Inventory Allocation Problem Research Articles

An application of deep reinforcement learning and vendor-managed inventory in perishable supply chain management

This article delves into the challenging supply chain management domain, explicitly addressing the intricate issue of perishable inventory allocation within a two-echelon supply chain. The approach outlined here leverages deep reinforcement learning with a keen understanding of the inherent stochasticity arising from uncertain demands and variable supply conditions. The examined supply chain encompasses two retailers and a central distribution center operating under a vendor-managed inventory system. The primary goal of this research is to combat the prevalent problems of wastage and shortages frequently encountered at the retail level in such supply chains. The study employs the Advantage Actor-Critic (A2C) algorithm, tailored to handle the continuous action space inherent in inventory allocation. To rigorously evaluate this approach, empirical data from a real-world blood supply chain in Tabriz is used for numerical experiments. This practical case study involves a single distribution center and two hospitals. The outcomes of these experiments affirm the effectiveness of the A2C algorithm, showcasing its ability to address the complex inventory allocation problem successfully. Furthermore, the research highlights that the algorithm outperforms existing supply chain policies, underscoring the pivotal role of optimal allocation in enhancing efficiency and operational excellence in perishable supply chains.

Inventory allocation with full downward substitution and monotone cost differences

We study a single-period multi-product inventory allocation problem with full downward substitution and monotone cost differences. The cost structure with monotone differences is more general than the additive cost structure usually assumed in literature. Using the notion of Monge sequences, we identify conditions under which the problem can be solved efficiently using greedy allocation. For problems that do not meet these conditions, we develop an efficient algorithm that solves the problem to optimality. For this specific problem, our algorithm has substantially lower computational complexity than existing efficient algorithms for the more general transportation problem; we numerically confirm this superior computational efficiency and illustrate the importance of using efficient algorithms at the allocation stage of the inventory management problem.

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.

Optimal blood issuing by comprehensive matching

Mass-scale red blood cell genotyping of donors and transfusion recipients increases the availability of extended antigen matched red blood cell units. Therefore, a new mathematical framework is developed that can be applied for general blood groups (i.e., beyond the ABO, RhD blood groups). It determines which red blood cell units should be issued from inventory, such that requests from hospitals can be satisfied with antigen compatible red blood cell units, shortages for future requests are avoided, and outdating is prevented. The optimization model consists of two steps: a binary vector representation for general blood groups and the formulation of the inventory allocation problem as a minimum cost flow problem. The potential practical performance of the optimization model is evaluated by iterative simulations, based on historical data on supply and demand of red blood cell units in the Netherlands. When including the fourteen clinically most relevant antigens, more than 90% of all requests can be satisfied with antigen identical red blood cell units. Shortages and outdating can be kept restricted and could even be reduced to virtually zero, when only the ABO, RhD blood groups are considered.

Dynamic Inventory Allocation with Demand Learning for Seasonal Goods

We study a multi‐period inventory allocation problem in a one‐warehouse multiple‐retailer setting with lost sales. At the start of a finite selling season, a fixed amount of inventory is available at the warehouse. Inventory can be allocated to the retailers over the course of the selling horizon (transshipment is not allowed). The objective is to minimize the total expected lost sales and holding costs. In each period, the decision maker can use the realized and possibly censored demand observations to dynamically update demand forecast and consequently make allocation decisions. Our model allows a general demand updating framework, which includes ARMA models or Bayesian methods as special cases. We propose a computationally tractable algorithm to solve the inventory allocation problem under demand learning using a Lagrangian relaxation technique, and show that the algorithm is asymptotically optimal. We further use this technique to investigate how demand learning would affect inventory allocation decisions in a two‐period setting. Using a combination of theoretical and numerical analysis, we show that demand learning provides an incentive for the decision maker to withhold inventory at the warehouse rather than allocating it in early periods.

Deep reinforcement learning in seat inventory control problem: an action generation approach

Nowadays, firms intend to use customer choice-based models instead of an independent demand paradigm to generate more revenue. In this paper, we address choice-based seat inventory control problem with stochastic demand using a deep reinforcement learning technique named Deep Q-Network (DQN). DQN can naturally address large state space problems with its integrated function approximation. However, it becomes intractable in the case of large discrete action space. To address this issue, we propose an Action Generation (AGen) algorithm. AGen is a greedy heuristic algorithm designed to be integrated into DQN to overcome the complexity of the original problem. It aims to greedily generate a set of “effective” actions to replace the original action space. This leads to the main achievement of this study which is to dramatically decrease the complexity of the solution method without negatively affecting its performance in a large-scale choice-based seat inventory allocation problem.

