Inventory Replenishment Decisions Research Articles

Three-echelon circular economic production–inventory model for deteriorating items with imperfect quality and carbon emissions considerations under various emissions policies

Traditional production systems have a sole focus of maximising economic outcomes but due to the world’s ever-growing awareness about environmental issues, circular production systems, with a dual focus of maximising economic output and minimising environmental impact, have become prevalent in recent years. These types of production systems incorporate circular economy initiatives in their operational processes with the aim of reducing their carbon footprints. However, this is a voluntary measure to reduce carbon footprints and for this reason, various governments have introduced regulatory measures to involuntarily reduce carbon footprints of production systems. These regulatory measures include carbon tax, cap, cap-and-trade and cap-and-offset policies that are designed to reduce carbon emissions from production processes. With this in mind, this paper proposes an integrated sustainable production–inventory model for a three-echelon supply chain for imperfect quality deteriorating items with a circular economy indicator under various carbon emissions regulations. Using four different combinations of functions for both the demand rate and unit gross profit and four different carbon emissions regulations, 16 variants of the model are solved and analysed using heuristic algorithms. The model variants are not only aimed at optimising inventory replenishment decisions but also the circularity economy indicator of the deteriorating inventory. Of the 16 variants, the highest profit is achieved for the logistic demand and linear profit functions combination under cap-and-offset, despite a circularity indicator of 81.75%. The results also show that carbon emissions policies are effective at reducing the supply chain’s carbon footprint, albeit with a slight impact on the profit.

Inventory replenishment decisions with uncertain price and demand

This paper studies the multiple period inventory replenishment problem for a capacitated warehouse when procurement prices and market demands are both uncertain, with the goal to minimise the procuring and holding costs. We analyse this problem under the framework of competitive analysis, where neither probabilistic distributions nor sets are available to characterise the unknown price and demand parameters. An efficient online real-time replenishment algorithm is developed, which is free of any distribution assumption, and the decisions are made based entirely on past and present information. We derive an instance-independent competitive ratio of the algorithm, which provides a worst-case theoretical performance guarantee, and shows that the proposed algorithm performs well for situations with high volatility uncertainty over time and is naturally risk-averse. Finally, a set of numerical experiments further verifies the effectiveness of the algorithm.

Fractional order inventory system for time-dependent demand influenced by reliability and memory effect of promotional efforts

In this paper, an optimal replenishment strategy is developed for a sales environment influenced by the factors of reliability and promotional efforts with their pertinent impression on customers’ purchase behavior. The first part of this study focuses on formulating an inventory system aiming to evaluate order quantity and corresponding replenishment time. The memory effect of promotional efforts is incorporated into the model by formulating the same through a fractional order differential equation. The subsequent part of our work focuses on studying the variational effect on optimal values of replenishment quantity and time due to dissimilation in various parameters, which represent the governing factors considered in our model formulation. Results of the study have been analyzed through a data set obtained from a retailer who is into the business through e-commerce trade. The analysis of model parameters infers some managerial insights enabling an appropriate modification in inventory replenishment decisions in a response to any changes in the state of the sales environment.

Ordering decisions under supply uncertainty and inventory record inaccuracy: An experimental investigation

AbstractUncertainty on the supply side is a common issue planners face. How do decision‐makers incorporate inventory uncertainty when placing orders? We investigate ordering decisions under two forms of uncertainty regarding total inventory available to satisfy demand: supply uncertainty (SU; unreliability in incoming shipments) and inventory record inaccuracy (IRI; internal inefficiencies leading to a discrepancy between physical and recorded inventories). The experimental results reveal behavioral regularities in ordering decisions under both forms of total inventory uncertainty. We find that subjects overstock in settings with low profit margins, and overstocking is more pronounced under IRI than under SU. This overstocking under low profit margins is similar to observed ordering decisions under demand uncertainty. In these settings, subjects show a stronger shortage aversion under IRI (which is internal uncertainty) than under SU (which is external uncertainty). Furthermore, we find that subjects chase past realizations of supply/on‐hand inventory, although the effect depends on the uncertainty type. Although SU and IRI are, in practice, often simultaneously present, their causes are different. By providing insight into the relative effect of the types of uncertainty on the quality of inventory replenishment decisions, this study highlights the importance of reducing SU and IRI for products with low profit margins.

