Optimal Inventory Level Research Articles

Application of Optimal Control Theory to Inventory Problems That Are Increasing at PT. Canang Indah

This journal discusses optimal control of inventory problems that are increasing. The inventory in the company is needed, to meet every incoming demand. Inventory in minimum quantity can result in shortage of inventory. But inventory quantity maximum can result in losses, due to the minimum demand. The purpose of this research is to determine the level of optimal inventory in PT. Canang Indah. Using the optimal control theory model and analyzing the stability of the dynamic differential equation, to find the optimal inventory level. Obtained optimal inventory levels achieve stability at the time . For the planning length of 12 months includes: raw material inventory (logs sengon and rambung), production (finished materials in process) and finished particle board products that are in the warehouse. From this research optimal control theory can be applied in PT. Canang Indah to optimize inventory on the problem of increasing inventory.

Expected Value Model of an Uncertain Production Inventory Problem with Deteriorating Items

In this study, we present an optimal control model for an uncertain production inventory problem with deteriorating items. The dynamics of the model includes perturbation by an uncertain canonical process. An expected value optimal control model is established based on the uncertainty theory. The aim of this study is to apply the optimal control theory to solve a production inventory problem with deteriorating items and derive an optimal inventory level and production rate that would maximize the expected revenue. The uncertainty theory is used to obtain the equation of optimality. The Hamilton–Jacobi–Bellman (HJB) principle is used to solve the equation of optimality. The results are discussed using numerical experiments for different demand functions.

Availability and reliability of information transmission for supply chain coordination with demand information sharing

Information sharing enhances coordination in a supply chain, which mitigates the bullwhip effect and enables smooth production and inventory management for members of the chain. This study considers a two-echelon supply chain in which an upstream manufacturer and a downstream retailer are coordinated by revenue sharing, and investigates the effects that the reliability and availability of information sharing have on the profits of entire supply chain. Also, the retailer shares the demand information with the manufacturer through an information transmission mechanism, where the demand is fit by an autoregressive model. The costs of information transmission are quantitatively evaluated with the linear, exponential, and power law functional forms, and the variations in profits are accordingly investigated. This study contributes to the literature by providing a practical view on information sharing among supply chain members, because the reliability and availability are taken into account in the assessment of sharing quality. Unlike the previous studies, the proposed approach of this study integrates the relevant factors, such as the quality of information sharing in terms of reliability and availability, and the information transmission costs, to probe into the variations in profits of supply chain members. In this regard, the accuracy of production decisions, such as the optimal order quantities and inventory levels, would be better compared to other approaches on the basis of profit maximization for the entire supply chain. The results of sensitivity analyses show that the greater the reliability and availability of information sharing is, the better the supply chain management performance would be, and the supply chain members, especially the upstream manufacturer, would thus gain more profits. However, higher reliability and availability of information sharing would often incur greater expenditures, and as a result, the trade-off for the determination of the optimal reliability and availability of information sharing is critical for supply chain coordination.

Optimal policy of ordering blood units in the hospital according to compatibility and priority transfers between blood groups under uncertainty conditions: A case study

In spite of significant advancements in medicine, there is still a shortage of human blood in the world. At present, there is no alternative chemical process or product that can produce blood, and only humans are capable of doing so. It is for this reason that blood is such an important component of our healthcare system. Due to the perishability of blood, managing blood inventories can be challenging. The challenge is to maintain a high level of supply while minimizing loss due to expiration. The purpose of this study is to present a mathematical model that reduces inventory costs, determines the optimal ordering policy in hospitals, and prevents the loss of blood units. To determine the optimal inventory level and order volume, a mixed integer programming model is presented in both deterministic and non-deterministic conditions. In order to address the uncertainty in the problem, a robust optimization approach is used. This model minimizes the transfer of blood groups and transmission between hospitals by considering compatibility and priority. A sensitivity analysis has also been conducted on the model. Based on a case study, it is demonstrated that the costs of buying, storing, ordering, and wasting two important RBCs and platelets can be reduced.

Newsvendors with customer referrals

AbstractFirms often encourage existing customers to recruit new customers. In this paper, we analytically study the customer referrals in a two‐period newsvendor model, where the demand generated by referrals increases in the previous sales. In this framework, we establish the structural results for the optimal inventory level, as well as evaluate the value of referral programs. We find that the customer referrals are more attractive for firms selling nonperishable products than for those selling perishable products. Overall, this study underscores the operational value of customer referrals, particularly for firms selling nonperishable products.