Leveraging the Newsvendor for Inventory Distribution at a Large Fashion E-Retailer With Depth and Capacity Constraints

Problem definition:We consider the problem of inventory allocation of multiple products, across a network of warehouses, faced by a large fashion e-retailer. The objective is to minimize overall shipment costs and to speed up deliveries to customers accounting for inventory constraints on products and capacity constraints of warehouses. Academic / Practical Relevance: Online retailers increasingly face the problem of optimizing inventory allocation for a wide variety of products, across a large network of warehouses. In most practical cases, demand of these products is unknown, and product level inventory available for distribution across the warehouses is very limited. Nevertheless, to the best of our knowledge, inventory allocation with both capacity and depth constraints has not been previously studied. Methodology: We formulate the inventory allocation problem as a Multi-Product, Multi-Warehouse Newsvendor (MPMWN) problem that balances overage and underage costs across products and warehouses. We then use Lagrangian duality to propose an efficient allocation algorithm (Optimal Distribution Algorithm (ODA)). ODA breaks the central MPMWN problem into two subproblems with either depth or capacity constraints. We show that these subproblems can be efficiently solved using binary search, due to the separability of the objective function and monotonicity of the constraints with respect to the dual variables. Results: Analytically, we show that the inventory allocation from the proposed algorithm converges to the optimal solution of the MPMWN problem. Furthermore, we analyze the rate of convergence of the algorithm to show fast convergence. Numerically, in collaboration with a large fashion retailer, we perform a large-scale real data study to show that the proposed algorithm, combined with a state-of-the-art demand prediction method can reduce inventory costs by as much as 7% and increase In-Class-Fulfillment (ICF) up to 10%. This improvement is also robust to changes in the demand distribution and the overage to underage cost ratio. Hence, the proposed method leads to considerable cost reduction and service improvement, both very important for the retailer. Managerial Implications: E-Retailers increasingly face the task of managing a very wide variety of products across a large network. Adding both capacity and depth constraints to the classical newsvendor problem poses computational challenges that make the current inventory optimization methods either impractical or inapplicable. We solve this problem by proposing an efficient and practical algorithm that combines transaction data for efficient inventory allocation.

Optimization of vehicle routing with inventory allocation problems in Cold Supply Chain Logistics

In this research, a new comprehensive mixed integer optimization model combining inventory allocation problem, vehicle routing problem, and cold supply chain (CSC) is formulated, denoted as IVRPCSC Model, to minimize the total cost paid for CSC, including the transportation and inventory costs. As the proposed model is NP-hard, a multi-phases solution approach is developed to solve the model in reasonable computational effort. Results of the proposed solution approach show that it is able to provide solutions with low gaps for the data-sets with different scales in very short computational time compared with the solutions for the same sets provided by commercial solvers, such as CPLEX. At the end, a real case study is solved by the proposed model, and the results show a saving of 9.25% of total distribution cost compared with the current cost paid by the organization.

Clearance Chain Design: Strategies Selection and unsold inventory allocation

The management of unsold inventory represents a significant issue for many retailers, wholesalers and manufacturers. Evaluating the various inventory clearance strategies, particularly in terms of business risk and performance represents a challenge that reaches well beyond the operational level. In this paper, a structured approach is developed to aid in the clearance chain decision-making process. The proposed approach uses the analytic hierarchy process (AHP) to select a clearance strategy with a focus on risk and performance indicators. AHP allows both quantitative and qualitative criteria to be considered. As for the unsold inventory allocation problem, a multi-objective optimisation method was adopted. The paper includes a discussion on managerial insights for clearance chain design where results give opportunities for future research.

A practical approach to revenue management in passenger train services: A case study of the Indonesian railways Argo Parahyangan

We proposed a practical approach to incorporating demand function in pricing optimization and its corresponding capacity allocation problem. Based on the willingness-to-pay approach, demand function was estimated from choice-based conjoint (CBC) data using a combination of hierarchical Bayes estimation, randomized first choice simulation, and cubic spline interpolation. The approach was implemented in the largest intercity passenger train service in Indonesia, assuming two customer segments and four fare classes. Solution to the mixed-integer nonlinear pricing optimization problem was obtained using enumeration. Subsequently, the expected marginal seat revenue heuristic was used in the seat inventory allocation problem.

