We consider periodic review perishable inventory systems with a fixed product lifetime. Unsatisfi... more We consider periodic review perishable inventory systems with a fixed product lifetime. 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 these systems is notoriously complex and computationally intractable because of the curse of dimensionality. Hence, various heuristic replenishment policies are proposed in the literature, including the base-stock policy, which raises the total inventory level to a constant in each review period. Whereas various studies show near-optimal numerical performances of base-stock policies in the classic system with zero replenishment lead time and a first-in-first-out issuance policy, the results on their theoretical performances are very limited. In this paper, we first focus on this classic system and show that a simple base-stock policy is asymptotically optimal when any one of the product lifetime, demand population size, unit penalty cost, and unit outdating cost becomes large; moreover, its optimality gap converges to zero exponentially fast in the first two parameters. We then study two important extensions. For a system under a last-in-first-out or even an arbitrary issuance policy, we prove that a simple base-stock policy is asymptotically optimal with large product lifetime, large unit penalty costs, and large unit outdating costs, and for a backlogging system with positive lead times, we prove that our results continue to hold with large product lifetime, large demand population sizes, and large unit outdating costs. Finally, we provide a numerical study to demonstrate the performances of base-stock policies in these systems. This paper was accepted by Victor Martinez de Albéniz, operations management. Funding: J. Bu was partially supported by a Hong Kong Polytechnic University Start-up Fund for New Recruits [Grant P0039585]. X. Gong was partially supported by a Chinese University of Hong Kong (CUHK) Direct Grant [Grant 4057147] and the Hong Kong Research Grants Council (RGC) General Research Fund [Grant CUHK14500120]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4400 .
We consider an online personalized assortment optimization problem where customers arrive sequent... more We consider an online personalized assortment optimization problem where customers arrive sequentially and make their choices (e.g., click an ad, purchase a product) following the multinomial logit (MNL) model with unknown parameters. Utilizing customer's personal information, the firm makes an assortment decision tailored for the individual customer's preference. We develop two algorithms which make assortment recommendations to maximize expected total revenue while concurrently learning the demand. The first algorithm constructs upper-confidence bounds (UCB) of product utilities using estimated demand parameters and personalized data to balance exploration and exploitation. The second algorithm incorporates a fast online convex optimization procedure in the first algorithm, which significantly reduces the computational effort; thus it is particularly useful when solving online personalized assortment optimization problem in a big data regime. We show that the algorithms can be modified to solve high dimensional problem (i.e., when the dimension of customer's personal information data is high) through a dimension reduction method known as random projection. The theoretical performance for our algorithms in terms of regret are derived, and numerical experiments using synthetic and real data demonstrate that they perform very well in both low and high dimensional settings compared with several benchmarks.
In the arid desert areas in Xinjiang, most limestone quarries are hillside open-pit mines (OPMs) ... more In the arid desert areas in Xinjiang, most limestone quarries are hillside open-pit mines (OPMs) where the limestone is hard, heterogeneous, and fractured, and can be easily broken into large blocks by blasting. This study tried to find effective technical methods for blasting heterogeneous rocks in such quarries based on an investigation into existing problems encountered in actual mining at Hongshun Limestone Quarry in Xinjiang. This study provided blasting schemes for hillside OPMs with different heights and slopes. These schemes involve the use of vertical deep holes, oblique shallow holes, and downslope hole-by-hole sublevel or simultaneous detonation techniques. In each bench, the detonations of holes in a detonation unit occur at intervals of 25-50 milliseconds. The research findings can offer technical guidance on how to blast heterogeneous rocks in hillside limestone quarries.
Manufacturing & Service Operations Management, 2011
Product returns have become a significant feature of many manufacturing systems. Because products... more Product returns have become a significant feature of many manufacturing systems. Because products are returned under different operational conditions, they usually require different remanufacturing effort/costs. Motivated by a project with a major energy company that manages its inventory through options of ordering and remanufacturing returned products (cores) in various condition, in this paper, we study a single-product, periodic-review inventory system with multiple types of cores. The serviceable products used to fulfill stochastic customer demand can be either manufactured from new parts or remanufactured from the cores, and the objective is to minimize the expected total discounted cost over a finite planning horizon. We show that the optimal manufacturing–remanufacturing–disposal policy has a simple structure and can be completely characterized by a sequence of constant control parameters when manufacturing and remanufacturing leadtimes are the same. To demonstrate the value of the optimal policy, we conduct a numerical study that compares its performance with two simple heuristics, namely, pull policy without and with sorting. The results show that the reduction in system cost by using the optimal policy can be significant. When manufacturing and remanufacturing leadtimes are different, we develop a heuristic method for computing the near-optimal control policy that performs quite well as demonstrated numerically.
