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“喆學（27）：精讀英文論文
《Supply chain coordination in a dual
sourcing system under the Tailored Base-Surge policy》
Problem description（2）”
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Today, the editor brings you
"Zhe Xue (27)：Intensive Reading of English Essays
《Supply Chain Coordination in a Dual Sourcing System under the Tailored Base-Surge Policy》Problem description（2）"
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本期推文小編将從思維導圖、精讀内容、知識補充三個方面為大家介紹期刊論文《Supply Chain Coordination in a Dual Sourcing System under the Tailored Base-Surge Policy》的問題描述。
In this issue, the editor will introduce the problem description of the journal article "Supply Chain Coordination in a Dual Sourcing System under the Tailored Base-Surge Policy" from three aspects: mind mapping, intensive reading content, and knowledge supplement.
一、思維導圖（Mind Map）
二、精讀内容（Intensive reading content）
在單産品多周期庫存管理系統中，隻涉及一個産品的庫存管理，庫存管理是多周期的，意味着在多個時間段内需要進行庫存控制和決策。買方面臨來自外部客戶的非負随機需求。這意味着需求的數量是随機的，但不會為負數。這種需求的不确定性增加了庫存管理的複雜性，需要考慮到可能的各種需求情況。僅有買方負責管理庫存。供應商不參與庫存的日常管理。供應商采用按訂單生産系統，即在收到買方的訂單後才開始生産或做出訂單決策。這意味着供應商不會提前生産或備貨，而是根據買方的具體訂單來安排生産和供應。
In a single-product multi-period inventory management system, only one product is involved in inventory management, and inventory management is multi-period, which means that inventory control and decision-making are required in multiple time periods. Buyers face non-negative random demand from external customers. This means that the quantity demanded is random, but not negative. This uncertainty in demand increases the complexity of inventory management, and various possible demand situations need to be considered. Only the buyer is responsible for managing the inventory. Suppliers are not involved in the day-to-day management of inventory. Suppliers use a make-to-order system, which means that they start production or make order decisions only after receiving the buyer's order. This means that suppliers do not produce or stock up in advance, but arrange production and supply according to the buyer's specific order.
正常供應商以成本Cr采購或制造一個機關的産品，并以價格Wr賣給買方。加急供應商以成本Ce采購或制造一個機關的産品，并以價格We賣給買方，且We>Wr。這意味着加急供應商的産品價格更高，通常是因為其交貨時間更短或服務更及時。
A regular supplier buys or manufactures one unit of a product at cost Cr and sells it to the buyer at price Wr. An expedited supplier buys or manufactures one unit of a product at cost Ce and sells it to the buyer at price We, where We>Wr. This means that the expedited supplier's product is more expensive, usually because of a shorter delivery time or more timely service.
如果買方的庫存無法滿足需求，未滿足的需求會被記入延期訂單（在整個時間段的最後一個周期則被視為失去的銷售）。這種政策允許買方在大部分時間段内通過延期交貨來彌補庫存不足，但在最後一個周期無法補救時，則會直接損失銷售。
If the buyer's inventory cannot meet the demand, the unmet demand will be recorded as a backorder (which is considered a lost sale in the last cycle of the entire time period). This strategy allows the buyer to make up for the inventory shortage through backorders during most of the time period, but when it cannot be remedied in the last cycle, it will directly lose sales.
買方采用TBS政策進行庫存控制。這種政策包括兩個方面：一方面，從正常供應商訂購固定且恒定的數量Qr。另一方面，從加急供應商訂購變化的數量，以應對需求的不确定性。通過這種政策，買方可以在大多數情況下利用成本較低的正常供應商來補充庫存，并在需求高于預期時通過成本較高的加急供應商來應對需求波動。
The buyer adopts the TBS strategy for inventory control. This strategy includes two aspects: on the one hand, ordering a fixed and constant quantity Qr from regular suppliers. On the other hand, ordering a variable quantity from expedited suppliers to cope with demand uncertainty. With this strategy, the buyer can use lower-cost regular suppliers to replenish inventory in most cases, and deal with demand fluctuations through higher-cost expedited suppliers when demand is higher than expected.
通過基準庫存水準和庫存位置來動态調整加急訂購數量的機制。這樣可以在需求不确定時，通過靈活的加急訂購來確定庫存水準，同時盡可能減少庫存成本。庫存位置是指淨庫存（現有庫存加上所有供應商的在途訂單，減去未滿足需求的數量）。加急訂購的數量是達到基準庫存水準所需要的差額。有可能出現庫存位置超過基準庫存水準的情況，這種情況被稱為超訂。
A mechanism to dynamically adjust rush order quantities using the baseline inventory level and inventory position. This allows for flexible rush ordering to ensure inventory levels when demand is uncertain, while minimizing inventory costs. The inventory position refers to the net inventory (the inventory on hand plus all suppliers' orders in transit, minus the quantity of unmet demand). The rush order quantity is the difference required to reach the baseline inventory level. It is possible for the inventory position to exceed the baseline inventory level, a situation known as overbooking.