Opaque Selling and Inventory Management in Vertically Differentiated Markets

Problem definition: We study the emerging practice of using opaque selling to dispose of leftover inventory in vertically differentiated markets. With this selling strategy, a firm offers a synthetic product (after the regular selling season) for which consumers do not know the exact identity until after purchase. Academic/practical relevance: This opaque-selling strategy is implemented in several industries—for example, travel and retail. However, its mechanisms are yet to be fully understood, as the extant literature considers other settings wherein opaque selling’s mechanisms do not carry over to ours. Methodology: We develop a game-theoretic model featuring a firm’s inventory and dynamic selling strategies and consumers’ strategic waiting. We characterize the optimal inventory levels, product offerings, and prices. Results: We find that, compared with last-minute selling (i.e., selling leftover inventory separately), opaque selling increases regular-season profits by softening intertemporal cannibalization from sales-season products to high-quality products sold in the regular season. However, it may decrease sales-season profits, as products with different qualities are probabilistically allocated to all purchasing consumers, irrespective of their valuations. We further demonstrate that these mechanisms are fundamentally different from those identified in the literature for other settings, and this contrast generates opposite recommendations as for the optimal usage of opaque selling. With endogenous inventory, interestingly, opaque selling is even more attractive, and it prompts the firm to procure fewer high-quality products than under last-minute selling. Managerial implications: We demonstrate the value of opaque selling as an inventory-clearance strategy in vertical markets. We show that a firm can further strengthen its profitability by combining opaque selling with inventory management. We also provide guidelines on managing inventory and illustrate the nontrivial impact of opaque selling.

Stochastic inventory routing with time-based shipment consolidation

Inspired by the retail industry, we consider a stochastic inventory routing problem where retailers are replenished from a central warehouse using a time-based shipment consolidation policy. Such a time-based dispatching policy, where retailers facing stochastic demand are repetitively replenished at fixed times, is essential in practice. It allows for easy incorporation with dependent up- and downstream planning problems such as personal staffing and warehouse operations, and has become a standard part of transportation contracts. We provide a new chance-constrained model that determines an optimal clustering of retailers in groups, their associated routing and shipment interval, and each retailers’ optimal inventory level. A newly developed branch-price-and-cut algorithm solves our model to optimality. Its efficiency comes from a tailored labeling algorithm for solving the pricing problem that relies, among others, on an optimality pruning criterion based on the approximate solution of a 0,1-knapsack problem. Computational experiments show that our exact method can solve instances of up to 60 retailers to optimality. Besides, we accommodate practitioners by providing a fast heuristic that provides excellent solutions with an optimality gap of less than 1%. Finally, we show that incorporating uncertainty already in the planning process is essential for stochastic inventory routing with time-based shipment consolidation, as it results in overall cost-savings of 7.7% compared to the current state-of-the-art.

Inventory Model and Pricing in the Supply Chain Approach VMI Considering Incremental Discount

Given the globalization of competition and the existence of many rivals, the optimization supply chain has been highly regarded. One of the key issues in optimizing supply chain is to increase profitability and cost reduction. Since inventories have a large part of the cost of supply chain, the determination of the optimal level of inventory can have an effective role in cost reductions. In addition to costs reduction, attracting a larger share of the demand market can increase profitability. One of the effective factors in attracting customers is market price. On the other hand, discounts on the supply chain will encourage more buy and, of course, buy will further increase the costs. Therefore, this article addresses the issues of simultaneous pricing and inventory control in a supply chain bi-level, and optimal buy policy the mode of existence of incremental discounts and optimal pricing policies has been determined. In this regard, the mathematical model and numerical examples have been solved.

THE FUZZY OPTIMISTIC-REASONABLE-PESSIMISTIC INVENTORY MODEL

In inventory and production decision problems, decision makers are interested to identify the optimal inventory and production level. In a certain decision environment, the optimal inventory level could be determined through traditional inventory methods and the optimal ptoduction level could be determined through linear programming algorithms. In an uncertain decision environment, the traditional methods and algorithms can not provide efficient and relevant solutions for these levels, due to the vague and changing parameters. In this case it is neccesary to develop new methods and models that can deal with vague variables and provide optimal levels. In this paper, the optimal inventory and production levels are determined through a single model that uses fuzzy linear programming. This new model is Fuzzy Optimistic-Reasonable-Pessimistic Inventory Model. It has three scenario: optimistic, reasonable and pessimistic, that are defined through triangular fuzzy numbers. In this way, decision makers can deal with vague parameters. These scenarios help managers to divide the Fuzzy ORP Model into three sub-models, that can be easily solved through traditional Simplex Algorithms. Each sub-model provides a crisp solution for each scenario. The solutions forms the final fuzzy optimal solution. The Fuzzy PRO Inventory Model helps managers to identify three optimal levels and to rank them according to their evaluations. This is useful, also, in predictions, where the decision makers should predict different scenarios for the production process. The limit of this model is the definition of the variables and scenarios. This model consider that all values for all variables and coefficients have the same definition: the inferior limit is related to the optimistic sceanrio, the peak is represents the reasonable limit and the superior limit is related to the pessimistic scenario. In real problem, the decision variables could have different definition than coefficients. The inferior limit of the cost is related to the optimistic scenario, but the superior limit of the production level can be related to the optimistic scenario. There are different representations for the scenarios.

