Optimal Inventory Allocation Research Articles

A Study of Two-level Inventory Allocation for E-commerce Pre-sales Based on Two Return Methods

In recent years, e-commerce shopping festivals based on the presale model have become increasingly popular. Under the pre-sale model, some e-commerce companies have used inventory front-loading methods to give consumers higher time satisfaction for alleviating the pressure caused by order piling. At the same time a new return method has been generated, but existing studies have only considered the traditional return method. In this paper, a dualobjective decision model based on NSGA-II algorithm is developed for maximizing enterprise profit and maximizing consumer time satisfaction under the premise of considering both return methods, and the optimal two-level inventory allocation decision scheme is calculated for e-commerce enterprises. The results show that the existence of two return methods will have a more significant impact on enterprise profit, and therefore is more practical for e-commerce enterprises to make two-level inventory allocation decisions.

Price Discrimination and Inventory Allocation in Bertrand Competition

Problem definition: It is common practice for firms to deploy strategies based on customer segmentation (by clustering customers into different segments) and price discrimination (by offering different prices to different customer segments). Price discrimination, although seemingly beneficial, can hurt firms in competitive environments. Academic/practical relevance: It is thus critical for firms to understand when to engage in price discrimination and how to support discriminatory pricing practices with appropriate inventory management strategies. This paper tackles this overarching question through operational lenses by studying the joint impact of price discrimination and the allocation of limited inventory across customer segments. Methodology: We develop a Bertrand competition game featuring capacity restrictions, quality differentiation, and customer heterogeneity. Results: We characterize (pure- or mixed-strategy) Nash equilibria for a single-stage game reflecting uniform pricing and for a two-stage inventory-price game reflecting discriminatory pricing along with endogenous inventory allocation. Managerial implications: We identify three sources of market friction in price competition enabling firms to earn higher profits: capacity limitations, quality differentiation, and customer heterogeneity. Price discrimination eliminates the market frictions from customer heterogeneity, but strategic inventory allocation restores (or strengthens) the market frictions from capacity limitations. As such, price discrimination is only beneficial when combined with optimal inventory allocation across segments. We discuss relevant real-world examples featuring regional price discrimination along with strategic inventory allocation, including fast fashion and vaccines. Otherwise, uniform pricing may outperform discriminatory pricing. Our results thus underscore the critical role of inventory allocation in the design of competitive pricing strategies. Funding: This research was partially supported by the National Natural Science Foundation of China [Grant 71821002]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1146 .

Automated targeting for green supply chain planning considering inventory storage losses, production and set-up time

ABSTRACT Aggregate planning has been used to maximize profit of a supply chain over a specified time horizon while satisfying customers’ demand. However, previous work on aggregate planning did not consider factors such as inventory sizing, inventory losses, production, and setup time simultaneously. These factors are imperative as they influence a decision-maker’s capability to ascertain the true performance of a given supply chain. This research gap is addressed in this work by developing an improved aggregate planning model to optimize inventory allocation in green production supply chains based on inventory storage size, storage losses, production, and set-up time. To demonstrate the applicability of the model, a biochar production supply chain case study was solved. Results from the case study confirm that optimal production and inventory allocation are dependent on storage losses and unit storage costs. These results were compared to those obtained via a published method. The comparison indicated that the presented method yielded more realistic results.

Optimal dynamic allocation of rental and sales inventory for fashion apparel products

There is a growing trend towards renting rather than permanent ownership of various product categories such as designer clothes and accessories. In this article, we study an emerging retail business model that simultaneously serves rental and sales markets. Specifically, we consider a retailer that primarily focuses on renting while also selectively meeting incidental sales demand. Once a unit is sold, the firm forgoes potentially recurring rental revenues from that unit during the remaining periods. Therefore, it is critical for a retailer to dynamically decide how much of its inventory to allocate for sales and rentals at each period. We first develop a consumer choice model that determines the fraction of the market that chooses renting over purchasing. We characterize the optimal inventory allocation policy and explore how market characteristics and prices impact inventory allocation. We discuss the value of dynamic allocation and observe that the profit improvement can be substantial. In addition, we propose a simple and efficient heuristic policy. Finally, we extend our analysis to study the optimal allocation policies for (i) a retailer that is primarily a seller that selectively meets rental demand, and (ii) a retailer that does not enforce any prioritization between rental and sales demand.