Numerical Validation of the Continuous Time Markov Chain Approximation as a Service Level Estimation Method for Heterogeneous Customer Demand Classes

In this article, we study a threshold level based inventory allocation and replenishment problem for two priority-demand classes under the lot-for-lot replenishment policy. Demands of low-priority class are backordered when on-hand stock is at or below a certain threshold level, while high-priority class demands are lost in case of stock-out situations. We assume a continuous review lot-for-lot ordering policy with both deterministic and stochastic replenishment lead times. Both priority classes exhibit mutually independent, stationary, Poisson demand processes. There is no exact solution yet in the literature except for the special case of exponentially distributed lead times. In this complementary study, we aim to numerically validate the Continuous-Time Markov Chain (CTMC) approximation as a service level approximation method by thoroughly analyzing the effect of the type of lead time distribution, lead time variability, and value of system parameters on the quality of the class-specific service level estimations. As long as expected lead times are identical, we also show empirically the near-insensitivity of the effect of the type of lead time distribution and the lead time variability on the achieved service levels. The CTMC approximation works well under variety of system parameters and lead time distributions. For the cases considered in the constant lead time scenarios with service levels which we expect to see in practice (with fill rate requirements at least 60 % and 90 % for the low-priority and high priority customer classes, respectively), the average absolute errors for the CTMC approximations are calculated as 0.09 % (for the low-priority class fill rate) and 0.05 % (for the high-priority class fill rate); while the maximum absolute errors for the CTMC approximations are calculated as 0.37 % (for the low-priority fill rate) and 0.18 % (for the high-priority fill rate). The CTMC approach also provides quality approximations for the Erlang, lognormal and gamma distributed lead times.

Allocation under a general substitution structure

We develop a novel solution approach for the single-period multi-product inventory allocation problem with general substitution structure. First, we construct an initial allocation sequence and present conditions for existence of a Monge sequence, implying optimality of a greedy solution. We prove that the greedy allocation along the initial sequence is optimal even if no Monge sequence exists, when in the solution all demand is satisfied and all inventory is used. For all other cases, we develop a correction algorithm and prove optimality of the resulting allocation. The worst-case computational complexity of our solution is superior to existing algorithms for the structurally related transportation problem.

Dynamic Inventory Allocation with Demand Learning for Seasonal Goods

We study an inventory allocation problem in a two-echelon (single-warehouse multiple-retailer) setting with lost sales. At the start of a finite selling season, a fixed amount of inventory is available at the warehouse, and can be allocated to the retailers over the course of the selling horizon with the objective of minimizing total expected lost sales costs and holding costs. We are particularly interested in demand learning in this context, where the decision maker can use historical demand observations to predict future demand, and consequently make allocation decisions. We thus model demand in order to capture learning, and show that our model can describe both demand forecasting (e.g. ARMA) frameworks, as well as a Bayesian framework. Then, we pose the questions of (1) how to solve the inventory allocation problem under demand learning in a computationally tractable way, and (2) how demand learning impacts effective inventory allocation policies. To address the first question, we adopt a Lagrangian relaxation-based technique. We show under general assumptions that the resulting heuristic remains near-optimal in our setting, compared to the original dynamic program. Finally, we use this analysis to investigate the relationship between demand learning and early allocation decisions. We show through a combination of theoretical and numerical analysis the following result: Demand learning provides an incentive for the decision maker to withhold inventory at the warehouse rather than allocating it in earlier periods.

Disaster preparedness using risk-assessment methods from earthquake engineering

Analyzing the uncertainties associated with disaster occurrences is critical to make effective disaster preparedness plans. In this study, we focus on pre-positioning emergency supplies for earthquake preparedness. We present a new method to compute earthquake likelihood and the number of the affected people. Our approach utilizes forecasting methods from the earthquake engineering literature, and avoids using probabilistic scenarios to represent the uncertainties related to earthquake occurrences. We validate the proposed technique by using historical earthquake data from Turkey, a country under significant earthquake risk. We also present a case study that illustrates the implementation of our method to solve the inventory allocation problem of the Turkish Red Crescent.

Multi‐Treatment Inventory Allocation in Humanitarian Health Settings under Funding Constraints

In humanitarian operations, the amount of funding received and the timing and predictability of funding strongly influence program performance. In this paper, we study the problem of allocating inventory procured using donor funding to patients in different health states over a finite horizon with the objective of minimizing the number of disease‐adjusted life periods lost. The funding received and the number of new patients of different health states entering the program in every period could be unpredictable and hence, resource allocation and rationing assume significance in this setting. We use a stochastic dynamic programming model with financial constraints to analyze the inventory allocation problem. We demonstrate that the optimal allocation policy is state dependent, provide analytical results regarding the impact of funding timing and funding variability in our problem context, and develop two heuristics for the inventory allocation problem. Our computational study indicates that the two heuristics perform reasonably well against the full information lower bound (roughly 5% gap on average) and in many instances, they offer significant benefits over the first‐come‐first‐serve heuristic frequently used in practice. We also provide computational insights regarding the impact of funding timing and funding level on program performance. Our analysis indicates that for short planning horizons (up to 4 periods), receiving additional funding is beneficial even if the funding is delayed while for medium to long planning horizons, there exist situations where receiving less overall funding in a timely manner might be better than receiving more total funding in a delayed fashion.