Sales Forecasting for Fashion Products Considering Lost Sales

Sales forecasting for new products is significantly important for fashion retailer companies because prediction with high accuracy helps the company improve management efficiency and customer satisfaction. The low inventory strategy of fashion products and the low stock level in each brick-and-mortar store lead to serious censored demand problems, making forecasting difficult. In this regard, a two layers (TLs) model is proposed in this paper to predict the total sales of new products. In the first layer, the demand is estimated by linear regression (LR). In the second layer, sales are modeled as a function of not only the demand but also the inventory. To solve the TLs model, a gradient-boosting decision tree method (GBDT) is used for feature selection. Considering the heterogeneity in products, a mixed k-mean algorithm is applied for product clustering and a genetic algorithm for parameter estimation in each cluster. The model is tested on real-world data from a Singapore company, and the experimental results show that our model is better than LR, GBDT, support vector regression (SVR) and artificial neural network (ANN) in most cases. Furthermore, two indicators are built: the average conversion rate and the marginal conversion rate, to measure products’ competitiveness and explore the optimal inventory level, respectively, which provide helpful guidance on decision-making for fashion industry managers.

Supplier inventory leanness and financial performance

AbstractNumerous studies have examined the relationship between inventory management and financial performance. However, the focus of such empirical work has primarily been on how a firm's own inventory characteristics affect its performance. Our objective is to extend this body of literature beyond the firm‐level. We draw on inventory theory and resource‐based theories to hypothesize about the effect of supplier inventory leanness on a focal firm's financial performance and how supplier and focal firm inventory leanness interact to affect such outcomes. We test our hypotheses using a large panel dataset of supplier‐focal firm relationships obtained from Compustat's Customer Segment database and aggregated to the focal firm‐quarter level, as well as firm financial information from Compustat's Fundamentals Quarterly database. The econometric analyses provide evidence that supplier inventory leanness influences focal firm financial performance indirectly through the interaction with the firm's own inventory leanness. In particular, our estimation results detail how supplier inventory leanness affects the non‐linearity of the focal firm's inventory leanness‐financial performance relationship and its optimal inventory leanness level. The findings broaden the scope of empirical inventory literature and highlight supplier inventory leanness as an important consideration in firm‐level inventory decision making.

An optimal ordering policy for a visitor-based purchasing system with stochastic delivery time and partial prepayment for profit maximization

The classical inventory control policies assume that orders are paid for at the time of their receipts, but in practice, suppliers may require retailers to pay a fraction of the purchasing cost in advance, and sometimes allow them to pay this cost in several prepayments during a predetermined period. Planning inventory replenishments and prepayments become challenging when decisions must be made under uncertainty, especially when delivery time is stochastic, and shortages may occur. This paper develops an inventory control model in a purchasing system in which a visitor sells the product of a manufacturer, and a buyer receives call from the visitor to make an order and items arrives at stochastic time. Both partial prepayments and partial backordering are assumed in the model. The main aim of the paper is to determine the optimal level of inventory of the buyer such that his total profit is maximized. A mathematical model with a general probability distribution for lead time is developed and globally optimal solutions are derived for the model. The applicability of the model is discussed through two special cases for uniform and exponential probability distributions. The results are supportive of the proposed ideas and they reflect an efficient approach.

The data-driven newsvendor problem: Achieving on-target service-levels using distributionally robust chance-constrained optimization

The classical approach to the newsvendor problem is to first estimate the demand distribution (or assume it to be given) and then determine the optimal inventory level. Data-driven optimization offers an alternative, where the inventory level is determined directly from the data. In this paper, we consider the data-driven newsvendor problem under a service-level constraint. We show that existing approaches to this problem suffer from overfitting, resulting in service-levels that are below the target service-level. We propose new data-driven approaches and corresponding mathematical optimization models based on methods of distributionally robust chance-constrained optimization—which have not yet been applied and empirically tested in the context of the data-driven newsvendor problem. We assess the effectiveness of our approaches by means of an extensive numerical study. To that end, we conduct structured experiments based on simulation as well as experiments based on a real-life bikesharing system where we consider the daily usage data along with information on weather and seasonal factors. The results demonstrate that our methods achieve on-target service-levels even in absence of large amounts of data. All in all, our study provides ample empirical evidence that distributionally robust chance-constrained optimization is a viable approach for addressing the data-driven newsvendor problem.

