Dynamic Inventory Problem Research Articles

Green supply chain management: a renewable energy planning and dynamic inventory operations for perishable products

The emergence of renewable energy microgrids (REM)-supported logistics parks reflects the urgent social requirement for sustainability facing energy crisis and climate change. Focusing on the emergency REM capacity planning and dynamic inventory operations problem for a REM-supported cold warehouse, this paper constructs a novel two-stage stochastic optimization method to comprehensively minimise long-term investment and short-term emergency operation costs of the system, while improving the resilience of energy-constrained supply chain management of perishable products. In particular, we formulate the second stage emergency operation problem as a Markov decision process that considers the interaction between energy and operational decisions constrained by intermittent of renewable energy, the randomness of the occurrence time, and the balance between power supply and temperature changes of the cold warehouse. We propose a novel two-phase PSO-based MPC algorithm to solve the entire problem. We also examine the effectiveness of our algorithm via an empirical study based on the data in East China. Nine typical scenarios clustered from the real data suggest different optimal capacity planning and operational policies. The empirical results show that it can reduce an overall 9% of operating costs on average compared to other heuristic policies. Moreover, installing REM can improve the resilience of power systems by 23% (risk impact area reduction ratio) and improve the resilience of inventory systems by 49%.

Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts

A total minimum commitment contract is a supply contract under which a firm commits to buying a minimum quantity of a product from its supplier during the contract duration (e.g., 1 year). Such contracts are widely used in industries, because they provide the buyer with flexibility in terms of the timing and size of each order and the supplier with a guaranteed total order volume. Previous studies on such contracts have focused primarily on the firm's inventory decisions, and none of them has considered the coordination of inventory and pricing decisions. In this study, we fill this gap by studying dynamic inventory and pricing problems under a commitment contract. Under a general demand model with backlogging and zero lead time, we prove that the optimal policy is a committed‐inventory‐position‐dependent base‐stock list‐price policy and characterize its structural properties. We also conduct an extensive numerical study to derive further managerial insights. In particular, we find that dynamic pricing can substantially improve the firm's profitability and enables it to select contracts with large committed quantities and price discount rates, and that ignoring the commitment in joint pricing and ordering decisions can result in substantial profit loss. Finally, we partly extend our results to a lost‐sales model and a backlogging model with lead times.

A variable-scale dynamic clustering method

With the high intensity and density of aerospace launch in China, aerospace project materials management faces various challenges, such as multiple aerospace projects concurrent, high supply timeliness and high quality level. Although several enterprises have successfully explored a versatile material management regulation for multiple aerospace projects, the low inventory turnover problem still exist due to the difficulty in versatile material recognition and inventory distribution. This paper studies the dynamic inventory management problem of aerospace project materials. Firstly, a numerical concept space model is established to describe the data characteristics of aerospace project materials. Then, we propose the variable-scale clustering algorithm based on the numerical concept space, which is utilized to automatically recognize versatile materials. Also, the obtained satisfy scale feature supports managers making inventory-related decision. Finally, a dynamic adjustment algorithm of inventory classification based on the variable-scale clustering is proposed, in order to dynamically maintain the inventory management plan of aerospace project materials. Experiments select the inventory data of aerospace project metal materials during Jan 1, 2015 to Mar 31, 2018 from the logistics center in China Academy of Launch Vehicle Technology. And experiment results illustrate that our proposed variable-scale clustering algorithm has high efficiency and practical application value in solving dynamic inventory management problem of aerospace project materials.