Solving multi-region multi-facility inventory allocation and transportation problem: A case of Indian public distribution system

In this paper, we study an inventory allocation and transportation problem in a supply chain consisting of multiple storage facilities (warehouses) located in different regions of a large geographic area, which is motivated by the case of the Indian public distribution system. The procurement in each region is known and the item procured within a region needs to be allocated for storage in the warehouses of the same region. The demand of each region is satisfied by the warehouses located in the respective regions. Consideration of region-wise aggregated demand/procurement over multiple facilities located in each region makes the proposed study different from the existing literature. There is a mismatch in procurement, demand, and available storage capacity of warehouses across all the regions. Therefore, the problem is to determine an optimal plan for holding inventory at different storage facilities and to satisfy the demand of all regions without shortages by transporting items between different storage facilities. A mixed integer linear programming model is formulated to minimize the total relevant costs over a finite planning horizon. A heuristic devising activity based decision rules is proposed to solve the problem by decomposing the problem into sub-problems. The performance of the proposed approach is compared with the exact solutions obtained using Cplex for several problem instances. The results of the computational analysis reveal that the proposed solution approach is computationally efficient and gives good quality solutions with an average cost deviation from the optimal solution of less than 6%.

Allocation of reliability--redundancy and spares inventory under Poisson fleet expansion

ABSTRACTThis article proposes an integrated product-service model to ensure the system availability by concurrently allocating reliability, redundancy, and spare parts for a variable fleet. In the literature, reliability and inventory allocation models are often developed based on a static installed base. The decision becomes really challenging during new product introduction, as the demand for spare parts is nonstationary due to the fleet expansion. Under the system availability criteria, our objective is to minimize the fleet costs associated with design, manufacturing, and after-sales support. We tackle this reliability--inventory allocation problem in two steps. First, to accommodate the fleet growth effects, the nonstationary spare parts demand stream is modeled as a sum of randomly delayed renewal processes. When the component's failure time is exponential, the mean and variance of the lead time inventory demand are explicitly derived. Second, we propose an adaptive base stock policy against the time-varying parts demand rate. A bisection search combined with metaheuristics is used to find the optimal solution. Numerical examples show that spare parts inventory results in a lower fleet cost under short-term performance-based contracts, whereas reliability--redundancy is preferred for long-term service programs.

A United Allocation Method of Spare Parts and Ground Maintenance Equipment for Civil Aircraft

Aimed at multi-echelon inventory allocation problem with finite repair capacity for civil aircraft,a united planning method based on queuing theory and Vari-Metric model is presented to deploy the aircraft spare parts and ground maintenance equipment. Through the analysis of actual engineering, the effect of repair time is quantified by the number of maintenance equipment. On this basis, the available of fleet and the cost expense are selected as the objective and constraint respectively, marginal analysis method is set as the optimization, a new allocation scheme which was suit to civil aircraft’s maintenance resources is put forward. By applied examples analysis, it is shows that this method is reasonable and feasible.

A Mix-Integer Programming Model for Inventory Slab Allocation Problem

This paper investigates the inventory slab allocation problem in the iron and steel production. Considering some practical production factors including allocation quality, slab and order preferences, and the order-fulfill situation, we formulate the problem as a mix-integer programming model to allocate inventory slabs to the orders so as to maximize material utilization rate and customer satisfaction. Our objectives are minimizing thesuitabilitycost concerning the allocation of slabs to orders and the cost associating with the unfulfilled or exceeded weight for each order, as well as maximizing the profit in terms of the allocated slab weight and the preferences of orders and slabs. Computational results using real-world data collected from the company show that the solutions generated by MILP are optimal.

A local search method for periodic inventory routing problem

Inventory routing problem considers inventory allocation and routing problems simultaneously, in which the replenishment policies and routing arrangement are determined by the supplier under the vendor managed inventory mode. What we consider here is a periodic inventory routing problem that once the delivery time, quantity and routing are determined, they will remain the same in the following periods. The problem is modeled concisely, and then it is decomposed into two subproblems, inventory problem and vehicle routing problem. The inventory problem is solved by proposing a local search method, which is achieved by four operators on delivery quantity and retailer’s demand. Insertion operator aims to insert a new replenishment point of a retailer while removal operator is to remove a replenishment point. Besides, addition operator is adopted as an assistant tool, and crossover operator is proposed for some special cases. We also propose a tabu search method to solve the routing problem. Finally, the computational results show that the method is efficient and stable.