Replenishment Orders Research Articles

Projected Inventory-Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

Inventory Projection and Asymptotic Optimality van Jaarsveld and Arts propose a new policy for the canonical periodic review lost sales inventory problem. Under this policy, orders are placed in each period such that the expected inventory level at the moment of replenishment order arrival is at a fixed level. This single-parameter policy is called the projected inventory-level (PIL) policy. The PIL inherits asymptotic optimality properties from the constant-order policy for long lead time and from the base-stock policy when the cost of losing a sale is large. The PIL policy has lower cost than competing heuristics in a numerical study. The PIL seems to be a promising approach for other inventory systems with a high-dimensional state space, such as the perishable item inventory management problem.

A modified variable neighborhood search algorithm for dynamic lot-sizing with supplier selection under varying delivery time quotation

This paper investigates a dynamic lot-sizing problem with supplier selection, where the manufacturer develops an aggregate plan to meet product delivery demand with the objective of minimizing the cost. Specifically, a novel supplier selection scenario with varying delivery time quotation is considered, i.e., the manufacturer places raw material replenishment orders with varying delivery time quotation and dynamically selects suppliers, and the suppliers guarantee delivery within the quoted delivery lead time. In the dynamic lot-sizing problem with supplier selection, a joint decision on the production plan, replenishment order, and supplier selection needs to be made. To tackle this complex problem, a modified Variable Neighborhood Search algorithm with nested two parallel neighborhoods (PN-VNS) is first developed for the decision on the production plan and replenishment order. Then, the decision on supplier selection needs to be made for the given replenishment order, and a pre-pruning optimization rule is proposed to obtain the optimal supplier scheme. Computational experiments are conducted to evaluate the performance of the proposed algorithm, and the experimental results demonstrate that our algorithm performs better both in terms of solution quality and running time.

Quick Response Under Strategic Manufacturer

Problem definition: Quick response is a classic operations strategy that allows a retailer to place a rapid replenishment order during the selling season using information learned from early sales. The benefits of quick response are widely studied in the literature under the condition that the manufacturer’s wholesale prices are exogenously given. Motivated by the practice of emerging small and medium-sized enterprise (SME) fashion brands, this paper revisits the value of quick response for a retailer when a manufacturer can strategically set its wholesale prices. Methodology/results: We develop a game-theoretic model consisting of one manufacturer and one retailer. In contrast to the traditional quick response setting, the manufacturer can dynamically adjust wholesale prices for both regular and replenishment orders. First, we investigate whether and when quick response still benefits the retailer. We find that, under low or significantly high demand uncertainties, the firms share a common preferred ordering strategy, and quick response benefits the retailer as well as the supply chain. But, under moderately high demand uncertainty, the retailer’s favored ordering strategy conflicts with the manufacturer’s interest; as a result, the manufacturer would set wholesale prices to counter the retailer’s ordering strategy, which makes quick response detrimental to the retailer. Second, we search for mechanisms that can resolve this conflict and restore the beneficial effect of quick response. We show that letting the manufacturer commit to wholesale prices up front is ineffective in fixing the problem. However, if the retailer can propose a take-it-or-leave-it wholesale price for the replenishment order (possibly with the replenishment quantity) once the regular wholesale price is set, then quick response leads to a win–win outcome for both firms. Managerial implications: The findings caution retailers with weak power (e.g., SMEs) when adopting quick response, especially when facing moderately high demand uncertainties. The retailer, although weak, should be aware of the retailer’s natural ability to propose replenishment terms because, otherwise, the retailer can always forgo quick response; this opens up an opportunity to design more favorable arrangements. Funding: The work of J. Chen was supported by the National Natural Science Foundation of China [Grants 72171202, 72232007]; the work of Q. Hu was supported by the National Natural Science Foundation of China [Grants 72271057, 72091211]; the work of D. Shi was supported by the National Natural Science Foundation of China [Grant 72102205] and Shenzhen Stable Support Program for Higher Education Institutions; the work of F. Zhang was supported by the National Natural Science Foundation of China [Grants 71929201, 72131004]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/msom.2021.0561 .