Adaptive Algorithms for Multi-Warehouse Multi-Store Inventory System with Lost Sales and Fixed Replenishment Cost

We consider a two-echelon inventory control problem for a Multi-Warehouse Multi-Store (MWMS) system with lost sales and fixed ordering cost at each store. We focus on a time horizon with no external replenishment, or the problem of “what to do until your (external) shipment comes in. The warehouses are stocked with inventories at the beginning of the horizon, and the stores dynamically replenish from the warehouses in each period. The delivery lead time is zero from a warehouse to any of the store it serves (e.g., each store is within 24 hrs driving distance from its servicing warehouses). This is a prevalent problem in many retail settings. The optimal policy for this problem is complex and state-dependent, and due to the well-known curse of dimensionality, computing the optimal policy using dynamic program is numerically intractable. In this paper, we develop provably near-optimal algorithms by integrating and extending three key ideas/approaches: (i) Lagrangian relaxation of the original complex dynamic inventory control problem, (ii) approximating the finite-horizon cost of an inventory problem with its infinite-horizon average cost, and (iii) dynamic re-adjustments of both replenishment and allocation policies. We first present a Lagrangian-based algorithm that is open-loop and non-adaptive, and discuss its performance in terms of loss rate (optimality gap) between its expected total cost and that of a true optimal policy. Then, we develop several easy-to-compute adaptive algorithms that dynamically re-adjust the policy parameters after observing sales at each store. We highlight the importance of proper policy adjustment to realize the benefit of pooling effect, which typically exists in the setting where one warehouse replenishes multiple stores. Our results show that adaptive readjustments significantly improve the performance of the base algorithm both theoretically and numerically.

Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts

A total minimum commitment contract is a supply contract under which a firm commits to buying a minimum quantity of a product from its supplier during the contract duration (e.g., one year). Such contracts are widely used in industries, because they provide the buyer with flexibility in terms of the timing and size of each individual order and the supplier with a guaranteed total order volume. Previous studies on such contracts are primarily concerned with the firm's inventory decisions, but none of them has considered the coordination of inventory and pricing decisions. In this paper, we fill this gap by studying dynamic inventory and pricing problems under a commitment contract. Under a general demand model with backlogging and zero lead time, we prove that the optimal policy is a committed-inventory-position-dependent base-stock list-price policy and characterize its structural properties. We also conduct an extensive numerical study to derive further managerial insights. In particular, we find that dynamic pricing can substantially improve the firm's profitability and enables it to select contracts with large committed quantities and price discount rates, and ignoring the commitment in joint pricing and ordering decisions can result in substantial profit loss. Finally, we partly extend our results to a lost-sales model and a backlogging model with positive lead times.

Discrete-item Inventory Control involving Fixed Setup Costs, Demand Censoring, and Unknown Distribution

We investigate a dynamic inventory control problem in which orderings involve fixed setup costs and unsatisfied demands are lost. Stepping off from the traditional literature which stresses the randomness of demand realizations, we move on to tolerate ambiguity. Now even the demand distribution $f\equiv (f(d))_{d=0,1,...}$ itself, out of which random realizations are sampled, can come from a vast and definitely non-singleton set. Lost sales and demand ambiguity would together complicate the problem through censoring, namely, the inability of the firm to observe the lost portion of the demand. Our main policy idea advocates periodically ordering up to seemingly wastefully high levels just to learn and in intervening periods, cleverly exploiting the information gained in these learning periods. By regret, we mean the price paid for ambiguity in long-run average performances. When demand support is unlimited, regret bounds in the orders of $\mathcal{O}(T^{8/9})$ and $\mathcal{O}(T^{(2+\sqrt{2})/4})\simeq \mathcal{O}(T^{0.854})$ can be established for, respectively, the case where $f(0)$ is bounded away from one and the other where the restriction is relaxed with the firm allowed to remove items from the inventory. When demand has a finite support, both bounds could be improved to the order of $\mathcal{O}(T^{2/3}\cdot (\ln T)^{1/2})$. We also propose other policies. % based on the general learning-while-doing idea but the different Kaplan-Meier (KM) estimation. Our simulation demonstrates the merits of the various policy ideas and the hurdles posed by the prospect of $f(0)\longrightarrow 1^-$.

