Backorder Costs Research Articles

Multi-Stage Multi-Product Production and Inventory Planning for Cold Rolling under Random Yield

This paper studies a multi-stage multi-product production and inventory planning problem with random yield derived from the cold rolling process in the steel industry. The cold rolling process has multiple stages, and intermediate inventory buffers are kept between stages to ensure continuous operation. Switching products during the cold rolling process is typically very costly. Backorder costs are incurred for unsatisfied demand while inventory holding costs are incurred for excess inventory. The process also experiences random yield. The objective of the production and inventory planning problem is to minimize the total cost including the switching costs, inventory holding costs, and backorder costs. We propose a stochastic formulation with a nonlinear objective function. Two lower bounds are proposed, which are based on full information relaxation and Jensen’s inequality, respectively. Then, we develop two heuristics from the proposed lower bounds. In addition, we propose a two-stage procedure motivated by newsvendor logic. To verify the performance of the proposed bounds and heuristics, computational tests are conducted on synthetic instances. The results show the efficiency of the proposed bounds and heuristics.

Operational planning in service control towers – heuristics and case study

We study performance improvement in multi-echelon, closed loop spare part supply chains using operational interventions based on real-time status information. Our objective is to minimize the total cost relevant costs, consisting of intervention costs and the backorder costs. In this paper, we focus on proactive interventions, aiming to avoid stockouts. We assume that all reactive interventions are fixed. Proactive interventions that we study include lateral transshipments, emergency shipments, stock reservations, expediting part repairs, and early new buys of parts. These interventions are invoked by using alert generation, when the supply chain status deviates from the plan. We propose heuristic rules to generate alerts. We also develop heuristic rules for the choice of operational interventions. We model and test our heuristics in a simulation test bed, based on data of a global IT company by using the case data in Germany. Numerical experiments reveal the following key insights: (i) downstream interventions – proactive lateral and emergency shipments – have most impact in reducing costs, (ii) communicating losses in the supply chain (no returns, failed repairs) for early new buys has positive impact on fill rates at negligible costs, and (iii) expedite repair and stock reservations using the proposed rules is not profitable.

Optimal Inventory Policies for Price and Time Sensitive Demand Under Advertisement

Aims: This article analyzes an inventory system for deteriorating items. The demand is quadratic function of time and is dependent on time, price and advertisement. Shortages are allowed and partially backlogged. Background: Demand and pricing are the two most crucial factors in inventory policy for any business to be successful. In today’s era of competitive circumstances, any product is promoted through advertisement, which plays a vital role in changing the demand pattern among the community. The marketing and demonstration of an item by time-to-time with fashionable advertisements through well-known media such as TV, radio, newspaper, magazine, etc. However, this idea is not always true for some goods like wheat, vegetables, fruits, food grains, medicines and other perishable goods due to their deteriorating nature and this in turn decreases demand for such goods. Deterioration may define as decay, damage, spoilage, evaporation, obsolescence, pilferage. Hence, deterioration effect is a major part in inventory control theory. So in this article demand rate is considered to be a function of selling price, time and occurrence of advertisement instantaneously. Objective: A solution procedure is obtained to find optimal number of price changes and optimal selling price to maximize the total profit. Method: Classical Optimization. Result: From the sensitivity analysis table, it can be seen that the optimal profit is highly sensible to advertisement coefficient and purchase cost. With an increment in rate of deterioration, selling price decreases. Scale demand has reasonable effect on cycle time and selling price. When the value of increase, the cycle length and profit goes on decreasing. Growth in profit is observed if we increase parameter b, higher will be the profit. Price elasticity is sensible parameter with respect to selling price. If backlogging rate increases, the profit will decreases. The inventory parameters holding cost, back order cost and lost sale cost have marginal effect on total profit. Conclusion: In this article, an inventory model is proposed for deteriorating items with variable demand depends upon the advertisement, selling price of the item and time. Shortages are allowed and partially backlogged and backlogging rate depends on the waiting time for the next replenishment. From this article, we can conclude that the parameters are insensible with respect to optimal profit, cycle time and selling price and rest of the parameters have practical output on total profit.

