基于MCMC的随机库存系统中提前期需求分布的计算

在需求和提前期均是随机的库存系统中,提前期需求的分布是由提前期分布与需求分布复合而成的,这个复合分布的计算通常是困难的。本文采用基于Gibbs抽样的马尔科夫链蒙特卡洛(MCMC,Markov chain Monte Carlo)方法,抽取条件分布样本作为提前期需求分布的样本,通过样本来计算提前期需求分布密度、服务水平和损失函数。这种方法避免了直接求解复杂积分计算上的困难,也克服了近似分布拟合偏差过大的问题,有效地解决了随机需求与随机提前期的复杂库存系统中提前期需求确定问题。理论与数值分析结果表明:与现有方法相比较,基于MCMC的方法具有计算简便、拟合精度高、通用性好等特点。     

Coal bank scheduling using a mathematical programming model

Coals are extracted from mines and upgraded on the surface for customers. The upgraded coals must be aged at least four weeks in a bank before being supplied to customers. Different sizes of banks are required for different lengths of time at different points in time. Bigger banks increase the floor space capacity and reduce handling costs. The proper location of banks reduces the total space requirement and bank movement after building. In this paper, we address the bank size and location problem and solve it by using a mathematical programming approach.     

Joint pricing and inventory control with a Markovian demand model

We consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples. The results indicate that it is more beneficial to implement dynamic pricing in a Markovian demand environment with a high fixed ordering cost or with high demand variability.     

A Dynamic Supplier Selection and Inventory Management Model for a Serial Supply Chain with a Novel Supplier Price Break Scheme and Flexible Time Periods

A new supplier price break and discount scheme taking into account order frequency and lead time is introduced and incorporated into an integrated inventory planning model for a serial supply chain that minimizes the overall incurred cost including procurement, inventory holding, production, and transportation. A mixed-integer linear programming (MILP) formulation is presented addressing this multi-period, multi-supplier, and multi-stage problem with predetermined time-varying demand for the case of a single product. Then, the length of the time period is considered as a variable. A new MILP formulation is derived when each period of the model is split into multiple sub-periods, and under certain conditions, it is proved that the optimal solution and objective value of the original model form a feasible solution and an upper bound for the derived model. In a numerical example, three scenarios of the derived model are solved where the number of sub-period is set to 2, 3, and 4. The results further show the decrease of the optimal objective value as the length of the time period is shortened. Sufficient evidence demonstrates that the length of the time period has a significant influence on supplier selection, lot sizing allocation, and inventory planning decisions. This poses the necessity of the selection of appropriate length of a time period, considering the trade-off between model complexity and cost savings.     

Aggregation and disaggregation in Markov decision models for inventory control

In this paper the possibility is investigated of using aggregation in the action space for some Markov decision processes of inventory control type. For the standard (s, S) inventory control model the policy improvement procedure can be executed in a very efficient way, therefore, aggregation in the action space is not of much use. However, in situations where the decisions have some aftereffect and, hence, the old decision has to be incorporated in the state, it might be rewarding to aggregate actions. Some variants for aggregation and disaggregation are formulated and analyzed. Numerical evidence is presented.     

An efficient approach for dual sourcing inventory systems with Tailored Base-Surge policies

Nowadays most companies use dual sourcing strategies to manage supply chains. Recently, a practical policy called the Tailored Base-Surge (TBS) policy has been proposed to manage the system, and shown to perform well. We study a dual sourcing inventory system with i.i.d. demands and TBS policies. Using the techniques of MacLaurin series analysis, we develop an efficient method to calculate the moments of the inventory position, the bullwhip effect, and performance measures. Numerical experiments show that our method works well.     

Managing supply chain backorders under vendor managed inventory: An incentive approach and empirical analysis

This paper shows how a manufacturer may use an incentive contract with a distributor under a VMI arrangement to gain market share. The manufacturer promises a distributor lower inventory levels in exchange for efforts by the distributor to convert potential lost sales due to stockouts to backorders. Data gathered from a third party provider of information services are then used to illustrate that this incentive arrangement may, at least implicitly, be employed in industry. Our data estimations show that when a manufacturer and distributor are operating under a VMI arrangement, lower inventory at the distributor is associated with a higher conversion rate of lost sales stockouts to backorders.     

A One-Time Excess Inventory Disposal Decision Under a Stationary Base-Stock Policy

We consider a stochastic inventory system that has been operated under a policy different from the one that will be implemented in the future. Such a situation may arise as a result of changes in model assumptions leading to the implementation of a different policy. Before the new policy is implemented, there may be some units on hand which may exceed the optimal order-up-to level. Hence, one needs to evaluate a one-time inventory disposal decision immediately before the new policy replaces the policy in use. For this purpose, we develop three models under different assumptions that describe the demand during the disposal period and present analytical results characterizing their optimal solutions.     

An analytical study of the modification ability of distribution centers

This paper considers a two-level vendor managed inventory (VMI) system comprising a distribution center (DC) and a retailer. Both the DC’s and the retailer’s replenishment decisions follow the order-up-to-level policy and aim at maximizing the profit of the overall system. We critically examine the potential of the DC’s ability to modify delivery decisions, identify and quantify the cost factors that influence the DC’s modification ability, establish a relationship between the DC’s location and its modification ability, and show the trade-off between the DC’s modification ability and related costs. Our analysis provides a new insight into the role of the DC and reveals the full potential of the VMI system. Our findings and their practical implications, demonstrated with the aid of computational examples, are helpful for enhancing the practice of VMI at both strategic and operational levels.     

A coordinated location-inventory model

We consider a coordinated location-inventory model where distribution centers (DCs) follow a periodic-review (R, S) inventory policy and system coordination is achieved by choosing review intervals at the DCs from a menu of permissible choices. We introduce two types of coordination: partial coordination where each DC may choose its own review interval from the menu, and full coordination where all the DCs have an identical review interval. While full coordination increases the location and inventory costs, it likely reduces the overall costs of running the system (when the operational costs such as delivery scheduling are taken into account). The problem is to determine the location of the DCs to be opened, the assignment of retailers to DCs, and the inventory policy parameters at the DCs such that the total system-wide cost is minimized. The model is formulated as a nonlinear integer-programming problem and a Lagrangian relaxation algorithm is proposed to solve it. Computational results show that the proposed algorithm is very efficient. The results of our computational experiments and case study suggest that the location and inventory cost increase due to full coordination, when compared to partial coordination, is not significant. Thus, full coordination, while enhancing the practicality of the model, is economically justifiable.