Dynamic Inventory Control with Fixed Setup Costs and Unknown Discrete Demand Distribution

We study a dynamic inventory control problem involving fixed setup costs and random demand distributions. With an infinite planning horizon, model primitives including costs and distributions are set to be stationary. Under a given demand distribution, an $(s,S)$ policy has been known to minimize the long-run per-period average cost. Out of the need to model situations involving new products or unencountered economic conditions, however, we depart from the traditional model by allowing the stationary demand distribution to be largely unknown, to the effect that it could be anywhere in a given ambiguity set. Our goal is to rein in the long-run growth of the regret resulting from applying a policy that strives to learn the underlying demand while simultaneously meting out ordering decisions based on its learning. We propose a policy that controls the pace at which a traditional $(s,S)$-computing algorithm is applied to the empirical distribution of the demand learned over time. The regret incurred from the policy has a bound of $O(T^{1/2}\cdot(\ln T)^{1/2})$.

Joint Quality Investment and Inventory Decisions for Perishable Items with Reference Quality Effect under the O2O Environment

Reference quality, as a benchmark against which the purchase quality of a product is judged, has an important impact on consumers’ purchase decision, especially perishable items. Thus, how to determine an appropriate quality investment and ordering strategies for perishable items to maximize retailers’ profit is an essential task. A joint dynamic quality investment and inventory replenishment problem for perishable items with consideration of reference quality effect is investigated, where the retailer sells its products using a combination of the offline and online stores, and the sales function is sensitive to products’ quality and consumers’ reference quality. The optimal control model is established to maximize the retailer’s total profit by making a joint quality and inventory strategy. The continuous time dynamic optimal quality investment and inventory replenishment strategies with reference quality effect are obtained by Pontryagin’s maximum principle. Numerical experiments are accounted for the key system parameters on the optimal strategies.

A cash constrained single item stochastic lot-sizing problem

We investigate a dynamic inventory management problem where a cash-constrained small retailer periodically purchases an item from a supplier and sells it to the customers with non-stationary demands. At each period, the retailer’s available cash restricts the maximum inventory level that it can replenish. There exists a fixed ordering cost for the retailer when ordering and this results in a stochastic lot-sizing problem. We build a stochastic dynamic programming model for this problem and find some characteristics of the optimal ordering pattern.

Efficient Computational Strategies for Dynamic Inventory Liquidation

We examine the dynamic inventory liquidation problem, in which a retailer liquidates a fixed number of identical items over a time period by strategically setting prices periodically according to knowledge about stochastic demand. We propose to solve the liquidation problem by deriving a deterministic representation of stochastic demand. Assuming that customer arrival and valuations follow known statistical distributions (e.g., estimated from past transaction data), the expected arrivals and expected order statistics of valuation distributions represent informative and advantageous approximations of demand. Under the deterministic demand representation, we develop a greedy heuristic for finding the optimal liquidation strategy that result in maximum total revenue. The heuristic approach is computationally highly efficient and provides optimal solutions under deterministic demand representation when customer valuation follows various typical statistical distributions. Compared with two simple and commonly used liquidation strategies (i.e., the fixed-price strategy and the fixed-quantity strategy), our heuristic yields higher liquidation revenue. Compared with sophisticated approaches that can find optimal liquidation strategies under stochastic demand (e.g., stochastic dynamic programming), our approach runs several magnitudes faster and still yields near optimal expected revenue. Therefore, the heuristic approach can serve as a useful tool for managers to make liquidation-related decisions in realistic, stochastic demand scenarios.

Dynamic inventory routing problem: Policies considering network disruptions

In this paper, we introduce an inventory routing problem with network disruptions. In this problem, not only decisions on inventory levels and vehicle routing are made simultaneously, but also, we consider disruptions over the networks in which a number of arcs are vulnerable to these disruptions, leading to an increase in travel times. We develop a dynamic programming approach to deal with this situation, and we also evaluate some policies adapting well-known instances from the literature. © 2018, Growing Science Ltd. All rights reserved.