Additive or Conventional Manufacturing for Spare Parts: Effect of Failure Rate Uncertainty on the Sourcing Option Decision

Additive manufacturing (AM) has recently been reported as enabler of digital spare parts supply. Thanks to its promise to produce spare parts with shorter lead times, AM may enable a make-to-order rather than a make-to-stock manufacturing process. Using AM, in fact, would allow to reduce the high inventory levels that are required by conventional manufacturing (CM) techniques to cope with spare parts’ intermittent demand. However, AM is characterized by two main drawbacks, i.e. first high production costs and second uncertain failure rates (often these uncertainties are higher than those of CM counterparts since AM is a manufacturing technique that is still subjected to substantial technological developments, while CM techniques are very well-established). While the former limitation can be counterbalanced with lower inventory costs, the latter remains an open issue, so far barely investigated. To the best of our knowledge, although researchers have considered the impact of failure rate uncertainties on the inventory costs and the total costs of spare parts management, no one has investigated how the failure rate uncertainty would affect the final decision on whether to manufacture spare parts in AM or CM. In this work, we aim to do so. Specifically, to make the analysis accurate and reliable, we have used realistic values of the failure rate uncertainties of AM and CM parts, obtained through a material science approach. From our results, which represents just a preliminary analysis where we have considered 40 different scenarios characterized by different combinations of spare part demands and backorder costs, we have observed that the failure rate uncertainty limits the conveniency of AM as sourcing option to only 7.5% of the analyzed scenarios (when the failure rate was considered too be known precisely, AM was the most convenient option 42.5% of the analyzed scenarios). These preliminary results indicate the need to reduce AM failure rate uncertainties to leverage the potential of AM for spare parts supply chains.

Optimal lot-sizing of an integrated EPQ model with partial backorders and re-workable products: an outer approximation

In this paper, we develop and optimise the lot-sizing policy in an integrated Economic Production Quantity (EPQ) model with partial backorders and re-workable products considering linear and fixed backordering costs. Time intervals, number of lots, and lot size are the decision variables of our model. The cost function includes the set-up costs, the holding costs, the goodwill loss costs, the fixed backorder costs, the backorder costs, the costs of reworking, the production costs, the disposal costs, and the screening costs. The profit function consists of the sale profits obtained from the sold products. The goal is to minimise the cost function and maximise the profit function under stochastic constraints simultaneously. A Lexicographic method is applied for integrating the conflicting objective functions. The integrated objective function, with stochastic constraints, is a Mix Integer Nonlinear Programming (MINLP) model. Accordingly, an Outer Approximation (OA) algorithm is provided for optimal lot-sizing the integrated EPQ model. Two numerical examples and a real large-scale example demonstrate the decent and acceptable performance of the presented OA with respect to the optimality criteria such as optimum solutions, complementarity, and taken iterations.

An Explainable Machine Learning Model for Material Backorder Prediction in Inventory Management.

Global competition among businesses imposes a more effective and low-cost supply chain allowing firms to provide products at a desired quality, quantity, and time, with lower production costs. The latter include holding cost, ordering cost, and backorder cost. Backorder occurs when a product is temporarily unavailable or out of stock and the customer places an order for future production and shipment. Therefore, stock unavailability and prolonged delays in product delivery will lead to additional production costs and unsatisfied customers, respectively. Thus, it is of high importance to develop models that will effectively predict the backorder rate in an inventory system with the aim of improving the effectiveness of the supply chain and, consequentially, the performance of the company. However, traditional approaches in the literature are based on stochastic approximation, without incorporating information from historical data. To this end, machine learning models should be employed for extracting knowledge of large historical data to develop predictive models. Therefore, to cover this need, in this study, the backorder prediction problem was addressed. Specifically, various machine learning models were compared for solving the binary classification problem of backorder prediction, followed by model calibration and a post-hoc explainability based on the SHAP model to identify and interpret the most important features that contribute to material backorder. The results showed that the RF, XGB, LGBM, and BB models reached an AUC score of 0.95, while the best-performing model was the LGBM model after calibration with the Isotonic Regression method. The explainability analysis showed that the inventory stock of a product, the volume of products that can be delivered, the imminent demand (sales), and the accurate prediction of the future demand can significantly contribute to the correct prediction of backorders.

Enhanced Inventory Management Using Blockchain Technology Under Cloud Sector Enabled by Hybrid Multi-Verse with Whale Optimization Algorithm

