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Zhe Xue (27): Intensive reading of English papers
《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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本期推文小编将从思维导图、精读内容、知识补充三个方面为大家介绍期刊论文《Supply Chain Coordination in a Dual Sourcing System under the Tailored Base-Surge Policy》的问题描述。
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、思维导图（Mind Map）
二、精读内容（Intensive reading content）
In a single-product multi-cycle inventory management system, the inventory management of only one product is involved, and inventory management is multi-cycle, which means that inventory control and decision-making are required in multiple time periods. The buyer is faced with non-negative random demand from external customers. This means that the quantity of demand is random, but not negative. This uncertainty of demand adds complexity to inventory management, which needs to take into account the various possible demand scenarios. Only the buyer is responsible for managing the inventory. Suppliers are not involved in the day-to-day management of inventory. Suppliers use a made-to-order system, i.e., they start production or make order decisions after receiving an order from a buyer. This means that the supplier does not produce or stock up in advance, but arranges production and supply according to the buyer's specific order.
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.
A regular supplier purchases or manufactures a unit of product at a cost Cr and sells it to the buyer at the price Wr. Expedited suppliers purchase or manufacture a unit of product at cost Ce and sell it to the buyer at the price We and We>Wr. This means that expedited suppliers have higher prices for their products, often because of their shorter delivery times or more timely service.
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.
If the buyer's inventory can't meet the demand, the unfulfilled demand is credited to the backorder (the last cycle of the entire time period is considered a lost sale). This strategy allows buyers to make up for inventory shortages with backorders for most of the time, but directly lose sales when the last cycle can't be remedied.
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.
The buyer adopts the TBS strategy for inventory control. This strategy consists of two aspects: on the one hand, ordering a fixed and constant quantity of Qr from a regular supplier. On the other hand, order varying quantities from expedited suppliers in response to uncertainty in demand. With this strategy, buyers can utilize lower-cost regular suppliers to replenish inventory in most cases, and respond to fluctuations in demand with higher-cost, expedited suppliers when demand is higher than expected.
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.
A mechanism to dynamically adjust rush order quantities by benchmarking inventory levels and inventory locations. This ensures inventory levels with flexible rush ordering while minimizing inventory costs when demand is uncertain. Inventory location refers to net inventory (on-hand inventory plus orders in transit from all suppliers, minus unmet quantities). The quantity ordered in an expedited order is the difference required to reach the baseline inventory level. It's possible for an inventory location to exceed the baseline inventory level, which is known as overbooking.
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.
The steps for inventory management and profitability calculations for the buyer are described in detail below. The buyer evaluates the location of its inventory, including initial inventory and all outstanding orders from both vendors. Then, based on the inventory location, 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.
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.
The next cycle of inventory is then calculated, and finally the buyer's profit, the profit of the regular supplier and the expedited supplier are calculated.
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.
The oversubscription distribution relies only on the fixed order quantity Qr of the regular supplier. The overordered quantity satisfies the Lindley recursive relation and acknowledges a steady-state distribution that satisfies the Lindley integral equation. The oversubscription distribution can be obtained by the Wiener–Hopf method, numerically solving integral equations, or by simulating the oversubscription process. In the numerical study, the Monte Carlo simulation was used to simulate the overbooking process with a long period (T=1000) and repeated 10000 times.
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、知识补充(Knowledge Supplement)
Lindley recursive relationship is an important concept in queuing theory and inventory management, which is used to describe the dynamic changes in waiting time or inventory location in a system. It is mainly used to analyze the stable behavior of a system over time. The specific expression is: 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}.
In the queuing system, Wn can represent the waiting time of the nth customer, and Xn+1 can represent the difference between the arrival time of the n+1 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).
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).
In inventory management, Wn can represent the inventory location at the end of the nth cycle, and Xn+1 represents the difference between the demand and the replenishment volume in the n+1 cycle. If Wn+Xn+1 is positive, there is an oversubscription, otherwise the inventory location is zero (no overordering).
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).
The nature of Lindley's recursive relationships includes the following:
The properties of the Lindley recurrence relation include the following:
1. Steady-state distribution: After a long period of operation, the system may reach an equilibrium state, at which time the distribution of Wn tends to be stable, which is called steady-state distribution.
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. Integral equation: The steady-state distribution satisfies a Lindley integral equation, which can be solved by numerical or simulation methods.
2. Integral equation: The steady-state distribution satisfies a Lindley integral equation, which can be solved by numerical methods or simulation methods.
3. Application methods: Wiener–Hopf method, numerical solution, Monte Carlo simulation.
3. Application methods: Common ones include Wiener–Hopf method, numerical solution, and Monte Carlo simulation.
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Translation: AI translation
References: Baidu, Wenxin Yiyan, Chatgpt
参考文献：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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