We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions a...We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity （sales quantity） under random yield is more （less） than that under certain yield.展开更多
We study the stochastic inventory problem with optimal （s,S） policies.In a finite horizon model with lost sales,we establish new lower and upper bounds of s and S.These bounds have structural implications for the op...We study the stochastic inventory problem with optimal （s,S） policies.In a finite horizon model with lost sales,we establish new lower and upper bounds of s and S.These bounds have structural implications for the optimal solutions.Consequently,when demand has a generalized phase type distribution,there are no more than a pre-determined number of minima.Similar bounds can also be found for the system where unsatisfied demand is backordered instead of lost sales.展开更多
We analyze a continuous review lost sales inventory system with two types of orders—regular and emergency. The regular order has a stochastic lead time and is placed with the cheapest acceptable supplier. The emergen...We analyze a continuous review lost sales inventory system with two types of orders—regular and emergency. The regular order has a stochastic lead time and is placed with the cheapest acceptable supplier. The emergency order has a deterministic lead time is placed with a local supplier who has a higher price. The emergency order is not always filled since the supplier may not have the ability to provide the order on an emergency basis at all times. This emergency order has a higher cost per item and has a known probability of being filled. The total costs for this system are compared to a system without emergency placement of orders. This paper provides managers with a tool to assess when dual sourcing is cost optimal by comparing the single sourcing and dual sourcing models.展开更多
In this paper, we study the optimal procurement management by reverse auctions for a price-setting newsvendor(retailer) in a single period setting. The retailer facing price-dependent stochastic demand first designs a...In this paper, we study the optimal procurement management by reverse auctions for a price-setting newsvendor(retailer) in a single period setting. The retailer facing price-dependent stochastic demand first designs a procurement contract and then invites the suppliers to bid for this contract in the reverse auction. The winning supplier produces and delivers the demanded quantity.The retailer obtains the procurement quantity and simultaneously determines the retail price. By using the price elasticity of the lost-sales rate, we show that the retailer’s expected profit(excluding the procurement cost) is a concave function of the purchased quantity, which can be used to obtain the optimal procurement and retail pricing decisions for the retailer. Further, when the underlying random term of demand function is normally distributed under left-truncation(at 0), we get the analytical expressions of the purchased quantity and expected profit function for the retailer. Moreover, some numerical examples are given.展开更多
基金Supported by the National Natural Science Foundation of China under Grants(No.606740852,No. 70731003,No.70221001)
文摘We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity （sales quantity） under random yield is more （less） than that under certain yield.
基金supported by the Shanghai Excellent Junior Faculty Foundation
文摘We study the stochastic inventory problem with optimal （s,S） policies.In a finite horizon model with lost sales,we establish new lower and upper bounds of s and S.These bounds have structural implications for the optimal solutions.Consequently,when demand has a generalized phase type distribution,there are no more than a pre-determined number of minima.Similar bounds can also be found for the system where unsatisfied demand is backordered instead of lost sales.
文摘We analyze a continuous review lost sales inventory system with two types of orders—regular and emergency. The regular order has a stochastic lead time and is placed with the cheapest acceptable supplier. The emergency order has a deterministic lead time is placed with a local supplier who has a higher price. The emergency order is not always filled since the supplier may not have the ability to provide the order on an emergency basis at all times. This emergency order has a higher cost per item and has a known probability of being filled. The total costs for this system are compared to a system without emergency placement of orders. This paper provides managers with a tool to assess when dual sourcing is cost optimal by comparing the single sourcing and dual sourcing models.
基金Supported by Hunan Provincial Department of Education Fund(20A485,19K093)National Center for Applied Mathematics in Hunan Province。
文摘In this paper, we study the optimal procurement management by reverse auctions for a price-setting newsvendor(retailer) in a single period setting. The retailer facing price-dependent stochastic demand first designs a procurement contract and then invites the suppliers to bid for this contract in the reverse auction. The winning supplier produces and delivers the demanded quantity.The retailer obtains the procurement quantity and simultaneously determines the retail price. By using the price elasticity of the lost-sales rate, we show that the retailer’s expected profit(excluding the procurement cost) is a concave function of the purchased quantity, which can be used to obtain the optimal procurement and retail pricing decisions for the retailer. Further, when the underlying random term of demand function is normally distributed under left-truncation(at 0), we get the analytical expressions of the purchased quantity and expected profit function for the retailer. Moreover, some numerical examples are given.