Coordination of pricing and inventory replenishment decisions in a supply chain with multiple geographically dispersed retailers

We study the efficiency of a multi-stage supply chain controlled by a single decision-maker with the goal of maximizing the total profit per time unit for a single product by coordinating the purchasing of raw materials from an external supplier, manufacturing and shipping the product between consecutive stages, and determining the selling price and final demand for the product sold by multiple retailers. Retailers are geographically dispersed, control their own market areas, and differ in terms of operating costs and marketing strategies. Each retailer has a different price-sensitive demand function. In this study, we propose a mixed integer nonlinear programming model that maximizes the total profit per time unit, which includes the revenue of the final product, echelon holding costs, and fixed costs for ordering and shipping items at each stage and at each retailer location. Using a numerical example, we show that the model with varying selling prices at the retailers yields higher profits than the model with the same selling price across all the retailers. We also perform an analysis comparing the coordinated approach versus the sequential approach for pricing and inventory replenishment decisions by varying the market size and demand function parameters. The results show that, as the market size parameter decreases, the coordinated approach yields a higher profit than the sequential approach does. Additionally, given a constant market size setting, the results show that pricing and inventory replenishment decisions are very sensitive to the demand function parameters. The analysis also shows that the coordinated approach yields an average profit gain of 24.18% compared to the profit of 3.53% yielded by the sequential approach. Similarly, it is shown that the coordinated approach always yields a better profit than the sequential approach across all scenarios generated by varying the demand parameters. Moreover, we propose a Simulated Annealing (SA) algorithm to obtain near-optimal solutions in a timely manner. A computational comparison shows that the average solution reached by the proposed SA algorithm is at 0.04% from the optimal solution.

Demand forecasting in supply chains: a review of aggregation and hierarchical approaches

Demand forecasts are the basis of most decisions in supply chain management. The granularity of these decisions lead to different forecast requirements. For example, inventory replenishment decisions require forecasts at the individual SKU level over lead time, whereas forecasts at higher levels, over longer horizons, are required for supply chain strategic decisions. The most accurate forecasts are not always obtained from data at the 'natural' level of aggregation. In some cases, forecast accuracy may be improved by aggregating data or forecasts at lower levels, or disaggregating data or forecasts at higher levels, or by combining forecasts at multiple levels of aggregation. Temporal and cross-sectional aggregation approaches are well established in the literature. More recently, it has been argued that these two approaches do not make the fullest use of data available at the different hierarchical levels of the supply chain. Therefore, consideration of forecasting hierarchies (over time and other dimensions), and combinations of forecasts across hierarchical levels, have been recommended. This paper provides a comprehensive review of research dealing with aggregation and hierarchical forecasting in supply chains, based on a systematic search. The review enables the identification of major research gaps and the presentation of an agenda for further research.

The average-cost formulation of lot sizing models and inventory carrying charges: a technical note

It is generally recognised that the present-value criterion should be preferred to the average-cost formulation in developing lot sizing models. Despite the advantages of the present-value measure, average-cost lot sizing models are far more widely applied. Because of the nature of the average-cost formulation, inventory carrying costs are evaluated according to a look-back approach, relying on historical values. In this regard, a general misconception in the inventory management literature concerned with average-cost models is that the unit stockholding cost rate should be established considering fixed warehouse costs, which are costs that are, in the short term, independent of the inventory level. This paper develops arguments supporting our belief that inventory carrying charges used in lot sizing models should take into account only those costs varying with the inventory level in the warehouse, and that considering fixed warehouse costs leads to pitfalls when making inventory replenishment decisions. To this aim, we first present an analytical treatment based on the classical Economic Order Quantity (EOQ) model, as its full analytical tractability permits us to better discuss the problem we are interested in. Finally, we present numerical experiments to assess the effect of the correct procedure to establish the unit stockholding cost rate on inventory management decisions. These experiments are performed considering warehouse costs taken from some industrial case studies presented in the literature.