A Study on the Optimal Inventory Allocation for Clinical Trial Supply Chains

With increasing competition in the pharmaceutical industry, pharmaceutical companies pay more attention to improving the efficiency of clinical trial supply chains to reduce the drug supplying cost, which takes up a considerable part of the total research and development expense. To improve the efficiency of clinical trial supply chains, this study investigates the inventory levels of clinical drugs in each period at a distribution center and clinics considering the reverse replenishment, transshipment, and generalized stockout cost. The inventory allocation problem in clinical trial supply chains is formulated as a rolling horizon-based two-stage stochastic mixed-integer model where the minimal operational cost constitutes the underage cost at the production planning level of clinical trial supply chains. An algorithm extending Benders decomposition is proposed as the solution approach. We also derive several structural results and develop the reformulation method and row generation strategy to improve the efficiency of the optimization process. The effectiveness of our approach is demonstrated in the numerical experiment.

Revisiting Bertrand Competition in the Face of Customer Heterogeneity and Price Discrimination

This paper compares uniform vs. discriminative pricing strategies in a competitive setting featuring capacity restrictions, quality differentiation, and customer heterogeneity. It tackles this overarching question through operational lenses, by studying the joint impact of price discrimination and the allocation of limited inventory across customer segments. Thanks to advances in information technology, firms have developed new capabilities in terms of customer segmentation (by clustering customers into different segments) and price discrimination (by offering different prices to different customer segments). Price discrimination, although seemingly beneficial, can hurt firms in competitive environments. It is thus critical for firms to understand when to engage in price discrimination, and how to support discriminative pricing practices with appropriate inventory management strategies. We develop a Bertrand competition game featuring capacity restrictions, quality differentiation, and customer heterogeneity. We characterize (pure- or mixed-strategy) Nash equilibria for a single-stage game reflecting uniform pricing and for a two-stage inventory-price game reflecting discriminative pricing. We identify three sources of market friction in price competition, enabling firms to earn higher profits: capacity limitations, quality differentiation, and customer heterogeneity. Price discrimination eliminates the market frictions from customer heterogeneity, but strategic inventory allocation restores (or strengthens) the market frictions from capacity limitations. Ultimately, price discrimination is only beneficial when combined with optimal inventory allocation, thus underscoring the critical role of inventory allocation in the design of competitive pricing strategies.

Optimal Inventory-allocation Integrated Model for Perishable Items with Stochastic Demand in a Single-vendor Multi-retailer Supply Chain

This study investigates an increasingly widespread supply chain system that involves a vendor cyclically supplying specific perishable item to multiple retailers. In general, the vendor has to earlier and accurately determine inventory quantity to meet aggregate demand, and exactly allocate the inventory among a number of retailers to reduce the adjustment costs. Meanwhile, a vital challenge faced for vendors is to develop an efficient inventory- allocation decision model for given perishable item with stochastic and correlated retailer demands during upcoming selling period. To this end, an effective and practical analytical approach, which extends the newsvendor model to incorporate the considered inventory- allocation decision, is proposed here to simultaneously solve the optimal inventory quantity and allocation policy for maximizing expected vendor profits of perishable items. Especially, the lognormal distribution and Ito process is used here to model the behaviors of individual demand shift. Also, an effective integrated approach is presented to work out the aggre- gate demand during next selling period. Finally, numerical experiments are conducted to demonstrate and validate the proposed model and extract the valuable managerial findings.

