http://repository.ust.hk/ir/ This version is available at HKUST Institutional Repository via If i... more http://repository.ust.hk/ir/ This version is available at HKUST Institutional Repository via If it is the author’s pre-published version, changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published version. Dynamic Pricing and Inventory Management for System with Dual Unreliable Suppliers Chao, Xiuli; Gong, Xiting; Zheng, Shaohui
Preservation Results for Proving Additively Convex Value Functions for High-Dimensional Stochasti... more Preservation Results for Proving Additively Convex Value Functions for High-Dimensional Stochastic Optimization Problems
We consider a classic periodic-review perishable inventory system with a fixed product lifetime a... more We consider a classic periodic-review perishable inventory system with a fixed product lifetime and zero replenishment lead time under a first-in-first-out issuance policy. Unsatisfied demand can be either lost or backlogged. The objective is to minimize the long-run average holding, penalty and outdating cost. The optimal policy for this system is notoriously complex and intractable due to the curse of dimensionality. Hence, various heuristic replenishment policies have been proposed in the literature, including the base-stock policy which raises the total on-hand inventory level to a constant at each review epoch. While extensive numerical studies have shown near-optimal performances of such base-stock policies, the results on their theoretical performances are very limited. In this paper, we construct a simple heuristic base-stock policy, and show that the optimality gap between its long-run average cost and that of the optimal replenishment policy converges to zero when any one of lifetime, demand population size, unit penalty cost, or unit outdating cost goes to infinity. Moreover, the convergence rate is exponentially fast in the lifetime and demand population size. We also characterize the convergence rate and the asymptotic long-run average cost in the unit penalty cost for several classes of demand distributions. Further, we extend some of our results to a class of base-stock policies, the system under a last-in-first-out issuance policy, and a backlogging system with positive lead time. Finally, we provide an extensive numerical study to demonstrate the performances of different base-stock policies in three different systems.
Asymptotic analysis of constant-order policies for lost-sales inventory models with positive lead... more Asymptotic analysis of constant-order policies for lost-sales inventory models with positive lead times and random supply functions.
We consider an infinite-horizon lost-sales inventory model where the supply takes positive lead t... more We consider an infinite-horizon lost-sales inventory model where the supply takes positive lead times and is a random function of the order quantity (e.g., random yield/capacity). The optimal policy for this model is computationally intractable; and no heuristic has been proposed in the literature. In this paper, we focus on a simple class of constant-order policies (COP) that place the same order in every period, regardless of the system state. Under some assumptions on the random supply function, we prove that the best COP is asymptotically optimal with large lead times and the optimality gap converges to zero exponentially fast in the lead time. We also prove that, if the mean supply capacity is less than the mean demand, then the best COP is also asymptotically optimal with large penalty costs; otherwise, the long-run average cost of the best COP asymptotically increases at the rate of square-root of the penalty cost. Further, we construct a simple heuristic COP and show that it performs very close to the best COP. Finally, we provide a numerical study to derive further insights into the performance of the best COP.
We study optimal policies for dual-supply inventory systems where a firm commits to buying a tota... more We study optimal policies for dual-supply inventory systems where a firm commits to buying a total minimum quantity from both supplies or two separate total minimum quantities from each supply over a finite planning horizon. The two supply options differ in their costs and lead times. For the system under the joint commitment, the optimal policy has a simple structure and can be fully characterized by three critical numbers in each period. For the system under the separate commitments, we show that the optimal order quantities in each period are monotonic in the starting inventory and the remaining commitments with bounded sensitivity. Moreover, we establish convergence results on the optimal order quantities when the committed quantity from either supply approaches infinity. These findings highlight the effects of order commitments on the optimal inventory policies. On the basis of these results, we develop a simple heuristic for the system under separate commitments and show numerically that it performs...
When solving the general EOQ model,the dominant solution method in literature is the differential... more When solving the general EOQ model,the dominant solution method in literature is the differential method designed to solve multi-dimensional optimization problems.In this paper,based on the model's mathematical structure,we propose an elementary solution method.This solution method is not only much easier,but also has an advantage to vividly demonstrate the model's important properties,e.g.,the set up cost equals the total cost of storage and shortage in one period,which are generally ignored by the differential method.
