significant, it is difficult to define the demand correlation among items, especially when the number of items increases. A large number of items reduces the efficiency and advantage of the multi-item inventory control. To overcome this difficulty, an association clustering algorithm this paper proposes to evaluate the correlated demands among items. The proposed algorithm utilizes the “support” concept in association rule analysis to measure the similarity among items. Based on these measurements a clustering method is developed to group items with close demand in a hierarchal way. The can-order policy is then applied to the optimal clustering result as decided by the proposed performance index. To illustrate the benefits of the proposed association clustering algorithm for replenishment systems, a set of simulations and a sensitivity analysis is conducted. The results of the experiments show that the proposed method outperforms several replenishment models.

Discounted multi-item inventory model via genetic algorithm with Roulette wheel selection, arithmetic crossover and uniform mutation in constraints bounded domains

Genetic Algorithm (GA) with different logic structures for price breaks has been developed and implemented for a multi-item inventory control system of breakable items like the items made of glass, mud, porcelain, etc. with all unit discount (AUD), incremental quantity discount (IQD) and a combination of these discounts. Here, AUD and IQD on purchasing price with two price breaks are allowed. Also, demand and breakability of the items are stock-dependent. Shortages are not allowed. Replenishment is instantaneous. Selling price is a mark-up of the purchasing cost. For storage, warehouse capacity is limited. For the present model, GA has been developed in real code representation using Roulette wheel selection, arithmetic crossover and uniform mutation. This algorithm has been implemented successfully to find the optimum order quantities for the above inventory control system to achieve the maximum possible profit. The algorithm and the inventory model have been illustrated numerically and some sensitivity analyses with respect to breakability and demand are presented.

Genetic algorithm for multi-item inventory control problem

The main purpose of this research is to apply an approximation approach - genetic algorithm to resolve the inventory control problems which maturely developed during 1960s to 1990s. However, it is still a tough work to deal with the multi-item inventory control optimization problems. Under the constraints on inventory space or budget limitations, to solve the multi-item inventory control problem by traditional approach, it is certainly in difficulty to collect the inventory data and in complexity to compute. Fortunately, an approach is applied into this study without the constraints on multi-item inventory system. It is so-called “optimal inventory policy surface.” This study utilizes the model of “optimal inventory policy surface” and the genetic algorithms (GAs), because of easiness, to resolve the multi-item inventory control optimization problems. In this research, a systematically experimental design of Taguchi method is used to analyze the different settings of both parameters and different ranges of variables of “optimal inventory policy surface” model using GAs as the calculation approach. In addition, the response effects (i.e., the percentage of requisitions short (or inventory shortages)) analysis of “optimal inventory policy surface” is obtained by applying in different settings of GAs program running conditions through a serial analysis.

Possibility and necessity constraints and their uses in inventory control system

In this paper, analogous to chance constraints, real-life necessary and possibility constraints in the context of a multi-item inventory control system are defined and defusified following fuzzy relations. Hence, a realistic multi-item inventory model without shortages and fuzzy constraints has been formulated and solved for minimum objective cost. Here, demand of the items is constant and known. The space required per unit item, available storage space is assumed to be imprecise. The space constraints are of necessity and/or possibility types. The models are formulated for different types of necessity or possibility constraints and solved using the Kuhn-Tucker conditions and Generalised Reduced Gradient (GRG) technique. The model is illustrated numerically, and values of demand and stock level are presented in tabular form.