Optimal inventory policies for finite horizon deterministic inventory models for non-instantaneous deteriorating items and permissible-delay in payment

This paper is concerned with the search for the optimal inventory policy for a finite horizon inventory model with time-varying demand, non-instantaneous deteriorating items, and permissible delay in payment. The optimal inventory policy consists of the determination of the number and timing of replenishment schedules that minimise some total inventory costs. The search for such policy is formulated as a mixed integer nonlinear programming problem (MINLP). It turns out that the non-instantaneous deterioration phenomenon coupled with permissible delay in payment introduce non-smoothness in the objective function of the MINLP. This leads to failure of direct applications of known solution methods to the MINLP. To circumvent this problem, a methodology is proposed for solving fully the MINLP problem. It is shown, through careful mathematical analysis, that earlier results on similar problems can be adapted to solve this problem. Conditions under which the solution of the MINLP is unique are identified. Moreover, convexity with respect to the number of replenishment orders is established. This makes the search for the optimal inventory policy handy. Numerical experiments are also conducted to test the applicability, to identify the key elements and to provide managerial insights to the model.

An optimal replenishment cycle and order quantity inventory model for deteriorating items with fluctuating demand

Suppliers often prefer to offer their retailers a delay period in payment to attract more sales and promote revenue in a supply chain. The retailers usually ask their customers to pay a portion of purchasing cost when receiving the product (i.e., a downstream partial trade credit) to reduce the default risk. On the other hand, the suppliers provide discounts for bulk purchases, and the retailer has enough capital to purchase more goods than can be stored in its warehouse. The retailer must store the excess quantities in a rented warehouse if the storage capacity is limited. A two-warehouse inventory system is needed to model this problem. In reality, the demand rate fluctuates with time, and the relevant cost is usually affected by the present value of time. This study focuses on the limited storage capacity inventory model for deteriorating items with fluctuating demand, downstream partial trade credit transactions, and discounted cash-flow considerations. The aim is to find the optimal replenishment cycle and order quantity and keep the present value of the total relevant cost per unit of time as low as possible. We further present numerical examples to demonstrate the applicability and develop managerial insights.

Supply chain management analysis of avocado in south Sumatra province through the Food Supply Chain Network (FSCN) method

One of the agricultural sub-sectors that occupy a strategic position in agricultural development is the horticultural sub-sector, with one of its potential commodities being avocado. Avocado is one of the export-based commodities, especially in South OKU Regency, South Sumatra Province. This study aims to obtain an overview of the Avocado Agribusiness Supply Chain management in South OKU Regency. The study was conducted in Warkuk Selatan District, South OKU Regency in February 2022. The research method used was a qualitative descriptive method with a type of data using primary data and secondary data. The data analysis method uses the Food Supply Chain Network (FSCN) method, which illustrates South Oku Regency's avocado supply chain model. The results showed that the Avocado Management Supply Chain Management model with the FSCN framework consisted of four main components: the supply chain structure, the business chain process, supply chain management, and supply chain resources. Avocado supply chain targets are still dominated to meet the domestic market and products in the form of fresh avocados for consumption. Avocado supply chain management comprises election partners, contractual agreements, transaction systems, government support, and supply chain collaboration. The avocado supply chain structure in South OKU Regency consists of farmers, collecting traders, local and non-local traders, retailers, and consumers with respective roles in the supply chain structure. Business processes in avocado supply chain management consist of procurement, replenishment, and customer order cycles. Based on marketing margin analysis, the lowest total marketing margin is found in channel IV, with a margin value of Rp 1,500 per kg. The four avocado marketing channels in South Warkuk Ranau District have Farmer’s Share ≥40%, so it is categorized as an efficient channel.

Optimal control of inventory level for perishable goods with uncertain decay factor and uncertain forecast information: a new robust MPC approach

This paper deals with the inventory control in supply chains under the following assumptions: (1) perishable goods with uncertain deteriorating factor, (2) a future uncertain customer demand that, over a limited prediction horizon, belongs to a known compact set. The problem is to define a smooth control policy maximising the fulfilled customer demand and minimising the inventory level. This problem is here solved through a new Robust Model Predictive Control (RMPC) approach. This implies solving a min–max optimisation problem with hard constraints on the control effort (i.e. the sequence of replenishment orders). To drastically reduce the numerical complexity of this problem, the control signal is sought in the space of B-spline functions, which are known to be universal approximators admitting a parsimonious parametric representation. This allows us: (1) to reduce the number of both decision variables and constraints involved in the optimisation procedure, (2) to reformulate the numerically demanding minimisation of the worst case cost functional as a simpler Weighted Constrained Robust Least Squares (WCRLS) estimation problem. The WCRLS algorithm can be efficiently solved using interior point methods. A rigorous analysis of stability and feasibility conditions is provided.

