Price-Directed Control of a Closed Logistics Queueing Network." Daniel Adelman; Operations Research, 2007, 55(6), pp. 1022-38

Adelman (2007) studies a dynamic fleet management problem on a closed logistics queueing network. The focal of this paper is to resolve the spacial (geographic) imbalance of the supply and demand from a central planner’s point of view. First, Adelman’s paper takes a centralized view for controlling the system. Second, the primary concern in his work is geographic (spacial) imbalance of supply and demand. He traces the state (location and idle time) of each box in a closed queueing network. The market segmentation (as he pointed in the end) is not taken into account in his work. In summary, his work is a centralized dynamic fleet-management problem with flavor. In terms of methodology, he uses LP and nonlinear LP to approximate the problem.

Price-Directed Control of a Closed Logistics Queueing Network.” Daniel Adelman; Operations Research, 2007, 55(6), pp. 1022-38

Technorati : LP, approximation, math programming, operations management, revenue management

on the value of a threat advisory system for managing supply chain disruptions, Tomlin and Snyder WP07

This paper studies the value of tracing the supply process in a periodic review inventory system. The supply process is modeled by a Markov chain with each state describes different level of threat, i.e., the probability of shutdown in the next period. The difference between two adjacent states is captured by a threat ratio of their probability of shutdown. Therefore, the threat ratio characterizes the heterogeneity of the supply states. The paper shows that the optimal policy is of supply state dependent base stock type. As the threat ratio goes up, the system gains more value of ramping up the inventory only in dangerous (high) states, which in other states the base stock level can be lowered, consistent with the intuition. Therefore, the value of supply information (Markov chain) comes from the fact that it enables the firm to carry a large quantity of inventory only if the threat level is high rather than carrying it continuously, as such practice may be too expensive for rare but long disruptions.

This paper also investigates the effects of capacitated supply, and shows that the supply capacity limits the effectiveness of such threat advisory system as it limits the firm’s ability to take advantage of threat-dependent coverage. This is intuitive since the information is valuable only when you can act upon on it. Due to the limited capacity, the system may not attain the optimal base stock level in one period and therefore, the coverage functions as a protection not only for the possible disruption in the next period but also the possible future disruptions, during which the inventory level has yet to reach the optimal level because of the capacity. An interesting effect unique in capacitated system is that due to the delay of bringing the inventory to the optimal level, the system can be down again during its recovery, i.e., ‘recovery effect’. Another similar effect is the disruption during the transition from one up state to another up state, ‘threat transition effect’. Therefore, compared to infinite capacity system, the base stock levels in capacitated system should be higher.

The paper also examines two-suppler cases. Two tactics are possible under such situations: (1) sourcing mitigation refers to a sourcing policy in which the firm routinely sources a positive fraction $w$ of its demand from a reliable but expensive supplier, besides the main unreliable supplier; (2) contingent rerouting refers to a sourcing policy whereby the firm temporarily increases the quantity sourced from the reliable supplier during the disruption of the unreliable supplier. Rerouting is only allowed during disruption. The paper finds that sourcing mitigation is preferable for low supplier reliability and high expected disruption duration, while the inventory mitigation is preferable for high reliability and short disruption during cases.

The paper also investigates the impact of the structure of the supply process upon the disruption management strategy. Two structures of the Markov chain are investigated, completely connected and sequential connected (birth and death process). It is intuitive that the sequential connected chain yields more value due to its higher predictivity.

the power of flexibility for mitigating supply chain risks, C. Tang and Brian Tomlin, WP08

This paper uses simple models to illustrate the idea that limited flexibility is sufficient to enhance the supply chain resilience. Five strategies are aimed at three aspects: supply, process and demand risks. They includes: multiple suppliers, flexible contracts, flexible manufacturing processes (1-1, or 1-n production), postponement, and responsive pricing (focus on time of pricing after observing demand signals).