Optimal policy for multi-item systems with stochastic demands, backlogged shortages and limited storage capacity

In this paper, an inventory model for multiple products with stochastic demands is developed. The scheduling period or inventory cycle is known and prescribed. Demands are independent random variables and they follow power patterns throughout the inventory cycle. For each product, an aggregate cycle demand is realized first and then the demand is released to the inventory system gradually according to power patterns within a cycle. These demand patterns express different ways of drawing units from inventory and can be a good approach to modelling customer demands in inventory systems. Shortages are allowed and they are fully backlogged. It is assumed that the warehouse where the items are stored has a limited capacity. For this inventory system, we determine the inventory policy that maximizes the expected profit per unit time. An efficient algorithmic approach is proposed to calculate the optimal inventory levels at the beginning of the inventory cycle and to obtain the maximum expected profit per unit time. This inventory model is applicable to on-line sales of a wide variety of products. In this type of sales, customers do not receive the products at the time of purchase, but sellers deliver goods a few days later. Also, this model can be used to represent inventories of products for in-shop sales when the withdrawal of items from the inventory is not at the purchasing time, but occurs in a period after the sale of the products. This inventory model extends various inventory systems studied by other authors. Numerical examples are introduced to illustrate the theoretical results presented in this work.

Information effect of buy-online-and-pick-up-in-store in omnichannel retailing with store replenishment

• “Buy-online-and-pick-up-in-store” has information effect about inventory level. • Customers choose the optimal behavior when the BOPS option is offered. • A retailer finds the optimal store inventory level to control customers' behavior. • There are two types of rational expectation equilibrium: with and without BOPS. This study aims to investigate the information effect of “buy-online-and-pick-up-in-store” (BOPS) in which inventory can be replenished. An analytic model is adopted to investigate the hassle costs of customers using different channels. With a linear or hyperbolic cost-reducing waiting time for BOPS, two types of equilibria are found: 1) where all customers go directly to the store without using BOPS and 2) where all customers use BOPS. The result reveals optimal omnichannel strategies whereby retailers can identify their optimal store inventory levels with information about customer behavior, hassle, and delivery costs. This study suggests a strong incentive to achieve a high density of stores so that retailers can fulfill replenishments at a lower cost. Essentially, this study considers a game-theoretical omnichannel structure for the customer-retailer relationship.

Solving a parallel-line capacitated lot-sizing and scheduling problem with sequence-dependent setup time/cost and preventive maintenance by a rolling horizon method

This paper presents a novel Mixed-Integer Nonlinear Programming (MINLP) model for a parallel-line Capacitated Lot-Sizing Problem (CLSP) with the sequence-dependent setup time/cost, due date, and preventive maintenance planning. The target of this integrated model is to specify optimal lot sizes, inventory, and shortage levels along with the optimal preventive maintenance plan and the best sequence, starting time, and completion time of the lots. The production and scheduling aspect of the problem is modeled as the CLSP with the sequence-dependent setup time/cost and due date, while maintenance sub-problem is modeled by using the time-based maintenance technique and age-reduction modeling concept with the actual run-time and Exponential lifetime distribution. For the complexity of the model, the MIP-based Rolling Horizon (RH) heuristic algorithms are developed to solve the linearized model in a reasonable truncated time. The computational results obtained from generated small- to large-sized instances show that the proposed RH1 and RH2 heuristic methods report the final solutions with better quality (lower relative gap and total cost) compared with the solutions reported by the truncated simple CPLEX method. Especially, the RH2 method provides a reasonable production plan, better-adjusted schedules with respect to the due dates, and a proper PM plan in comparison with the other solution methods. Also, the featured model develops an optimal production, scheduling, and maintenance plan with higher feasibility, more available production time, and lower total cost in comparison with the classic CLSP with the sequence-dependent setups that neglects the effects of sudden failures and corrective maintenance actions.