Stock control analytics: a data-driven approach to compute the fill rate considering undershoots

One of the most frequently used inventory policies is the order-point, order-up-to-level (s, S) system. In this system, the inventory is continuously reviewed and a replenishment request is placed whenever the inventory position drops to or below the order point, s. The variable replenishment order quantity and the variable replenishment cycle characterize the system by the use of complex mathematical computations. Different methodological approaches diminish the mathematical complexity by neglecting the undershoots, i.e., the quantity that the inventory position is below the order point when it is reached. In this paper, we conceptually and empirically analyse the bias that neglecting the undershoots introduces into the estimation of the fill rate. After that, we suggest a new methodology developed under a data-driven perspective that uses a state-dependent parameter algorithm to correct such a bias. As a result, we propose two new methods, one parametric and the other nonparametric, to enhance the fill rate estimate. Both methods, named analytics fill rate methods, remove the bias that neglecting the undershoots introduces and are used to illustrate the practical implications of this hypothesis on the performance and design of the (s, S) system. This research is developed in a lost sales context with simulated stochastic and i.i.d. discrete demands as well as actual sales data.

Stochastic decomposition in a queueing-inventory system with batch demands, randomized order policy and multiple vacations

This article studied a queueing-inventory system with batch demands, randomized order policy, and multiple vacations. Customers arrive in this system according to a Poisson process and take away batch items after a service time. The system sends a replenishment order and starts multiple vacations simultaneously once the on-hand inventory level drops to zero. The replenishment is based on a random order size policy. Customers arriving during this period are assumed to be lost. Under the assumption that all the underlying random variables are exponential, the stationary joint probability is obtained in product form. Based on the stationary distribution, the expected sojourn time of a permitted entering customer is derived in recursive form. Several numerical examples are processed to analyze the effect of variant parameters on the performance measures. The numerical results show that the expected total cost function is a convex function with respect to the maximum allowable inventory. The influence of various parameters on the optimal value is also displayed visually.

Integrated control policies of production, returns’ replenishment and inspection for unreliable hybrid manufacturing-remanufacturing systems with a quality constraint

This paper deals with the production planning and control problem within unreliable Hybrid Manufacturing-Remanufacturing Systems (HMRSs) evolving in a stochastic and dynamic environment. The customer demand can then be fulfilled by either manufacturing of new units or remanufacturing of returned ones. However, both used materials and returns may contain a fraction of defective items. The paper investigates how companies could benefit from such integrated control policy to assist their managers in determining production rates, the sequence and the size of replenishment orders as well as their sample size to be inspected. The corresponding problem aims to propose an efficient control policy integrating four central decisions to coordinate remanufacturing, manufacturing, replenishment of returns and their quality control while minimizing the total cost and satisfying a quality constraint requested by customers. A simulation-based optimization approach is used to tackle the problem. It aims to determine the optimal values of control parameters of the proposed policy minimizing the total cost. The results provide relevant insights and bring effective solutions to help decision makers manage simultaneously manufacturing, remanufacturing, replenishment of returns and their quality control activities. A comparative study is also performed showing that our policy, based on sampling inspection of delivered returns, outperforms in terms of costs those most used in the literature where complete (i.e. 100%) or no inspection strategies are used.

Analysis is a discrete time queueing-inventory model with back-order of items

This paper analyses a discrete-time (s, S) queueing inventory model with service time and back-order in inventory. The arrival of customers is assumed to be the Bernoulli process. Service time follows a geometric distribution. As soon as the inventory level reaches a pre-assigned level due to demands, an order for replenishment is placed. Replenishment time also follows a geometric distribution. When the inventory level reduces to zero due to the service of customers or non-replenishment of items, a maximum of k customers are allowed in the system and the remaining customers are assumed to be completely lost till the replenishment. Matrix-Analytic Method (MAM) is used to analyze the model. Stability conditions, various performance measures of the system, waiting-time distribution and reorder-time distribution are obtained. Numerical experiments are also incorporated.