Inventory cost control is an essential factor in supply chain management. If the supplier’s inventory is insufficient, then the chance to trade the product will be reduced. The manufacturer’s inadequate material inventory will have an effect in termination of production, delays, and a waste of resources and time. On the other hand, postponed transportation will certainly raise costs such as transportation costs and cancellation of orders. Therefore, the operation costs of enterprises will be more, which will lower profits. In conventional supply chains, inventory costs control is not feasible for the view of the entire supply chain. The main intent of this paper is to plan for intelligent inventory management using blockchain technology under the cloud sector. The inventory management of the supply chain includes “multiple suppliers, a manufacturer, and multiple distributors”. The proposed inventory management models consider some significant costs like “transaction cost, inventory holding cost, shortage cost, transportation cost, time cost, setup cost, backordering cost, and quality improvement cost”. This multi-objective cost function is minimized by a novel hybrid optimization algorithm; the concept of WOA is integrated to produce the new algorithm which is termed as Whale-based Multi Verse Optimization (W-MVO) algorithm. For securing the data of distributors, using blockchain technology in a cloud environment helps from the leakage of data to other unauthorized users. Once the cost is reduced in all aspects based on the proposed hybrid optimization algorithm, the distributer will store the concerning data in the blockchain under the cloud sector, where each distributer holds a hash function to store its data, which cannot be restored by the other distributers. The valuable performance analysis over the conventional optimization algorithms proves the effective and reliable performance of the proposed model over the conventional models.

Age-based preventive maintenance with multiple printing options

In today's economic context, production systems must be readily available and machinery downtime kept to a minimum. Maintenance and spare parts inventory management play a vital role in achieving these goals, and preventive maintenance has increasingly been considered in maintenance policies. Additive manufacturing (AM) has recently been combined with preventive maintenance, and thus represents an emerging research direction. However, few studies have as yet been conducted in this research stream, and we intend to fill this gap. Our study makes three main contributions. First, we address the main limitations of two current models (i.e., assuming that no failure occurs during the replenishment lead time of the spare parts). Second, we propose a new maintenance policy that considers two printing options with different levels of reliability and unitary purchase costs. Third, we develop a decision support system (DSS) to assist managers in deciding whether to implement a preventive maintenance policy that includes AM or conventional manufacturing (CM) parts. We take an interdisciplinary approach to conducting a parametrical analysis where we consider real data on the reliability of CM and AM parts, in addition to the impact of post-processing operations and optimization routines. We find that AM-based preventive maintenance policies are favored when the MTTF and the backorder costs are low and when the failure and maintenance costs are high. These findings have been incorporated into the DSS, which provides thresholds for every parameter to guide practitioners in choosing between AM and CM parts for preventive maintenance, without requiring time-expensive calculations.

A new methodology for secured inventory management by average fitness‐based colliding bodies optimization integrated with block chain under cloud

AbstractThis article tries to develop the intelligent secured inventory management strategy by blockchain technology under cloud sector. Multiple suppliers, a manufacturer and multiple distributors are considered in the proposed model. The proposed inventory management is derived as a multi‐objective model, which is solved by the average fitness‐based colliding bodies optimization. A set of cost parameters like “transaction cost, inventory holding cost, shortage cost, transportation cost, time cost, setup cost, backordering cost, quality improvement cost, procurement cost, and stock‐out cost” is used for deriving the multi‐objective function. The optimal solution with the reduced cost function is stored in the block chain under cloud sector by each distributor, where a hash function is used by the distributor to secure the data that could not be visible to any other distributors. The proposed methodology aims to provide an important tool for the management of proposed echelon tree structured supply chains with block chain security under cloud sector that overcomes some of the deficiencies of competing methodologies.

Optimization of an inventory system with partial backlogging from a financial investment perspective

AbstractIn some real inventory systems, item sales can be adjusted to a stable demand rate along the inventory cycle. For instance, home appliances, electrical products, lounge furniture, home water supply, etc., are items with a stable demand rate. In this work, we analyze an inventory system for an item of this type, where the demand rate is constant. Shortages are allowed, and it is assumed that a fraction of demand during the stock‐out period is backlogged. It is supposed that the shortage costs (backorder cost and lost sales cost) have an affine structure: a fixed cost plus a linear cost that depends on the period of time where shortages exist. In this paper, instead of the maximization of the profit per unit time, or the minimization of the average inventory cost per unit time, the objective is the maximization of the return on inventory investment, which is a quotient defined as the average profit divided by the average inventory cost. The optimal inventory policy is obtained in a closed form under this new perspective. Moreover, it is shown that the optimal policy that maximizes the return on inventory investment is, in general, different from the one that maximizes the profit per unit time. In addition, the new optimal perspective offers some advantages. The optimal inventory policy that maximizes the return on investment does not depend on the unit selling price. Therefore, the inventory manager does not need to change his/her inventory policy if this price changes. These advantages are not usually present when the objective is the maximization of the profit per unit time. Numerical examples are provided to illustrate the theoretical results developed in this work. A sensitivity analysis of the optimal policy with respect to the system input parameters is also developed.