Stochastic Dynamic Inventory Problem Under Explicit Inbound Transportation Cost and Capacity

We study a practical generalization of the classical stochastic dynamic inventory problem where privately owned trucks with limited cargo capacity are used to transport the replenishment quantity. The resulting replenishment cost function also includes the traditional fixed setup cost, and it is known as a multiple setup cost structure, which leads to complicated cost-to-go functions in the problem of interest. We introduce the concepts of non-(Δ, C)-decreasing and [Formula: see text], and we develop a sophisticated replenishment policy called the [Formula: see text] policy. We examine the sufficient conditions under which the new policy is optimal. Our results offer a detailed characterization of optimal policies and generalize the existing theory on the concepts of K-convexity and non-K-decreasing. In doing so, we are able to investigate a traditional stochastic inventory problem which has remained open in the literature for more than four decades. The online appendix is available at https://doi.org/10.1287/opre.2017.1625 .

Optimal inventory policy for a dynamic stochastic inventory problem with order revision

A buyer wishes to satisfy independent demands for a product by ordering the product from a supplier. The buyer places an order one period before delivery and the supplier allows the buyer to revise the size of order before delivery. The buyer seeks an ordering and order-revision policy with minimum expected cost over a finite time horizon. The structure of the buyer’s optimal ordering and order-revision policy is developed under the assumptions about the ordering costs, the storage and shortage costs, and the revision that the supplier allows and the charges the supplier imposes.

Dynamic procurement management by reverse auctions with fixed setup costs and sales levers

In this paper, we study a dynamic procurement problem for a retailer with fixed setup costs and sales levers (such as pricing, advertising, etc.). The retailer runs a reverse auction with a procurement contract in each period. A number of potential suppliers bid for this contract, and the winner is the supplier with the highest bid and is given the decision right for the quantity produced and delivered. The demand is either realized by selling via Internet auctions and unmet demand is lost, or is a price-sensitive nonnegative random variable and all shortages are backlogged. We show the existence of the retailer’s optimal procurement contract, under which the suppliers’ Bayesian–Nash equilibrium bidding strategy is (q(·),Q(·)), similar to the classic (s, S) policy for the retailers in dynamic inventory control problems. However, the (q(·),Q(·)) strategy here is for the suppliers and is realized through the suppliers’ marginal production costs and so consists of two random variables for the retailer.

The Data-Driven (s, S) Policy: Why You Can Have Confidence in Censored Demand Data

We revisit the classical dynamic inventory management problem of Scarf (1959b) from the perspective of a decision-maker who has n historical selling seasons of data and must make sensible ordering decisions for the upcoming season. We first prescribe a nonparametric estimation procedure for the (s; S) policy that is asymptotically optimal. We then characterize the finite-sample performance of the estimated (s; S) levels by deriving their asymptotic confidence intervals using the Central Limit Theorem. We further consider having at least some of the past selling seasons of data censored from the absence of backlogging. We show that the intuitive and widely-used procedure of correcting for censoring in the demand data directly yields an inconsistent estimate. We then show how to correctly use the censored data to obtain consistent decisions and derive asymptotic confidence intervals for this policy using Stein’s method to handle the serial correlation that arises due to the correctioning. Surprisingly, censored data can be beneficial under some conditions; that is, estimated decisions with censored data may have smaller variance and mean squared error (MSE) than those with fully uncensored data. We thus arrive at the remarkable result that a decision maker with fully uncensored data can add artificial censored data to optimally estimate the (s; S) policy. We provide a prescription for the optimal level and amount of artificial demand data to add. Our results also apply to the repeated newsvendor problem and the base-stock policy problem by appropriate parameter choices.