接下來較長的描述了買方的庫存管理和盈利計算的步驟。買方評估其庫存位置，包括初始庫存和來自兩個供應商的所有未完成訂單。接着，根據庫存位置，買方确定從加急供應商訂購的數量，以達到基準庫存水準。買方觀察實際需求，并通過加上從兩個供應商收到的貨物來更新庫存水準。
Next, the buyer's inventory management and profitability calculation steps are described in detail. The buyer evaluates its inventory position, including the initial inventory and all outstanding orders from both suppliers. Next, based on the inventory position, the buyer determines the quantity to order from the expedited supplier to reach the baseline inventory level. The buyer observes the actual demand and updates the inventory level by adding the goods received from the two suppliers.
接着計算下一周期庫存，并最後計算得出買方利潤、正常供應商和加急供應商的利潤。
The inventory for the next cycle is then calculated, and finally the buyer's profit, the profit of the regular supplier, and the profit of the expedited supplier are calculated.
超訂分布僅依賴于正常供應商的固定訂購量Qr。超訂量滿足Lindley 遞歸關系并承認一個穩态分布，該分布滿足 Lindley 積分方程。超訂分布可以通過 Wiener–Hopf 方法、數值求解積分方程或模拟超訂過程獲得。在數值研究中，采用蒙特卡羅模拟進行了長周期（T=1000）的超訂過程模拟，并重複了10000次。
The overbooking distribution depends only on the fixed order quantity Qr of the regular suppliers. The overbooking quantity satisfies the Lindley recurrence relation and admits a steady-state distribution that satisfies the Lindley integral equation. The overbooking distribution can be obtained by the Wiener–Hopf method, numerically solving the integral equation or simulating the overbooking process. In the numerical study, a long-term (T=1000) overbooking process was simulated using Monte Carlo simulation and repeated 10,000 times.
三、知識補充(Knowledge Supplement)
Lindley遞歸關系是排隊論和庫存管理中的一個重要概念，用于描述系統中等待時間或庫存位置的動态變化。它主要用于分析一個随時間變化的系統的穩定行為。具體表達式為：Wn+1=max{Wn+Xn+1,0}。
Lindley recurrence relation is an important concept in queuing theory and inventory management. It is used to describe the dynamic changes of waiting time or inventory position in the system. It is mainly used to analyze the stable behavior of a system that changes over time. The specific expression is: Wn+1=max{Wn+Xn+1,0}.
在排隊系統中，Wn可以表示第n個顧客的等待時間，Xn+1表示第 n+1個顧客的到達時間與前一個顧客的服務時間之差。如果Wn+Xn+1為正，說明目前顧客到達時有等待時間，否則為零（無等待）。
In the queuing system, Wn can represent the waiting time of the nth customer, and Xn+1 represents the difference between the arrival time of the n+1th customer and the service time of the previous customer. If Wn+Xn+1 is positive, it means that there is a waiting time when the current customer arrives, otherwise it is zero (no waiting).
在庫存管理中，Wn可以表示第n個周期末的庫存位置，Xn+1表示第n+1個周期内的需求與補貨量之差。如果Wn+Xn+1為正，說明有超訂現象，否則庫存位置為零（無超訂）。
In inventory management, Wn can represent the inventory position at the end of the nth period, and Xn+1 represents the difference between the demand and replenishment in the n+1th period. If Wn+Xn+1 is positive, it means there is overordering, otherwise the inventory position is zero (no overordering).
Lindley 遞歸關系的性質包括以下幾點：
The properties of the Lindley recurrence relation include the following:
1、穩态分布：在長時間運作後，系統可能達到一個平衡狀态，此時Wn的分布趨于穩定，這被稱為穩态分布。
1. Steady-state distribution: After a long period of operation, the system may reach an equilibrium state, at which the distribution of Wn tends to be stable, which is called steady-state distribution.
2、積分方程：穩态分布滿足一個Lindley 積分方程，可以通過數值方法或模拟方法求解。
2. Integral equation: The steady-state distribution satisfies a Lindley integral equation, which can be solved by numerical methods or simulation methods.
3、應用方法：常見的有Wiener–Hopf方法、數值求解、蒙特卡羅模拟。
3. Application methods: Common ones include Wiener–Hopf method, numerical solution, and Monte Carlo simulation.
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翻譯：AI翻譯
參考資料：百度、文心一言、Chatgpt
參考文獻：Ghoudi K, Hamdouch Y, Boulaksil Y, et al. Supply chain coordination in a dual sourcing system under the Tailored Base-Surge policy [J]. European Journal of Operational Research, 2024, 317(2): 533-549.
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