Profit maximization in an inventory system with time-varying demand, partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

A supply chain model with service level constraints and strategies under uncertainty

In the current socio-economic situation, the daily demand for essential goods in the business sector is always changing owing to various unavoidable reasons. As a result, choosing the right method for profitable business has become quite tricky. This study introduces different business strategies based on constant and fuzzy demands. There are two types of constraints considered in this model to avoid the backorder cost. However, combining the service-level constraints with the constant and fuzzy demand, this study compares the total costs, and finally, the best strategy is established. Moreover, investing a small amount, this model improves the quality of the products and reduces the vendor’s setup cost. Depending on the number of transported products, this model follows the transportation discount policy for hassle-free delivery of the products with a minimum delivery rate. The Kuhn-Tucker optimization technique is employed, and global optimality is verified numerically, analytically using the Hessian matrix. This model’s robustness is discussed through a comparative study, numerical examples, sensitivity analysis, graphical representation, and managerial insights. Finally, some concluding remarks along with future extensions are discussed.

Mathematical Modelling Of Inventory System With Parabolic Holding Cost, Weibull Distributed Deterioration Backlogging Under Pentagonal Fuzzy Parameters

In the present study, an inventory model with parabolic holding cost, quadratic demand rate, partial backlogging over a time horizon for weibull rate of deteriorating item is proposed. We have supposed the demand rate to be a quadratic function of time. Since the outbreak of pandemic COVID- 19 problem disturbed the political, social, economic, and financial structure of the whole world and both the demand and supply chain management have been affected badly therefore, parabolic holding cost is far better to be taken in account. We explore the inventory system to incorporate three parameters .i.e. purchase cost , backordering cost and cycle time which have been fuzzified using pentagonal fuzzy numbers to obtain total inventory cost. Graded mean integration method and Signed distance method are used to de-fuzzify the total cost. The main aim of the paper is to minimize the total cost per unit time in fuzzy environment. Sensitivity analysis of the optimal solution and its effects have been discussed.

Joint pricing and inventory decisions for substitutable and perishable products under demand uncertainty

In this paper, we develop a model for dynamic pricing and inventory decisions for multiple substitutable and perishable products under a multiple-period lifetime. Retailers place orders at the beginning of the first period, and products will be sold at full price during that period. All leftover products will then be carried over to the subsequent periods and sold at discounted prices. Demands for leftover products are assumed to follow a linear stochastic model depending on the discounted prices of the substitutable products. The optimal order quantities and prices are obtained by maximizing the total expected profit over the lifetime, taking into account the revenue, the backorder cost and the holding cost. We provide analytical properties of the optimal policy such as the concavity of the value functions and then utilise these in the numerical scheme for finding the optimal prices and ordering quantities. Experimental results are reported through a case study of a high-street fashion company, demonstrating the benefits of considering pricing and inventory decisions simultaneously for substitutable products.

Transfer of Risk in Supply Chain Management with Joint Pricing and Inventory Decision Considering Shortages

This study is the first to consider a distribution-free approach in a newsvendor model with a transfer of risk and back-ordering. Previously, in many articles, discrete demand is considered. In this model, we consider a newsvendor selling a single seasonal item with price-dependent stochastic demand. Competition in markets has forced the retailer and manufacturer to coordinate in decentralized supply chain management. A coordination contract is made between a retailer and manufacturer to overcome the randomness of demand for a short-life-cycle product. The retailer pays an additional amount per product to transfer the risk of unsold items. The manufacturer bears the cost of unsold products from the retailer. Shortages are allowed with back-ordering costs during the season. The distribution-free model is developed and solved with only available demand data of mean and standard deviation. Stackelberg’s game approach is used to calculate the optimal ordering quality and price. This model aims to maximize expected profit by optimizing unit selling price and ordered quantity through coordination. To illustrate that the model is robust, numerical experiment and sensitivity analyses are conducted for both decentralized and centralized supply chain management. For applicability of the model in the real-world business scenario, managerial insights are provided with sensitivity analysis.

The Research of Monte-Carlo Method for Aviation Materials Demand Forecast Based on the Life of the Reliability

With the rapid development of the aviation industry, the increasing number of missions and the impact of other new circumstances, the contradiction between supply and demand in aviation materials has become increasingly prominent. Consequently, more uncertainty and unpredictability in spare parts’ demand, as well as the absence of accurate value of holding, overstocking and backordering costs, result in traditional inventory control policies ineffective. In order to make better use of the existing stock aviation material resources, it is necessary to study the optimization of aviation materials inventory management. In this paper, the reliability analysis of aviation materials maintenance data is conducted to grasp the occurrence rules of aviation materials failures, determine the failure distribution function, and establish a mathematical model of spare parts guarantee and demand based on stochastic process theory. The Monte-Carlo simulation method is used to calculate the aviation materials demand. The calculation results show that the method can achieve the purpose of controlling the inventory level through the demand under varying guarantee degrees, which makes the management of aviation materials more scientific.

