A Two-Echelon Inventory System with a Minimum Order Quantity Requirement

Shen, Huaxiao; Tian, Tian; Han, Zhu

doi:10.3390/su11185059

Cited by 11 publications

(9 citation statements)

References 47 publications

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“…Zhu et al (2015) study an inventory system with both MOQ and batch ordering requirements. Shen et al (2019) consider a two‐echelon inventory system with one warehouse and multiple retailers. They designed a new heuristic ordering policy for the warehouse, called the refined base‐stock policy, which conforms to the MOQ requirement.…”

Section: Literature Reviewmentioning

confidence: 99%

“…For example, Sport Obermeyer, a fashion sport ski‐wear manufacturer, has a minimum production level of 600 garments in Hong Kong and 1200 garments in China per order (Zhao and Katehakis, 2006). In addition, MOQs have been widely used in online B2B sourcing portals such as alibaba.com, where suppliers often impose such requirements (Shen et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

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Managing inventory systems with dual delivery modes and minimum order quantities

Yang

2023

Naval Research Logistics

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We consider an infinite‐horizon periodic‐review inventory system with dual delivery modes, each with a minimum order quantity (MOQ). The expedited mode provides a shorter lead time than the regular mode but has a higher unit ordering cost. As the optimal ordering policy for a system with dual delivery modes and MOQ requirements is unknown and expected to be very complicated, we propose a class of simple policies called single‐index policies, and we provide an exact procedure to compute the expected long‐run average total cost. Specifically, we first analyze the steady‐state distribution of the inventory position. Then we develop a recursive procedure to determine the steady‐state distribution of the inventory level. In addition, for a special case where ordering from the regular mode follows a base‐stock policy, we apply normal approximation to simplify the exact calculation of the cost. We also study a more complicated class of policies called dual‐index policies. In numerical studies, we first compare the average cost of the single‐index policy with that of a modified single‐index policy without MOQ consideration and the policy for the single‐mode system respectively to investigate the value of the single‐index policy. In addition, we find that the simpler single‐index policy performs close to the dual‐index policy and the optimal policy computed via dynamic programming. Finally, to assess the effectiveness of the normal approximation in the special case, we numerically compare the cost and policy parameters of the exact calculation with those of the normal approximation. The results illustrate that normal approximation not only improves the calculation speed, but also has near‐optimal solutions.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Managing inventory systems with dual delivery modes and minimum order quantities

Yang

2023

Naval Research Logistics

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“…Based on the same inventory system settings, Kiesmüller [37] proposed a periodic review policy, called (R, S, Q min ) policy, where the order quantity of a single item was calculated as the inventory on hand plus orders on hand minus stalled orders, equal to or greater than level S. A more straightforward one-parameter policy called S policy was proposed when considering a single-item inventory system with both MOQ and batch orders [38]. Shen studied a two-echelon inventory system with one warehouse and multiple retailers [39]. In particular, the warehouse had a minimum order quantity requirement according to the supplier's regulations.…”

Section: Literature Reviewmentioning

confidence: 99%

An Efficient Algorithm for the Joint Replenishment Problem with Quantity Discounts, Minimum Order Quantity and Transport Capacity Constraints

Liu

Jiang

2023

Mathematics

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The joint replenishment problem has been extensively studied and the joint replenishment strategy has been adopted by a large variety of retailers in recent years. However, the joint replenishment problem under minimum order quantity and other constraints does not receive sufficient attention. This paper analyzes a retailing supply chain involving a supplier that provides quantity discount schedules and limits the order quantity. The order quantity constraints include minimum order requirements for each item and as to the total quantity; additionally, the latter cannot exceed the transport capacity constraint. These are common constraints in the retail industry today and create greater complexity and difficulty in the retailer’s decision-making. To analyze the problem, an integer nonlinear programming model is set up to maximize retailers’ profit with all practical constraints. A two-layer efficient algorithm named the Marginal and Cumulative Profit-Based Algorithm (MCPB) is then proposed to find whether to order and the optimal order quantity for each item. The results of computational experiments show that the proposed algorithm can find near-optimal solutions to the problem efficiently and is a reference for retailers to solve practical joint replenishment problems.

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“…In another example, Shen et al. ( 2019 ) consider a multi-echelon inventory system where the upstream installation faces an MinOQ requirement. Motivated by Zhou et al.…”

Section: Literature Reviewmentioning

confidence: 99%

A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements

Han

2022

Ann Oper Res

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In this paper, we consider a periodic-review stochastic inventory system with both minimum and maximum order quantity (MinOQ and MaxOQ, respectively) requirements. In each period, if an order is placed, the order quantity is bounded, at least at the MinOQ and at most the MaxOQ. The optimal policy of such a system is unknown, and even if it exists, it must be quite complicated. We propose a heuristic policy, called the modified ( s , S ) policy, under which whenever the inventory position drops to the reorder point s or below, an order is placed to raise the inventory position as close as possible to the order-up-to level S . Applying a discrete-time Markov chain approach, we are able to compute the system-wide long-run average cost. We provide bounds for the optimal values of s and S and design an efficient algorithm to optimize our proposed policy. In addition, the proposed heuristic policy has excellent performance in our numerical studies. We also measure the impact of some inventory parameters. Supplementary Information The online version supplementary material available at 10.1007/s10479-021-04441-1.

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A Two-Echelon Inventory System with a Minimum Order Quantity Requirement

Cited by 11 publications

References 47 publications

Managing inventory systems with dual delivery modes and minimum order quantities

Managing inventory systems with dual delivery modes and minimum order quantities

An Efficient Algorithm for the Joint Replenishment Problem with Quantity Discounts, Minimum Order Quantity and Transport Capacity Constraints

A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements

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