Multimodularity and Its Applications in Three Stochastic Dynamic Inventory Problems

We apply the concept of multimodularity in three stochastic dynamic inventory problems in which state and decision variables are economic substitutes. The first is clearance sales of perishable goods. The second is sourcing from multiple suppliers with different lead times. The third is transshipment under capacity constraints. In all three problems, we establish monotone optimal polices with bounded sensitivity. Multimodularity proves to be an effective tool for these problems because it implies substitutability, it is preserved under minimization, and it leads directly to monotone optimal policies with bounded sensitivity.

Inventory policies and dynamic pricing under possibility and rivals

Income management has recently become a desirable service in many circumstances. Decision makers recognize that even small developments in their operations can have a notable effect on their benefits. Nonetheless, the specification of pricing and optimal inventory policies in more practical situations may not be a manageable task. Eventually, competitors influence a supplier’s best strategy by affecting their demand, incomes, and other related actions. This paper considers a continual time optimal control model for the learning of a dynamic pricing and inventory control problem in a make-to-stock system. We evaluate a product-capacitated, dynamic setting and present a demand-based model with convex prices. Our results explain the role of capacity and the effects of the dynamic nature of demand. We then propose an additive model of demand uncertainty. We show that the strong formulation is of the same level of complication as the deterministic problem and indicate how to modify the solution method.

Dynamic inventory control with limited capital and short-term financing

For most firms, especially the small- and medium-sized ones, the operational decisions are affected by their internal capital and ability to obtain external capital. However, the majority of the literature on dynamic inventory control ignores the firm's financial status and financing issues. An important question that arises is: what are the optimal inventory and financing policies for firms with limited internal capital and limited access to external capital? In this article, we study a dynamic inventory control problem where a capital-constrained firm periodically purchases a product from a supplier and sells it to a market with random demands. In each period, the firm can use its own capital and/or borrow a short-term loan to purchase the product, with the interest rate being nondecreasing in the loan size. The objective is to maximize the firm's expected terminal wealth at the end of the planning horizon. We show that the optimal inventory policy in each period is an equity-level-dependent base-stock policy, where the equity level is the sum of the firm's capital level and the value of its on-hand inventory evaluated at the purchasing cost; and the structure of the optimal policy can be characterized by four intervals of the equity level. Our results shed light on the dynamic inventory control for firms with limited capital and short-term financing capabilities.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 184–201, 2014

A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints

In this paper, we consider a finite-horizon stochastic mixed-integer program involving dynamic decisions under a constraint on the overall performance or reliability of the system. We formulate this problem as a multistage (dynamic) chance-constrained program, whose deterministic equivalent is a large-scale mixed-integer program. We study the structure of the formulation and develop a branch-and-cut method for its solution. We illustrate the efficacy of the proposed model and method on a dynamic inventory control problem with stochastic demand in which a specific service level must be met over the entire planning horizon. We compare our dynamic model with a static chance-constrained model, a dynamic risk-averse optimization model, a robust optimization model, and a pseudo-dynamic approach and show that significant cost savings can be achieved at high service levels using our model. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1822 . This paper was accepted by Dimitris Bertsimas, optimization.

Integrated dynamic single-facility location and inventory planning problems

This article considers a class of dynamic single-article facility location problems in which the facility must determine order and inventory levels to meet the dynamic demands of the customers over a finite horizon. The motivating application of this class of problems is in military logistics and the decision makers in this area are not only concerned with the logistical costs of the facility but also with centering the facility among the customers in each time period in order to be able to provide other services. Both the location plan and inventory plan of the facility in the problem must be determined while considering these different metrics associated with the performance of these plans. Effective dynamic programming algorithms for this class of problem are provided for both of these metrics. These dynamic programming algorithms are utilized in order to construct the efficient frontier associated with these two metrics in polynomial time. Computational testing indicates that these algorithms can be used in planning activities for military logistics. [Supplemental materials are available for this article. Go to the publisher’s online edition of IIE Transactions for a worst-case example of constructing the efficient frontier.]