Simulation-based optimisation of replenishment policy in supply chains

Classic replenishment strategy may no longer be effective due to the increasing complexity of supply chains. The article presents the problem of inventory management while presenting a practical methodology for supporting inventory replenishment decisions in order to reduce maintenance costs. Therefore, the possibility has been shown of using simulation modelling of the supply chain. The aim of the article is to present the methodology, using computer simulation with optimisation, of searching for the optimal strategy of replenishment of stocks in supply chains, especially when there is a problem of uncertainty of the demand. A case study was presented - optimisation of inventory of an online shop with electronics. The results obtained prove the high usefulness of the proposed methodology, as compared to the initial method of replenishing, it was possible to reduce the time of storage of goods by 66%, which translates into lowering the costs in a simple way.

An Algebraic Decision Support Model for Inventory Coordination in the Generalized n-Stage Non-Serial Supply Chain with Fixed and Linear Backorders Costs

This paper extends and generalizes former inventory models that apply algebraic methods to derive optimal supply chain inventory decisions. In particular this paper considers the problem of coordinating production-inventory decisions in an integrated n-stage supply chain system with linear and fixed backorder costs. This supply chain system assumes information symmetry which implies that all partners share their operational information. First, a mathematical model for the supply chain system total cost is formulated under the integer multipliers coordination mechanism. Then, a recursive algebraic algorithm to derive the optimal inventory replenishment decisions is developed. The applicability of the proposed algorithm is demonstrated using two different numerical examples. Results from the numerical examples indicate that adopting the integer multiplier mechanism will reduce the overall total system cost as compared to using the common cycle time mechanism.

Studying the effect of stochastic breakdowns, overtime, and rework on inventory replenishment decision

This study investigates the effect of stochastic breakdowns, overtime, and rework on the inventory replenishment decision. The overtime capacity and inevitable situations during the manufacturing process, such as the production of imperfect items and random breakdowns, are often considered in advance by production manager to smoothen fabrication schedules, maintain the desired quality, and reduce the impact from undesirable interruptions. This study builds a model to characterize these real features of a manufacturing process and derive the total relevant expenses of the system. Although a closed-form solution is unobtainable, a recursive algorithm is proposed to help find the optimal runtime for the batch fabrication plan. A numerical illustration shows how the proposed procedure and algorithm function. It also demonstrates the ability of the proposed model to reveal diverse crucial information regarding the individual and combined influences of deviations in overtime factors, the mean-time-to-failure, and rework- related variables, on the optimal replenishment runtime, total operating expenses, and different cost contributors. The research results will facilitate better decision-making aimed at increasing the competitive advantages of a manufacturing firm.

A robust location-inventory model for food supply chains operating under disruptions with ripple effects

Given the inevitable globalisation in the food sector and the specific security challenges this industry faces, designing food supply chains has become a substantial topic for academics and practitioners. The integration of food product-specific characteristics and potential disruptions has continuously gained importance because it better reflects real-world problems and responds to a crucial need for resilience, robustness, and competitiveness. In this article, a generic two-stage mixed-integer mathematical model is developed to integrate key features of location-allocation and inventory-replenishment decisions. Then, food-specific disruptions with ripple effects are incorporated through plausible scenarios. For such a setting, three resiliency strategies – namely, readiness, flexibility, and responsiveness – are used to deal with uncertainties. Based on extensive numerical experiments, the solutions obtained highlight behaviour of different design models to hedge against ripple effects as well as the importance of incorporating food-specific assumptions and risk aversion attitudes.

Joint optimization of condition-based maintenance and inventory control for a k-out-of-n:F system of multi-state degrading components

Maintaining a system of multiple degrading components requires having a supply of spare components to replace deteriorated ones in a timely manner. Decisions on whether to replace the deteriorated components are made based on the statuses of components and the system and are further restricted by the inventory level of spares. Inventory replenishment decisions themselves depend both on system status and maintenance policy. Both maintenance and replenishment decisions affect the system reliability and system maintenance and spare inventory cost. This paper considers the joint optimization of periodic condition-based replacement of components and inventory control for a k-out-of-n:F system of non-repairable degrading components under various system statuses. For modeling the degradation of components, both the Wiener process and gamma process are considered. We model the maintenance and inventory policy using the number of components in each discretized degradation state rather than the traditional approach, which uses the state of each component. Our approach considerably reduces the solution space. Based on that, we address the joint optimization using Markov decision process along with dynamic programming; we then analyze the complexity of the algorithm. We provide a numerical study on a 2-out-of-3:F system of components in three states to illustrate structural insights regarding the proposed model, including a sensitivity analysis on the length of inspection interval, system downtime cost, and inventory holding cost. We demonstrate the efficiency of the model and solution method by testing k-out-of-n:F systems with different numbers of components and discretized degradation states.