A variant SDDP approach for periodic-review approximately optimal pricing of a slow-moving a item in a duopoly under price protection with end-of-life return and retail fixed markdown policy

In this paper, we examine a selling environment where a manufacturer-controlled retailer and an independent retailer sell a slow-moving A item. The manufacturer offers the independent retailer a price protection contract stipulating that the manufacturer reimburses the independent retailer in case of a reduction in the wholesale price. The price set by the independent retailer is assumed to be determined by Retail Fixed Markdown (RFM) policy. The manufacturer also offers the independent retailer a special discount rate for the replenishment orders and the retailers are assumed to follow (R, S) inventory replenishment policy. The manufacturer adopts a periodic-review pricing strategy and the mean demand observed by each retailer in a given period depends on the prices. We also take the customers choosing no-purchase option into account. We employ multinomial logit (MNL) models to forecast customers’ preferences based on retail prices. The retailers’ market shares are estimated by customized choice probability functions. We propose stochastic programming models to determine the manufacturer’s pricing strategy. Then, we propose a variant Stochastic Dual Dynamic Programming (SDDP) algorithm to determine the manufacturer’s approximately optimal pricing strategy by getting around three curses of dimensionality. Then, we move on to the observations on the impact of four critically important contractual parameters on the price, the market shares and the expected total net profits and finally discuss some possible approaches for the selection of the best compromise values of those contractual parameters.

Controlling inventories in omni/multi-channel distribution systems with variable customer order-sizes

The fast growth of e-commerce and omni/multi-channel retailing brings new challenges for efficient inventory management. One such challenge concerns service differentiation across channels when upstream central warehouses satisfy both direct customer demand and replenishment orders from downstream retailers. Motivated by industry collaboration, we address this issue by developing a combined stock method for control of one-warehouse-multiple-retailer inventory systems with direct customer demand at the central warehouse. The combined stock method, used for service differentiation at the central warehouse, may be described as a critical level policy. The computationally efficient heuristics we present are designed to deal with real-life one warehouse multiple retailer inventory systems characterized by highly variable customer order-sizes, (R,Q) policies at all stock points, and fill rate constraints. A numerical study, including real data from two different companies, illustrates that the heuristics perform well; offering near optimal solutions close to target fill rates, with significant opportunities to reduce total inventory costs compared to existing methods.

Volume flexibility at responsive suppliers in reshoring decisions: Analysis of a dual sourcing inventory model

AbstractWe investigate how volume flexibility, defined by a sourcing cost premium beyond a base capacity, at a local responsive supplier impacts the decision to reshore supply. The buyer also has access to a remote supplier that is cheaper with no restrictions on volume flexibility. We show that with unit lead time difference between both suppliers, the optimal dual sourcing policy is a modified dual base‐stock policy with three base‐stock levels , , and . The replenishment orders are generated by first placing a base order from the fast supplier of at most units to raise the inventory position to , if that is possible. After this base order, if the adjusted inventory position is still below , additional units are ordered from the fast supplier at an overtime premium to reach . Finally, if the adjusted inventory position is below , an order from the slow supplier is placed to bring the final inventory position to . Surprisingly, in contrast to single sourcing with limited volume flexibility, a more complex dual sourcing model often results in a “simpler” policy that replaces demand in each period. The latter allows analytical insights into the sourcing split between the responsive and the remote supplier. Our analysis shows how increased volume flexibility at the responsive supplier promotes the decision to reshore operations and effectively serves as a cost benefit. It also shows how investing in base capacity or additional volume flexibility act as strategic substitutes.

Quantity-based emergency shipment policies

Either structurally or in an ad hoc manner, emergency shipments are widely utilized for preventing the potentially negative impacts of stock-outs. In addition to having policies for their regular orders, companies need to decide when and for how many units to place emergency orders. In this article, we consider the periodic-review problem of a retailer who uses a quantity-based emergency shipment policy. Under this policy an emergency order is triggered if the inventory level within the review period falls below a certain level. We consider the base-stock policy for the regular replenishment orders. The goal is to determine the optimal base-stock level, the optimal period length as well as the optimal size and threshold value of emergency orders such that the total expected cost rate is minimized. We use renewal reward theory to derive the expressions of operating characteristics. The expected cost rate’s properties are analyzed to develop an optimization algorithm for finding the optimal policy parameters. We compare our policy with the time-based and hybrid emergency shipment policies and conclude that the quantity-based policy can bring substantial benefits compared to other policies.

On the estimation of the fill rate for the continuous (s, S) inventory system for the lost sales context.

In the continuous review reorder point, base-stock (s, S) policy, the replenishment order is launched when the inventory position reaches the reorder point, s. It is commonly assumed that the inventory position is exactly equal to the reorder point at the moment the order is launched, when actually it could be lower at that moment. This implies neglecting the possible undershoots at the reorder point, which has a direct impact on the calculation of the expected shortages per replenishment cycle. This article presents a method for an exact calculation of the fill rate (fraction of demand that is immediately satisfied from shelf) which takes explicit account of the existence of undershoots and is applicable to any discrete demand distribution function in a context of lost sales. This method is based on the determination of the stock probability vector at the moment the replenishment order is launched. Furthermore, neglecting the undershoots is shown to lead to an overestimation of the fill rate, particularly when we move farther away from the unitary demand assumption. From a practical point of view, this behaviour involves underestimating the base-stock level, S, when a target fill rate is set for its determination. The method proposed in this paper overcomes these shortcomings.