This paper evaluates the discrete bid first-price sealed-bid (FPSB) auction in a model with a gen... more This paper evaluates the discrete bid first-price sealed-bid (FPSB) auction in a model with a general value distribution. We show that a symmetric Bayesian Nash equilibrium exists for the discrete bid FPSB auction. We further prove that the discrete bid FPSB equilibrium conditionally converges to that of a continuous bid FPSB auction.
http://repository.ust.hk/ir/ This version is available at HKUST Institutional Repository via If i... more http://repository.ust.hk/ir/ This version is available at HKUST Institutional Repository via If it is the author’s pre-published version, changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published version. Dynamic Pricing and Inventory Management for System with Dual Unreliable Suppliers Chao, Xiuli; Gong, Xiting; Zheng, Shaohui
Preservation Results for Proving Additively Convex Value Functions for High-Dimensional Stochasti... more Preservation Results for Proving Additively Convex Value Functions for High-Dimensional Stochastic Optimization Problems
We consider a classic periodic-review perishable inventory system with a fixed product lifetime a... more We consider a classic periodic-review perishable inventory system with a fixed product lifetime and zero replenishment lead time under a first-in-first-out issuance policy. Unsatisfied demand can be either lost or backlogged. The objective is to minimize the long-run average holding, penalty and outdating cost. The optimal policy for this system is notoriously complex and intractable due to the curse of dimensionality. Hence, various heuristic replenishment policies have been proposed in the literature, including the base-stock policy which raises the total on-hand inventory level to a constant at each review epoch. While extensive numerical studies have shown near-optimal performances of such base-stock policies, the results on their theoretical performances are very limited. In this paper, we construct a simple heuristic base-stock policy, and show that the optimality gap between its long-run average cost and that of the optimal replenishment policy converges to zero when any one of lifetime, demand population size, unit penalty cost, or unit outdating cost goes to infinity. Moreover, the convergence rate is exponentially fast in the lifetime and demand population size. We also characterize the convergence rate and the asymptotic long-run average cost in the unit penalty cost for several classes of demand distributions. Further, we extend some of our results to a class of base-stock policies, the system under a last-in-first-out issuance policy, and a backlogging system with positive lead time. Finally, we provide an extensive numerical study to demonstrate the performances of different base-stock policies in three different systems.
Asymptotic analysis of constant-order policies for lost-sales inventory models with positive lead... more Asymptotic analysis of constant-order policies for lost-sales inventory models with positive lead times and random supply functions.
We consider an infinite-horizon lost-sales inventory model where the supply takes positive lead t... more We consider an infinite-horizon lost-sales inventory model where the supply takes positive lead times and is a random function of the order quantity (e.g., random yield/capacity). The optimal policy for this model is computationally intractable; and no heuristic has been proposed in the literature. In this paper, we focus on a simple class of constant-order policies (COP) that place the same order in every period, regardless of the system state. Under some assumptions on the random supply function, we prove that the best COP is asymptotically optimal with large lead times and the optimality gap converges to zero exponentially fast in the lead time. We also prove that, if the mean supply capacity is less than the mean demand, then the best COP is also asymptotically optimal with large penalty costs; otherwise, the long-run average cost of the best COP asymptotically increases at the rate of square-root of the penalty cost. Further, we construct a simple heuristic COP and show that it performs very close to the best COP. Finally, we provide a numerical study to derive further insights into the performance of the best COP.
We study optimal policies for dual-supply inventory systems where a firm commits to buying a tota... more We study optimal policies for dual-supply inventory systems where a firm commits to buying a total minimum quantity from both supplies or two separate total minimum quantities from each supply over a finite planning horizon. The two supply options differ in their costs and lead times. For the system under the joint commitment, the optimal policy has a simple structure and can be fully characterized by three critical numbers in each period. For the system under the separate commitments, we show that the optimal order quantities in each period are monotonic in the starting inventory and the remaining commitments with bounded sensitivity. Moreover, we establish convergence results on the optimal order quantities when the committed quantity from either supply approaches infinity. These findings highlight the effects of order commitments on the optimal inventory policies. On the basis of these results, we develop a simple heuristic for the system under separate commitments and show numerically that it performs...
When solving the general EOQ model,the dominant solution method in literature is the differential... more When solving the general EOQ model,the dominant solution method in literature is the differential method designed to solve multi-dimensional optimization problems.In this paper,based on the model's mathematical structure,we propose an elementary solution method.This solution method is not only much easier,but also has an advantage to vividly demonstrate the model's important properties,e.g.,the set up cost equals the total cost of storage and shortage in one period,which are generally ignored by the differential method.
This paper evaluates the discrete bid first-price sealed-bid (FPSB) auction in a model with a gen... more This paper evaluates the discrete bid first-price sealed-bid (FPSB) auction in a model with a general value distribution. We show that a symmetric Bayesian Nash equilibrium exists for the discrete bid FPSB auction. We further prove that the discrete bid FPSB equilibrium conditionally converges to that of a continuous bid FPSB auction.
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