We consider a joint pricing and inventory control problem in which the customer’s response to sel... more We consider a joint pricing and inventory control problem in which the customer’s response to selling price and the demand distribution are not known a priori. Unsatisfied demand is lost and unobserved, and the only available information for decision making is the observed sales data (also known as censored demand). Conventional approaches, such as stochastic approximation, online convex optimization, and continuum-armed bandit algorithms, cannot be employed, because neither the realized values of the profit function nor its derivatives are known. A major challenge of this problem lies in that the estimated profit function constructed from observed sales data is multimodal in price. We develop a nonparametric spline approximation–based learning algorithm. The algorithm separates the planning horizon into a disjoint exploration phase and an exploitation phase. During the exploration phase, a spline approximation of the demand-price function is constructed based on sales data, and then the corresponding surrogate optimization problem is solved on a sparse grid to obtain a pair of recommended price and target inventory level. During the exploitation phase, the algorithm implements the recommended strategies. We establish a (nearly) square-root regret rate, which (almost) matches the theoretical lower bound.
Simple Algorithms for Complex Multiwarehouse, Multistore Inventory Control Problems Retailers (bo... more Simple Algorithms for Complex Multiwarehouse, Multistore Inventory Control Problems Retailers (both brick-and-mortar and e-commerce) have always faced the problem of allocating inventories in their warehouses (or central distribution centers) to the stores (or smaller local warehouses) in order to minimize total costs. The problem is particularly challenging when the network structure is large and complex, the selling season is long, and the replenishment is frequent. For example, giant retail chains such as Macy’s typically have many warehouses and hundreds of stores across the United States, and online retailers such as Amazon have many distribution centers and over one hundred fulfillment centers. The authors develop algorithms to solve this multiwarehouse, multistore (MWMS) inventory control problem. Their algorithms are computationally efficient and asymptotically optimal as the problem becomes large and complex. This feature is very appealing to today’s fast-moving retail industry with rapidly expanding business scale.
In this chapter we will consider networks of queues. Simple analytical results are usually only p... more In this chapter we will consider networks of queues. Simple analytical results are usually only possible for Markovian queueing networks. We will start by establishing the product form solution for the equilibrium state probabilities for such networks in section 3.2. The existence of the product form solution basically means that the joint state probability can be expressed as a simple product of functions associated with a network’s individual queues. In the case of open queueing networks of state-independent queues these functions are simply the marginal state probabilities so that it seems that the queues act as if they were independent. This interesting observation was first noted by J. R. Jackson [JACK 57] in the original product form paper for open networks in 1957 and later generalized in [JACK 64]. In 1967, W. J. Gordon and G. F. Newell [GORD] demonstrated the existence of the product form solution for closed networks. In 1975 F. Baskett, K. M. Chandy, R. R. Muntz and F. G. Palacios [BASK 75] generalized the families of queueing networks known to have the product form solution.
We consider periodic review perishable inventory systems with a fixed product lifetime. Unsatisfi... more We consider periodic review perishable inventory systems with a fixed product lifetime. 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 these systems is notoriously complex and computationally intractable because of the curse of dimensionality. Hence, various heuristic replenishment policies are proposed in the literature, including the base-stock policy, which raises the total inventory level to a constant in each review period. Whereas various studies show near-optimal numerical performances of base-stock policies in the classic system with zero replenishment lead time and a first-in-first-out issuance policy, the results on their theoretical performances are very limited. In this paper, we first focus on this classic system and show that a simple base-stock policy is asymptotically optimal when any one of the product lifetime, demand population size, unit penalty cost, and unit outdating cost becomes large; moreover, its optimality gap converges to zero exponentially fast in the first two parameters. We then study two important extensions. For a system under a last-in-first-out or even an arbitrary issuance policy, we prove that a simple base-stock policy is asymptotically optimal with large product lifetime, large unit penalty costs, and large unit outdating costs, and for a backlogging system with positive lead times, we prove that our results continue to hold with large product lifetime, large demand population sizes, and large unit outdating costs. Finally, we provide a numerical study to demonstrate the performances of base-stock policies in these systems. This paper was accepted by Victor Martinez de Albéniz, operations management. Funding: J. Bu was partially supported by a Hong Kong Polytechnic University Start-up Fund for New Recruits [Grant P0039585]. X. Gong was partially supported by a Chinese University of Hong Kong (CUHK) Direct Grant [Grant 4057147] and the Hong Kong Research Grants Council (RGC) General Research Fund [Grant CUHK14500120]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4400 .
We consider an online personalized assortment optimization problem where customers arrive sequent... more We consider an online personalized assortment optimization problem where customers arrive sequentially and make their choices (e.g., click an ad, purchase a product) following the multinomial logit (MNL) model with unknown parameters. Utilizing customer's personal information, the firm makes an assortment decision tailored for the individual customer's preference. We develop two algorithms which make assortment recommendations to maximize expected total revenue while concurrently learning the demand. The first algorithm constructs upper-confidence bounds (UCB) of product utilities using estimated demand parameters and personalized data to balance exploration and exploitation. The second algorithm incorporates a fast online convex optimization procedure in the first algorithm, which significantly reduces the computational effort; thus it is particularly useful when solving online personalized assortment optimization problem in a big data regime. We show that the algorithms can be modified to solve high dimensional problem (i.e., when the dimension of customer's personal information data is high) through a dimension reduction method known as random projection. The theoretical performance for our algorithms in terms of regret are derived, and numerical experiments using synthetic and real data demonstrate that they perform very well in both low and high dimensional settings compared with several benchmarks.