Optimal Dynamic Allocation of Sales and Rental Inventory at a Retailer

There is a growing trend towards renting rather than permanent ownership of various product categories such as designer clothes and accessories. In this paper, we study an emerging retail business model that simultaneously serves rental and sales markets. Specifically, we consider a retailer that primarily focuses on renting while also selectively meeting incidental sales demand. Once a unit is sold, the firm forgoes potentially recurring rental revenues from that unit during the remaining periods. Therefore, it is critical for a retailer to dynamically decide how much of its inventory to allocate for sales and rentals at each period. We first develop a consumer choice model that considers heterogeneities in usage frequency, fashion-consciousness, and valuation that determines the fraction of the market that chooses renting over purchasing. We characterize the optimal inventory allocation policy and explore how market characteristics impact inventory allocation. We then discuss the value of dynamic allocation and observe that the profit improvement can be substantial, especially with lower inventory levels and a long rental season. In addition, we also propose a simple and efficient heuristic policy. Finally, we extend our model to study a retailer that is primarily a seller while selectively meeting rental demand.

Optimal Inventory Allocation for Short Life Cycle Product in Distribution System

Optimal Inventory Allocation for Short Life Cycle Product in Distribution System

Optimal Markdown Pricing and Inventory Allocation for Retail Chains with Inventory Dependent Demand

We analyze how inventory dependence of demand affects the optimal pricing and distribution of inventory across multiple retail locations. Our problem formulation corresponds to the typical markdown management decisions in a retail chain. The solution methodology determines the optimal combinations of three important operational levers—pricing, inventory allocation, and store consolidation. Inventory dependence causes the optimal price trajectory to decrease over time as the current on-hand inventory decreases. The optimal inventory allocation shifts more inventory to the larger stores as the inventory effect becomes stronger. Solution methodologies are also developed for the case of optimal constant prices, which leads to the same optimal inventory allocations. If all stores have the same seasonal variations and the inventory is allocated optimally, then all stores have identical price trajectories. Optimal consolidation of the inventory to a subset of the stores is also determined. Consolidation of inventory to a subset of stores can be beneficial even when there are no fixed costs of stocking a store. Using some typical parameter values for retail items, our calculations show that significant benefits can result from taking the inventory effect into account in pricing, inventory allocation, and store consolidation decisions. The online appendix is available at https://doi.org/10.1287/msom.2016.0609 .

Inventory allocation models for a two-stage, two-product, capacitated supplier and retailer problem with random demand

The objective of this research is to develop an optimal inventory allocation methodology for a supply chain consisting of a capacitated retailer with limited shelf space, and two unreliable capacitated suppliers in an uncertain environment. We develop conceptual and analytical models that provide allocation preferences between shelf-space and warehouse in both deterministic and stochastic demand cases, and develop managerial insights based on them. For each case, we provide both a closed-form solution and a heuristic method, and illustrate the bounds on the optimal solution. Further, we show that the cost function is L⋄-convex in some cases. Finally, we prove that the expected profit decreases as the variance of demand increases.

Optimal two-period inventory allocation under multiple service level contracts

Optimal inventory allocation policies have a significant impact on profits in the retail industry. A manufacturer ships products to the retailers’ stores where the end customers buy the product during the selling season. It has been put forward that it is beneficial for the manufacturer to reserve a certain fraction of the inventory for a second replenishment. Then the manufacturer can replenish the retailers’ inventories optimally and can take advantage of the risk pooling effect. In practice, retailers require a certain availability of the product throughout the selling season. Supply contracts are used to coordinate the delivery of products. Under such a contract, the manufacturer agrees to achieve a certain service level and to pay a financial penalty if she misses it. We analyze how a manufacturer responds to a service level contract if she wants to minimize her expected costs. We develop an allocation strategy for the multiple retailer case and find that our results allow for a better understanding of the effect of service level contracts on manufacturers and retailers.

Towards an Optimal Order Planning in Global Supply Chain

This paper presents the optimal order planning and parts inventory allocation method which imitates multiple negotiation among various parties with combinatorial auction. Each company which constitutes the supply chain estimates the satisfaction value of each order. Proposal method decides an order planning to aim maximizing an average of each company's satisfaction value. The method mimics that each company negotiates with others by using combinatorial auction. A numerical example is then discussed to demonstrate its suitability in obtaining an optimal order under multiple negotiations with participating companies.