READING: supply disruptions, asymmetric information, and a backup production option, Zhibin Yang, Aydin, Babich, Beil, MS 08

This paper uses one period economic model to investigate the relationships of the supplier’s reliability, asymmetric information, and the value of backup options, and to design the optimal menu , where is down payment, is the contract quantity, is the unit penalty for un-delivery shortage. The demand is deterministic. There are two types of suppliers, with high or low reliability. The manufacturer designs his contract so that the suppliers will reveal their true reliability. For high reliability, the manufacturer needs to pay information rents for eliciting the high-type suppliers to reveal their type(?), while using low reliable supplier the manufacturer suffers channel loss. Note that the information rent is defined as the benefit of being high-type supplier over low-type for a given contract: . Channel loss is defined by , the profit loss due to the derivation from the optimal contract.

The authors characterize the parameter range so that the action of each type of supplier can be specified, where is the unit revenue, is the unit backup option cost. The value of supplier backup option for the manufacturer is not necessarily larger under asymmetric information. The manufacturer is willing to pay the most for information when supplier backup option is moderately expensive. This is because when the backup option either extremely cheap or expensive, the actions of suppliers have already been certain and their is no need for the additional information to infer it. The value of information may increase as supplier types become uniformly more reliable. Higher reliability need not be a substitute for better information. In other words, they can be complements to each other.

See also, Supply disruptions, asymmetric information and a dual-sourcing option, by Yang, Aydin, Babich, and Beil, working paper, 08.

revenue management and E-commerce, Boyd and Bilegan, MS02

This paper provides a very good summary of RM, particularly the practice side.

Tow points are worth attention. DP is not widely adopted by the practitioners largely due to the different mind set. Traditional RM models based on the independent demand and ignorance of the network effect have severe flaws. It also impacts how the systems should be controlled. Bid price should a more promising and superior control mechanism, compared with virtual nesting. But there is no consensus among practitioners yet.

The major issue in the forecasting is the level of detail. The paper suggests that a bottom-up approach may be more accurate than a top-down one. Also, the passenger name records (PNR) is a more desirable data source than historical transaction data.

OPTIMAL PRODUCTION AND INVENTORY POLICIES OF PRIORITY AND PRICE-DIFFERENTIATED CUSTOMERS, by Duran, Liu, Simchi-Levi, Swann, IIE07

The system can be a reservation-inventory system or backlog system, depending on the relationship of and , where and are prices, holding cost, and lost sales (rejection) penalty, and backlog cost. We need it to establish the assumption that the backlog a class-1 is more profitable than accept a class-2 now.

A more nature approach is to model the acceptance decision directly, say and , the amount of order accepted. This paper builds the structure of the policy into the model, and therefore, the actual amount of acceptance is implies by the policy embedded. On advantage of this approach is that, we can explicitly express each quantities and assess their costs, so the objective function is expressed in terms of the policy parameters, which are easy to handle. In particular, different quantities of reservation and backlogs can be written out explicitly.

The benchmark case is the system that has no customer differentiation, zero leadtime (due date), and no tactical inventory. NDS case is the one with leadtime 1, but no customer differentiation, therefore reservation is impossible but backlog can be done. The optimal policy allows leadtime 1, thus backlog, and customer differentiation (so reservation is possible).

The paper also discusses the value of price differentiation. When both premium and discount prices are offered, rather than a single discount or premium prices, the increased capacity flexibility (availability due leadtime 1) can outweight the lost due to the lower average price.

The impact of pricing trend is also investigated numerically. Let be the rate of price growth. Then when the growth is slow, then backlog is a more effective level for single class problem since it allows more capacity availability to meet the realized demand and the future will not be much better than now. If we can fulfill the realized orders now, we would rather borrow future to serve the current realized demand.

When the growth is strong, i.e., future is significantly better than the current, then reservation (rationing) is more effective because the system want to sell to more profitable future. However, the system may still backlog, since the realized demand has its value, in case there is no demand in the future at all. In this case, the demand variability plays an important role. If the future is certain, then there may be no need to backlog.

Even if part of demand may switch to discount classes when two prices are offered, it may still be profitable to do so. One reason is that, the discount class allows more capacity flexibility to capture the realized demand, which may be lost if the system only offers premium price and service (zero leadtime).
The price should be average by the demand: , not just arithmetic average.

The other paper, “POLICIES UTILIZING TACTICAL INVENTORY FOR SERVICE-DIFFERENTIATED CUSTOMERS”, is almost the same as this model.