A Cluster-First Route-Second Constructive Heuristic Method for Emergency Logistics Scheduling in Urban Transport Networks

Advanced strategies for emergency logistics scheduling problems in urban transport networks have been a challenging topic for centuries. This study proposed a cluster-first route-second constructive heuristic method based on the continuous approximation (CA) for ‘one-to-many’ vehicle routing to dispatch commidities after an emergency. The objective of the study is to provide a replenish schedule and routing solution from the government/provider’s end in order to minimize the total motion cost, pipeline inventory cost, and holding cost with backorder for the disaster relief operation. The developed method can turn the complicated vehicle routing problem (VRP) into a relatively simple travel salesman problem (TSP) for pre-assigned customer sets. The CA is employed to determine the optimal replenish amount and inventory level for the route serving a given location. The Christofides method is then applied to solve the TSP for the selected cluster. Two clustering methods are investigated in this research: (1) a local-based approach where clustering and routing are determined; and (2) a K-mean clustering method where points are clustered upfront by the CA solution. A case study in Miami-Dade County in Florida to dispatch fuels from the depot to 72 gas stations is presented, demonstrating the proposed approach and comparing two clustering methods. The numerical results illustrate the effectiveness of the algorithms and conclude that the local-based clustering approach may yield a lower total cost with a higher motion cost.

A New Approach for EOQ Calculation Using Modified Opportunity Cost

Introduction: Optimal inventory levels are necessary for a firm to avoid shortage/excess of an item. Shortage of an item leads to stock out conditions which results in loss of profit. When items are correlated with each other, stock out condition of one item may result in non purchase of its associated items also which, in turn, further brings down the profit. In this paper, this loss in profit is used to modify opportunity cost of an item resulting in its modified EOQ. Method: One illustrative example has been discussed which incorporates purchase dependencies in retail multi-item inventory management. The model discussed in this research paper will be motivational for researchers and inventory managers and provides a method for incorporating correlation among items while managing inventory. Result: The EOQs of items are estimated both by using traditional method and then by using modified opportunity cost (modeled as loss profit). Results show that in frequent item set A, B, D, EOQs of all three items increased when correlation among them is considered resulting in increase in profit. Conclusion: One of the major focus areas of inventory management is to determine when and how much quantity of items needs to be ordered so that total inventory cost can be minimized and profit of a firm can be maximized. However, while calculating the true value of an item and the profit it brings to the firm, it is very essential to analyze its effect on the sale of other items. Asso-ciation rule mining provides a way to correlate items by calculating support and confidence factor. Discussion: In inventory management system, for increasing the profit of a firm, EOQs of items need to be calculated in order to avoid shortage or excess of inventory. For explaining the approach a very small database is taken consisting of only 5 items and 10 transactions therefore the increase in profit is minimal however, when this approach applies on real database consisting of thousands of items and transactions, the increase in profit will be significant.

Distributionally robust front distribution center inventory optimization with uncertain multi-item orders

<p style='text-indent:20px;'>As a new retail model, the front distribution center (FDC) has been recognized as an effective instrument for timely order delivery. However, the high customer demand uncertainty, multi-item order pattern, and limited inventory capacity pose a challenging task for FDC managers to determine the optimal inventory level. To this end, this paper proposes a two-stage distributionally robust (DR) FDC inventory model and an efficient row-and-column generation (RCG) algorithm. The proposed DR model uses a Wasserstein distance-based distributional set to describe the uncertain demand and utilizes a robust conditional value at risk decision criterion to mitigate the risk of distribution ambiguity. The proposed RCG is able to solve the complex max-min-max DR model exactly by repeatedly solving relaxed master problems and feasibility subproblems. We show that the optimal solution of the non-convex feasibility subproblem can be obtained by solving two linear programming problems. Numerical experiments based on real-world data highlight the superior out-of-sample performance of the proposed DR model in comparison with an existing benchmark approach and validate the computational efficiency of the proposed algorithm.</p>

Inventory Management: Bi-objective Optimization Models for Mass Customization

In recent years, the problem of establishing the inventory levels in the manufacturing industry has considerably worsened due to the accelerated growth in demand for customized products, this behavior in the customers has created heterogeneous and unstable demands too difficult to forecast generating an increase in inventory levels. In response to this behavior, the strategy that companies have commonly used to offer a wide variety of products to meet this demand is Mass Customization. However, this response has created products with shorter life cycles significantly increasing the risks and costs in inventories due to deterioration, re-manufacturing, and obsolescence. Little attention has been paid to determining inventory levels when a company uses mass customization as its main production strategy. This paper develops two bi-objective optimization models to determine the optimal inventory levels for those industries that, due to the nature of the product, use mass customization to meet the needs of their customers. The performance of the models is compared with the performance offered by the traditional continuous review (Q,R) policy, the results show a significant reduction in total inventory costs while maintaining high levels of customer service level.