Replenishment and Fulfillment Based Aggregation for General Assemble-to-Order Systems

We consider an assemble-to-order system with multiple products, multiple components which may be demanded in different quantities by different products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process under the discounted cost criterion. A control policy specifies when a batch of components should be produced (i.e., inventory replenishment) and whether an arriving demand for each product should be satisfied (i.e., inventory allocation). As optimal solutions for such problems are computationally intractable for even moderate sized systems, we approximate the optimal cost function by reducing the state space of the original problem via a novel aggregation technique that uses knowledge of products' component requirements and components' replenishment batch sizes.We establish that a lattice-dependent base-stock and lattice-dependent rationing policy is the optimal inventory replenishment and allocation policy for the aggregate problem under a disaggregation rule that disaggregates each aggregate state into its two extreme original states. This rule drastically reduces the per iteration computational complexity of the value iteration algorithm for the aggregate problem (without sacrificing much accuracy, according to our numerical experiments). We further alleviate the value iteration computational burden by eliminating suboptimal actions based on our optimal policy structure.For systems in which there is a product that has fulfillment priority over all other products at optimality, we are able to derive finite error bound for the cost function of the aggregate problem. With these bounds we show that the value iteration algorithm in the original problem that starts with the aggregate solution converges to the optimal cost function. Numerical experiments indicate that such an algorithm has distinct computational advantage over the standard value iteration method in the original problem.

Optimal Inventory Control and Allocation for Sequential Internet Auctions

We study an optimal inventory control and allocation for a seller who uses sequential Internet auctions to sell replenishment products. This problem is faced not only by retailers/distributors in the retail industry but also by manufacturers who use sequential Internet auctions to sell products that can be replenished. We consider the total expected discounted profit criterion in a finite horizon and both the discounted and average profit criteria over an infinite horizon, and show the optimality of the so-called base-stock-allocate-all (BSAA) policies. Then, we simplify the problem of computing the optimal policies and profits for either the discounted or average profit criterion in an infinite horizon to an optimization problem with only one integer decision variable. We show these results for the list price case, and also for the case where the reserve price is a decision variable. Finally, numerical results are given, where the effects of several model parameters on the optimal policies and profits are numerically analyzed.

A newsvendor approach to inventory and pricing decisions in NYOP channels

In opaque selling certain characteristics of the product or service are hidden from the consumer until after purchase, transforming a differentiated good into somewhat of a commodity. Opaque selling has become popular in travel service pricing as it allows firms to sell their differentiated products at higher prices to regular brand loyal customers while simultaneously selling to non-loyal customers at discounted prices. At its simplest level, the process can be regarded as a Newsvendor problem where a supplier has to make both pricing and quantity allocation decisions for a perishable good or service. As the originator of opaque selling, Priceline.com provides unique data to sellers that allows them to better utilize their opaque selling mechanism. Recently Priceline has made some changes to their mechanism that have potential impacts on how firms set prices and control inventory within the channel. In this framework, the problem has the characteristics of Newsvendor problems with multiple price points. In this article, we develop optimal pricing and inventory policies for a seller releasing inventory to an opaque sales channel. Furthermore, we investigate the impacts of Priceline’s changes upon optimal prices and inventory allocation policies. The model is empirically illustrated using Priceline data for a 3.5 star hotel.