Two-echelon Inventory Management for Sustainable Pharmaceutical Supply Chain through Waste Reduction

Improving sustainability in Pharmaceutical Supply Chain (PSC) becomes the primary concern for its involved members. It lends major challenges to its management as it has economic, social, and environmental responsibilities more weighed than other supply chains. Providing the day-to-day need for medicines must be satisfied while taking into account the use of the economic resource, customer satisfaction, and the impact of pharmaceutical waste on the environment. Medicines waste affects healthcare expenses and harms the environment. Therefore, avoiding unused medication leftover through the pharmaceutical chain presents an efficient approach to attaining a sustainable supply of medicines. This article aims to deal with the sustainability of a PSC by minimizing the deterioration rate of medicines at both distributor and hospitals sites. We propose an inventory management model based on a mixed-integer non-linear program (MINLP) that seeks the optimal replenishment order quantity of multiple types of products and the shipment time in a two-echelon PSC consisting of a pharmaceutical company (PC), a central pharmacy (CP), and multiple hospitals over a planning horizon, while considering shipment costs, perishability, and shortage constraints.

Average Cost Optimality in Partially Observed Lost-Sales Inventory Systems

We consider a partially observable inventory system in which the inventory level can only be observed when it reaches zero, the unmet demand is lost, and replenishment orders must be decided so as to minimize the long-run average cost. This problem has an infinite-dimensional state space and is therefore difficult to analyze. We prove the existence of an average-cost optimal policy, using the so-called vanishing discount factor approach. As a main methodological contribution, we provide a way to verify the key condition -- the uniform boundedness of the relative discounted value function -- for the partially observed system. To accomplish that we construct -- for the partially observed system -- a valid policy which in a certain sense copies the actions of another policy for the process with a different initial state. To our best knowledge, this paper is the first dealing with inventory models with partially observable inventory levels under the long-run average cost criterion.

An inventory model with self-generation of priorities and retrial of customers

This paper mainly focuses on a single server retrial inventory system. The arrival of customers follows the Poisson process, and when the inventory level depletes to the reorder level s due to service, replenishment order placed according to (s, Q) policy. The lead-time governed by an exponential distribution with parameter β. A customer who finds the server busy or inventory dry moves to an orbit of infinite capacity with probability σ. Customers in orbit independently tries to access the server at a rate of θ, which depends on the number of customers in orbit. A retrial customer returns to the orbit with probability δ if the server is busy or inventory is dry. Each customer in orbit generates priority according to an exponential distribution with rate γ. If the server is free, a priority generated customer will get immediate service. Else such a customer have to wait in a space A 1 of capacity one, which is reserved only for priority generated customers. The service times follows exponential distribution with different rates for ordinary and priority generated customers. The model turned out to be a level-dependent quasi birth-death(LDQBD) process, and we use Matrix-Analytic Method as a tool for obtaining a solution.

The beneficial effect of information sharing in the integrated production–distribution planning of textile and apparel supply chain

The present paper proposes an integrated production–distribution planning approach for a textile and apparel supply chain. Tactical and operational decisions are considered in the proposed multi-product and multi-period planning problem. Using a rolling horizon, the approach aims at defining optimal quantities to produce, to store and to deliver. The integration consists in coordinating informational flows between producer and retailer. Information sharing will allow the producer to estimate more accurately the future replenishment orders that may happen at the operational level and adjust production capacity requirements accordingly. For this purpose, a two-stage planning approach is devised; the first stage deals with the tactical level while the second stage deals with the operational level. The monthly decisions taken at the tactical planning level are accounted for in the operational planning considering a variable rolling horizon. Moreover, accurate forecasts of future replenishment orders are established based on information sharing and introduced in the operational planning to determine the weekly decisions. Linear programming models are used to build production and distribution plans at the tactical and operational levels. Using real-life data from a textile and apparel Tunisian firm, we show that producer-retailer coordination based on the sharing of current sales information, yields significant cost savings reaching up to 20% of the supply chain cost. These findings can only motivate the partnership between producer and retailer through reliable information sharing in joint tactical-operational and production–distribution planning.