In the arid desert areas in Xinjiang, most limestone quarries are hillside open-pit mines (OPMs) ... more In the arid desert areas in Xinjiang, most limestone quarries are hillside open-pit mines (OPMs) where the limestone is hard, heterogeneous, and fractured, and can be easily broken into large blocks by blasting. This study tried to find effective technical methods for blasting heterogeneous rocks in such quarries based on an investigation into existing problems encountered in actual mining at Hongshun Limestone Quarry in Xinjiang. This study provided blasting schemes for hillside OPMs with different heights and slopes. These schemes involve the use of vertical deep holes, oblique shallow holes, and downslope hole-by-hole sublevel or simultaneous detonation techniques. In each bench, the detonations of holes in a detonation unit occur at intervals of 25-50 milliseconds. The research findings can offer technical guidance on how to blast heterogeneous rocks in hillside limestone quarries.
Manufacturing & Service Operations Management, 2011
Product returns have become a significant feature of many manufacturing systems. Because products... more Product returns have become a significant feature of many manufacturing systems. Because products are returned under different operational conditions, they usually require different remanufacturing effort/costs. Motivated by a project with a major energy company that manages its inventory through options of ordering and remanufacturing returned products (cores) in various condition, in this paper, we study a single-product, periodic-review inventory system with multiple types of cores. The serviceable products used to fulfill stochastic customer demand can be either manufactured from new parts or remanufactured from the cores, and the objective is to minimize the expected total discounted cost over a finite planning horizon. We show that the optimal manufacturing–remanufacturing–disposal policy has a simple structure and can be completely characterized by a sequence of constant control parameters when manufacturing and remanufacturing leadtimes are the same. To demonstrate the value of the optimal policy, we conduct a numerical study that compares its performance with two simple heuristics, namely, pull policy without and with sorting. The results show that the reduction in system cost by using the optimal policy can be significant. When manufacturing and remanufacturing leadtimes are different, we develop a heuristic method for computing the near-optimal control policy that performs quite well as demonstrated numerically.
We consider a joint pricing and inventory control problem in which the customer’s response to sel... more We consider a joint pricing and inventory control problem in which the customer’s response to selling price and the demand distribution are not known a priori. Unsatisfied demand is lost and unobserved, and the only available information for decision making is the observed sales data (also known as censored demand). Conventional approaches, such as stochastic approximation, online convex optimization, and continuum-armed bandit algorithms, cannot be employed, because neither the realized values of the profit function nor its derivatives are known. A major challenge of this problem lies in that the estimated profit function constructed from observed sales data is multimodal in price. We develop a nonparametric spline approximation–based learning algorithm. The algorithm separates the planning horizon into a disjoint exploration phase and an exploitation phase. During the exploration phase, a spline approximation of the demand-price function is constructed based on sales data, and then the corresponding surrogate optimization problem is solved on a sparse grid to obtain a pair of recommended price and target inventory level. During the exploitation phase, the algorithm implements the recommended strategies. We establish a (nearly) square-root regret rate, which (almost) matches the theoretical lower bound.
Simple Algorithms for Complex Multiwarehouse, Multistore Inventory Control Problems Retailers (bo... more Simple Algorithms for Complex Multiwarehouse, Multistore Inventory Control Problems Retailers (both brick-and-mortar and e-commerce) have always faced the problem of allocating inventories in their warehouses (or central distribution centers) to the stores (or smaller local warehouses) in order to minimize total costs. The problem is particularly challenging when the network structure is large and complex, the selling season is long, and the replenishment is frequent. For example, giant retail chains such as Macy’s typically have many warehouses and hundreds of stores across the United States, and online retailers such as Amazon have many distribution centers and over one hundred fulfillment centers. The authors develop algorithms to solve this multiwarehouse, multistore (MWMS) inventory control problem. Their algorithms are computationally efficient and asymptotically optimal as the problem becomes large and complex. This feature is very appealing to today’s fast-moving retail industry with rapidly expanding business scale.
In this chapter we will consider networks of queues. Simple analytical results are usually only p... more In this chapter we will consider networks of queues. Simple analytical results are usually only possible for Markovian queueing networks. We will start by establishing the product form solution for the equilibrium state probabilities for such networks in section 3.2. The existence of the product form solution basically means that the joint state probability can be expressed as a simple product of functions associated with a network’s individual queues. In the case of open queueing networks of state-independent queues these functions are simply the marginal state probabilities so that it seems that the queues act as if they were independent. This interesting observation was first noted by J. R. Jackson [JACK 57] in the original product form paper for open networks in 1957 and later generalized in [JACK 64]. In 1967, W. J. Gordon and G. F. Newell [GORD] demonstrated the existence of the product form solution for closed networks. In 1975 F. Baskett, K. M. Chandy, R. R. Muntz and F. G. Palacios [BASK 75] generalized the families of queueing networks known to have the product form solution.
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