Markdown optimization at multiple stores

This article studies a markdown optimization problem commonly faced by many large retailers that involves joint decisions on inventory allocation and markdown pricing at multiple stores subject to various business rules. At the beginning of the markdown planning horizon, there is a certain amount of inventory of a product at a warehouse that needs to be allocated to many retail stores served by the warehouse over the planning horizon. In the same time, a markdown pricing scheme needs to be determined for each store over the planning horizon. A number of business rules for inventory allocation and markdown prices at the stores must be satisfied. The retailer does not have a complete knowledge about the probability distribution of the demand at a given store in a given time period. The retailer’s knowledge about the demand distributions improves over time as new information becomes available. Hence, the retailer employs a rolling horizon approach where the problem is re-solved at the beginning of each period by incorporating the latest demand information. It is shown that the problem involved at the beginning of each period is NP-hard even if the demand functions are deterministic and there is only a single store or a single time period. Thus, attention is focused on heuristic solution approaches. The stochastic demand is modeled using discrete demand scenarios based on the retailer’s latest knowledge about the demand distributions. This enables possible demand correlations to be modeled across different time periods. The problem involved at the beginning of each period is formulated as a mixed-integer program with demand scenarios and it is solved using a Lagrangian relaxation – based decomposition approach. The approach is implimented on a rolling horizon basis and it is compared with several commonly used benchmark approaches in practice. An extensive set of computational experiments is perfomed under various practical situations, and it is demonstrated that the proposed approach significantly outperforms the benchmark approaches. A number of managerial insights are derived about the impact of business rules and price sensitivity of individual stores on the total expected revenue and on the optimal inventory allocation and pricing decisions.

Inventory control and replenishment with flexible delivery‐time upgrade

AbstractWe consider a capacitated inventory model with flexible delivery upgrades, in which the seller allocates its on‐hand inventory to price‐ and delivery‐time‐sensitive customers. The seller has two decisions: inventory commitment and replenishment. The former addresses how the on‐hand inventories are allocated between the two classes of customers within an inventory cycle. The latter addresses how the inventory is replenished between inventory cycles. We develop optimal inventory allocation, upgrade, and replenishment policies and demonstrate that the optimal policy can be characterized by a set of switching curves. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 418–426, 2014

An assemble-to-order system with product and components demand with lost sales

This paper studies a single end product assemble-to-order system serving both the demand of the end product and the individual components. Demands are assumed to form independent Poisson streams with different rates. Unsatisfied demand, both for the end product and for components, is assumed lost and thus incurs a per unit lost sale penalty. The end product is assembled from K distinct components each produced on a different production facility (or procured from independent suppliers). Production lead times are non-identical and are assumed to be independent and exponentially distributed. Produced components are held in stock in anticipation of future demands. The goal is to determine the optimal component production and inventory allocation policy. The optimal policy is characterised using a Markov Decision Process model. It is shown that, in addition to the state-dependent threshold type, the optimal policy exhibits counter-intuitive features which have not been observed in systems without components demand. In particular, for certain combinations of system parameters, the optimal inventory allocation policy switches priority as the inventory level of components changes. Furthermore, for a particular component k, as the inventory level of other components increases, the desirability of satisfying Component k demand decreases. Finally, because in general the optimal policy is fairly complicated and is difficult to obtain numerically, due to the curse of dimensionality of dynamic programming, three heuristic policies are proposed. Extensive numerical experiments indicate that the three heuristics perform very well compared to the optimal policy.

Optimal inventory management for a retail chain with diverse store demands

Item demands at individual retail stores in a chain often differ significantly, due to local economic conditions, cultural and demographic differences and variations in store format. Accounting for these variations appropriately in inventory management can significantly improve retailers’ profits. For example, it is shown that having greater differences across the mean store demands leads to a higher expected profit, for a given inventory and total mean demand. If more than one inventory shipment per season is possible, the analysis becomes dynamic by including updated demand forecasts for each store and re-optimizing store inventory policies in midseason. In this paper, we formulate a dynamic stochastic optimization model that determines the total order size and the optimal inventory allocation across nonidentical stores in each period. A generalized Bayesian inference model is used for demands that are partially correlated across the stores and time periods. We also derive a normal approximation for the excess inventory from the previous period, which allows the dynamic programming formulation to be easily solved. We analyze the tradeoffs between obtaining information and profitability, e.g., stocking more stores in period 1 provides more demand information for period 2, but does not necessarily lead to higher total profit. Numerical analyses compare the expected profits of alternative supply chain strategies, as well as the sensitivity to different distributions of demand across the stores. This leads to novel strategic insights that arise from adopting inventory policies that vary by store type.