Inventory replenishment decision model for the supplier selection problem using metaheuristic algorithms.

In supply chain management, fast and accurate decisions in supplier selection and order quantity allocation have a strong influence on the company's profitability and the total cost of finished products. In this paper, a novel and non-linear model is proposed for solving the supplier selection and order quantity allocation problem. The model is introduced for minimizing the total cost per time unit, considering ordering, purchasing, inventory, and transportation cost with freight rate discounts. Perfect rate and capacity constraints are also considered in the model. Since metaheuristic algorithms have been successfully applied in supplier selection, and due to the non-linearity of the proposed model, particle swarm optimization (PSO), genetic algorithm (GA), and differential evolution (DE), are implemented as optimizing solvers instead of analytical methods. The model is tested by solving a reference model using PSO, GA, and DE. The performance is evaluated by comparing the solution to the problem against other solutions reported in the literature. Experimental results prove the effectiveness of the proposed model, and demonstrate that metaheuristic algorithms can find lower-cost solutions in less time than analytical methods.

Inventory replenishment decisions model for the supplier selection problem facing low perfect rate situations

This article addresses the supplier selection and order quantity allocation problem. It introduces a model to minimize the total cost per time unit considering inventory and transportation costs. In selecting suppliers, two feasibility constraints are considered: capacity and perfect rate. The acceptable perfect rate of raw materials is ensured with a mathematical inequality in the model constraints. The proposed model addresses the desired perfect rate by including it as part of the order cycle parameters calculation and not as an individual constraint. Two main advantages of the proposed model are: (i) it leads to lower cost solutions compared to an existing model; and (ii) it effectively faces the low perfect rate situation, by providing feasible solutions when the perfect rate of suppliers is smaller than the minimum acceptable perfect rate required by the customer. A sensitivity analysis was carried out on the proposed model to analyze the effect of some parameters on the total cost per time unit. Results showed that transportation costs have an important effect on the order quantity and, also, that price levels do not necessarily affect the amount of purchased units. Hence the importance of considering transportation costs when making order quantity allocation decisions.

Integrated Vendor–Buyer Lot-Sizing Model with Transportation and Quality Improvement Consideration under Just-in-Time Problem

This paper deals with the problem of transportation and quality within a Just-in-Time (JIT) inventory replenishment system. Formerly, transportation and quality problem are often modelled separately in most integrated inventory lot-sizing models. Hence, this paper develops an integrated vendor-buyer lot-sizing model by considering transportation and quality improvements into a JIT environment. The model is developed for minimising a total vendor–buyer system cost by optimising decisions such as delivery quantity, production batch, number of shipments, and process quality. Numerical examples and sensitivity analysis are provided to illustrate the proposed model. The developed model was also compared with an enumeration method to analyse the effectiveness of the proposed model to find the optimum solution. The results emphasise that the proposed model contributes to a new approach and obtains a near optimum solution for inventory replenishment decisions. The results are also beneficial to JIT practices as the model can improve the transport payload and reduce the chance of defective products and improving quality-related costs.

Simulation-based optimisation of replenishment policy in supply chains

Classic replenishment strategy may no longer be effective due to the increasing complexity of supply chains. The article presents the problem of inventory management while presenting a practical methodology for supporting inventory replenishment decisions in order to reduce maintenance costs. Therefore, the possibility has been shown of using simulation modelling of the supply chain. The aim of the article is to present the methodology, using computer simulation with optimisation, of searching for the optimal strategy of replenishment of stocks in supply chains, especially when there is a problem of uncertainty of the demand. A case study was presented - optimisation of inventory of an online shop with electronics. The results obtained prove the high usefulness of the proposed methodology, as compared to the initial method of replenishing, it was possible to reduce the time of storage of goods by 66%, which translates into lowering the costs in a simple way.