A Novel MILP Model for the Production, Lot Sizing, and Scheduling of Automotive Plastic Components on Parallel Flexible Injection Machines with Setup Common Operators

In this article, a mixed integer linear program (MILP) model is proposed for the production, lot sizing, and scheduling of automotive plastic components to minimize the setup, inventory, stockout, and backorder costs, by taking into account injection molds as the main index to schedule on parallel flexible injection machines. The proposed MILP considers the minimum and maximum inventory capacities and penalizes stockout. A relevant characteristic of the modeled problem is the dependence between mold setups to produce plastic components. The lot sizing and scheduling problem solution results in the assignment of molds to machines during a specific time period and in the calculation of the number of components to be produced, which is often called lot size, following a sequence-dependent setup time. Depending on the machine on which the mold is setup, the number of units to be produced will be distinct because machines differ from one another. The stock coverage, defined in demand days, is also included in the MILP to avoid backorders, which is highly penalized in the automotive supply chain. Added to this, the proposed model is extended by considering setup common operators to respond to and fulfill the constraints that appear in automotive plastic enterprises. In this regard, the MILP presented solves a lot-sizing and scheduling problem, emerged in a second-tier supplier of a real automotive supply chain. Finally, this article validates the MILP by performing experiments with different sized instances, including small, medium, and large. The large-sized dataset is characterized by replicating the amount of data used in the real enterprise, which is the object of this study. The goodness of the model is evaluated with the computational time and the deviation of the obtained results as regards to the optimal solution.

Demand Management and Inventory Control for Substitutable Products

This paper studies dynamic inventory and pricing decisions for a set of substitutable products over a flnite planning horizon. We present a general stochastic, price-dependent demand model that unifles many commonly used demand models in the literature. Unsatisfled demands are backlogged. There are linear purchasing, inventory-holding, and backordering costs. The objective is to maximize the total expected discounted proflt. The original formulation is not jointly concave in the decision variables and is therefore intractable. One key observation here is that the problem becomes jointly concave if we work with the inverse of the price vector { the market share vector. We characterize the optimal policy and develop algorithms to compute it. We establish conditions under which the optimal policy demonstrates certain monotonicity property, which, in turn, can greatly enhance computation. We also analyze the myopic policy and its optimality, and present a numerical study to illustrate the interplay of the pricing and inventory decisions.

Order release planning with predictive lead times: a machine learning approach

An essential task in manufacturing planning and control is to determine when to release orders to the shop floor. One key parameter is the lead time which is the planned time that elapses between the release of an order and its completion. Lead times are normally determined based on the observed time orders previously took to traverse the production system (flow times). Traditional order release models assume static lead times, although it has been shown that they should be set dynamically to reflect the dynamics of the system. Therefore, we present a flow time estimation procedure to set lead times dynamically using an artificial neural network. Additionally, we implement a safety lead time to incorporate the underlying cost ratio between finished inventory holding and backorder costs in the order release model. We test our proposed approach using a simulation model of a three-stage make-to-order flow-shop and compare the forecast accuracy and the cost performance to other forecast-based order release models from the literature. We show that our proposed model using artificial neural networks outperforms the other tested approaches, especially for scenarios with high utilisation and high variability in processing times.

REPLENISHMENT POLICY FOR A PROCESSING SYSTEM WITH STOCHASTIC CONSTRAINTS, DISCOUNT AND IMPERFECT ITEMS

In this paper, a processing system with multiple products, single-vendor and single-buyer is considered to maximize the inventory system’s profit. In order to be more suit for real-world applications, this model contains five stochastic constraints including backordering cost, space, ordering, procurement, and available budget. It is assumed that orders are subjected to quantity discount and also imperfect goods are permitted. The price of the perfect and imperfect goods are assumed to be different. The imperfect goods are assumed to be returned to the system for rework process. The objective is to find the optimal order quantities of products such that the total inventory profit to be maximized while satisfying all the constraints. The problem is formulated as a mixed integer nonlinear programming problem. Two algorithms, based on GA and GRASP are developed to solve the resulting model. Performance of the algorithms are analyzed based on 45 numerical examples with different sizes.