Coordination of Multiechelon Supply Chains Using the Guaranteed Service Framework

Problem definition: We use the guaranteed service (GS) framework to investigate how to coordinate a multiechelon supply chain when two self-interested parties control different parts of the supply chain. For purposes of supply chain planning, we assume that each stage in a supply chain operates with a local base-stock policy and can provide guaranteed service to its customers, as long as the customer demand falls within certain bounds. Academic/practical relevance: The GS framework for supply chain inventory optimization has been deployed successfully in multiple industrial contexts with centralized control. In this paper, we show how to apply this framework to achieve coordination in a decentralized setting in which two parties control different parts of the supply chain. Methodology: The primary methodology is the analysis of a multiechelon supply chain under the assumptions of the GS model. Results: We find that the GS framework is naturally well suited for this decentralized decision making, and we propose a specific contract structure that facilitates such relationships. This contract is incentive compatible and has several other desirable properties. Under assumptions of complete and incomplete information, a reasonable negotiation process should lead the parties to contract terms that coordinate the supply chain. The contract is simpler than contracts proposed for coordination in the stochastic service (SS) framework. We also highlight the role of markup on the holding costs and some of the difficulties that this might cause in coordinating a decentralized supply chain. Managerial implications: The value from the paper is to show that a simple contract coordinates the chain when both parties plan with a GS model and framework; hence, we provide more evidence for the utility of this model. Furthermore, the simple coordinating contract matches reasonably well with practice; we observe that the most common contract terms include a per-unit wholesale price (possibly with a minimum order quantity and/or quantity discounts), along with a service time from order placement until delivery or until ready to ship. We also observe that firms need to pay a higher price if they want better service. What may differ from practice is the contract provision of a demand bound; our contract specifies that the supplier will provide GS as long as the buyer’s order are within the agreed on demand bound. This provision is essential so that each party can apply the GS framework for planning their supply chain. Of course, contracts have many other provisions for handling exceptions. Nevertheless, our research provides some validation for the GS model and the contracting practices we observe in practice.

Technical Note—A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems

Analyzing Capacitated Two-Echelon Systems with Permutation-Dependent Separability Capacitated multiechelon systems are common in practice due to the escalating costs of labor and advanced manufacturing technology. However, identifying the optimal replenishment policies for such systems is a largely open area of research due to the intrinsic complexity, especially when there is an upstream bottleneck. In “A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems”, Shen, Yu, and Huh propose a new approach, that is, permutation-dependent separability, to tackle a capacitated two-echelon system in which the capacity of upstream stage can be the bottleneck. They show that the value function for the capacitated two-echelon system in each period is permutation-dependent separable, and that for each echelon, a permutation-dependent echelon base stock policy is optimal. The authors also develop efficient solution procedures on how to obtain the optimal policy.

Adaptive Supply Chain: Demand–Supply Synchronization Using Deep Reinforcement Learning

Adaptive and highly synchronized supply chains can avoid a cascading rise-and-fall inventory dynamic and mitigate ripple effects caused by operational failures. This paper aims to demonstrate how a deep reinforcement learning agent based on the proximal policy optimization algorithm can synchronize inbound and outbound flows and support business continuity operating in the stochastic and nonstationary environment if end-to-end visibility is provided. The deep reinforcement learning agent is built upon the Proximal Policy Optimization algorithm, which does not require hardcoded action space and exhaustive hyperparameter tuning. These features, complimented with a straightforward supply chain environment, give rise to a general and task unspecific approach to adaptive control in multi-echelon supply chains. The proposed approach is compared with the base-stock policy, a well-known method in classic operations research and inventory control theory. The base-stock policy is prevalent in continuous-review inventory systems. The paper concludes with the statement that the proposed solution can perform adaptive control in complex supply chains. The paper also postulates fully fledged supply chain digital twins as a necessary infrastructural condition for scalable real-world applications.

Two-Echelon Inventory Model With Service Consideration and Lateral Transshipment

This paper considers a two-echelon inventory system with service consideration and lateral transshipment. So far, researchers have not extensively considered the use of lateral transshipment for such systems. Demand arrivals at both echelons follow the Poisson process. We introduce a continuous review base stock policy for the system in steady state, which determined the expected level for on-hand inventory, expected lateral transshipment level and expected backorder level. We showed that the model satisfied convexity with respect to base stock level. Computational experiments showed that the model with lateral transshipment performed better that the model without lateral transshipment.

A Deep Q-Network for the Beer Game: Deep Reinforcement Learning for Inventory Optimization

Problem definition: The beer game is widely used in supply chain management classes to demonstrate the bullwhip effect and the importance of supply chain coordination. The game is a decentralized, multiagent, cooperative problem that can be modeled as a serial supply chain network in which agents choose order quantities while cooperatively attempting to minimize the network’s total cost, although each agent only observes local information. Academic/practical relevance: Under some conditions, a base-stock replenishment policy is optimal. However, in a decentralized supply chain in which some agents act irrationally, there is no known optimal policy for an agent wishing to act optimally. Methodology: We propose a deep reinforcement learning (RL) algorithm to play the beer game. Our algorithm makes no assumptions about costs or other settings. As with any deep RL algorithm, training is computationally intensive, but once trained, the algorithm executes in real time. We propose a transfer-learning approach so that training performed for one agent can be adapted quickly for other agents and settings. Results: When playing with teammates who follow a base-stock policy, our algorithm obtains near-optimal order quantities. More important, it performs significantly better than a base-stock policy when other agents use a more realistic model of human ordering behavior. We observe similar results using a real-world data set. Sensitivity analysis shows that a trained model is robust to changes in the cost coefficients. Finally, applying transfer learning reduces the training time by one order of magnitude. Managerial implications: This paper shows how artificial intelligence can be applied to inventory optimization. Our approach can be extended to other supply chain optimization problems, especially those in which supply chain partners act in irrational or unpredictable ways. Our RL agent has been integrated into a new online beer game, which has been played more than 17,000 times by more than 4,000 people.

Understanding the Performance of Capped Base-Stock Policies in Lost-Sales Inventory Models

Single-sourcing lost-sales inventory systems with lead times are notoriously difficult to optimize. In this paper, we propose a new family of capped base-stock policies and provide a new perspective on constructing a practical hybrid policy combining two well-known heuristics: base-stock and constant-order policies. Each capped base-stock policy is associated with two parameters: a base-stock level and an order cap. We prove that for any fixed order cap, the capped base-stock policy converges exponentially fast in the base-stock level to a constant-order policy, providing a theoretical foundation for a phenomenon by which a capped dual-index policy converges numerically to a tailored base-surge policy recently observed in other work in a different but related dual-sourcing inventory model. As a consequence, there exists a sequence of capped base-stock policies that are asymptotically optimal as the lead time grows. We also numerically demonstrate its superior performance in general (including small lead times) by comparing it with otherwell-known heuristics.