Joint Pricing and Inventory Replenishment Decisions with Returns and Expediting under Reference Price Effects

This paper considers a single-item joint pricing and inventory replenishment problem under reference price effects in consecutive T periods. Demands in consecutive periods are sensitive to price and reference price with general demand distribution. At the end of each period, after the demand realization, a firm can return excess stocks to a supplier or place an expediting order to reduce the loss by shortage. Unfilled demands are fully backlogged. In order to maximize the total expected discounted profit with reference price effects the optimal pricing and inventory replenishment policies for regular order and the inventory adjustment decisions for returning/expediting are derived. The optimal replenishment policy for regular order is a base-stock policy, the optimal pricing policy is a base-stock-list-price policy, and the optimal policy for returning/expediting inventory adjustment follows a dual-threshold policy. Furthermore, the analysis of the operational impacts (from the perspective of adding returning/expediting and reference price effects, respectively) is researched. Numerical results also show that considering both returning/expediting and reference price effects is more profitable than considering only one of them.

Parametric demand learning with limited price explorations in a backlog stochastic inventory system

We study a multi-period stochastic inventory system with backlogs. Demand in each period is random and price sensitive, but the firm has little or no prior knowledge about the demand distribution and how each customer responds to the selling price, so the firm has to learn the demand process when making periodic pricing and inventory replenishment decisions to maximize its expected total profit. We consider the scenario where the firm is faced with the business constraint that prevents it from conducting extensive price exploration, and develop parametric data-driven algorithms for pricing and inventory decisions. We measure the performances of the algorithms by regret, which is the profit loss compared with a clairvoyant who has complete information about the demand distribution. We analyze the cases where the number of price changes is restricted to a given number or a small number relative to the planning horizon, and show that the regrets for the corresponding learning algorithms converge at the best possible rates in the sense that they reach the theoretical lower bounds. Numerical results indicate that these algorithms empirically perform very well. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transaction, for datasets, additional tables, detailed proofs, etc.

Designing a Centralized Distribution System for Omni-Channel Retailing

We study the optimal supply chain design for a dual-channel retailer that operates a physical and a web-based store, and traditionally, managed each one separately. However, with increased pressures from customers and decreased profits due to marked down leftover inventories in each channel, the retailer considers integrating the supply chain operations of both channels. In contrast to the existing literature, we focus on the firm's choice on the best omni-channel strategies considering demand segmentation, cost structure, and more importantly, the execution ability of the firm. We formulate our problem as a two-stage stochastic programming model and use first-order optimality conditions to study the optimal inventory replenishment decisions. Based on different omni-channel strategy decisions, we explore four supply chain design options. We identify the optimal inventory replenishment policy under each option and explicitly describe the optimality conditions on cost and demand under perfect and imperfect demand information. When the demand information is imperfect, the demand fulfillment decisions can be characterized as nested protection-level policies. First, we show that omni-channel strategies are not necessarily profitable under all settings as imposed by the market conditions. Second, we demonstrate that when the company can allocate its inventory perfectly, running omni-channel strategies may help serve not only the web-based customers but also in-store customers better. Finally, we demonstrate that, in the worst case, the imperfect demand information may result in losing all of the claimed inventory pooling benefits when running omni-channel strategies.

Replenishment behaviour in sequential supply chains

Inventory managers do not predominantly follow normative optimisation models. At best, they introduce a level of bounded rationality in their inventory replenishment decisions. This paper examines the behaviour of inventory decision-makers under continuous review in a decentralised supply chain, using an experimental approach with unknown market demand and local information availability. The analysis reveals that not only the magnitude and the variability of order quantity tend to be larger, but also that the order-time intervals is lengthen and highly variable while moving upstream along the supply chain. The role of the inventory managers' replenishment decisions on the echelon holding, backorder, and total costs, is also investigated. Finally, a normative model is designed and its solutions are compared to the experimental results. It is observed that humans do not operate in a perfectly optimal way, but are generally reluctant to risk increasing backorder costs and reducing inventory carrying cost, even if this would lead to lower total cost.