Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales

This paper studies a periodic‐review pricing and inventory control problem for a retailer, which faces stochastic price‐sensitive demand, under quite general modeling assumptions. Any unsatisfied demand is lost, and any leftover inventory at the end of the finite selling horizon has a salvage value. The cost component for the retailer includes holding, shortage, and both variable and fixed ordering costs. The retailer's objective is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We show that, under a mild assumption on the additive demand function, at the beginning of each period an (s,S) policy is optimal for replenishment, and the value of the optimal price depends on the inventory level after the replenishment decision has been done. Our numerical study also suggests that for a sufficiently long selling horizon, the optimal policy is almost stationary. Furthermore, the fixed ordering cost (K) plays a significant role in our modeling framework. Specifically, any increase in K results in lower s and higher S. On the other hand, the profit impact of dynamically changing the retail price, contrasted with a single fixed price throughout the selling horizon, also increases with K. We demonstrate that using the optimal policy values from a model with backordering of unmet demands as approximations in our model might result in significant profit penalty. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Algorithms for the multi‐item multi‐vehicles dynamic lot sizing problem

We consider a two‐stage supply chain, in which multi‐items are shipped from a manufacturing facility or a central warehouse to a downstream retailer that faces deterministic external demand for each of the items over a finite planning horizon. The items are shipped through identical capacitated vehicles, each incurring a fixed cost per trip. In addition, there exist item‐dependent variable shipping costs and inventory holding costs at the retailer for items stored at the end of the period; these costs are constant over time. The sum of all costs must be minimized while satisfying the external demand without backlogging. In this paper we develop a search algorithm to solve the problem optimally. Our search algorithm, although exponential in the worst case, is very efficient empirically due to new properties of the optimal solution that we found, which allow us to restrict the number of solutions examined. Second, we perform a computational study that compares the empirical running time of our search methods to other available exact solution methods to the problem. Finally, we characterize the conditions under which each of the solution methods is likely to be faster than the others and suggest efficient heuristic solutions that we recommend using when the problem is large in all dimensions. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations

We consider the coordination problem between a vendor and a buyer operating under generalized replenishment costs that include fixed costs as well as stepwise freight costs. We study the stochastic demand, single‐period setting where the buyer must decide on the order quantity to satisfy random demand for a single item with a short product life cycle. The full order for the cycle is placed before the cycle begins and no additional orders are accepted by the vendor. Due to the nonrecurring nature of the problem, the vendor's replenishment quantity is determined by the buyer's order quantity. Consequently, by using an appropriate pricing schedule to influence the buyer's ordering behavior, there is an opportunity for the vendor to achieve substantial savings from transportation expenses, which are represented in the generalized replenishment cost function. For the problem of interest, we prove that the vendor's expected profit is not increasing in buyer's order quantity. Therefore, unlike the earlier work in the area, it is not necessarily profitable for the vendor to encourage larger order quantities. Using this nontraditional result, we demonstrate that the concept of economies of scale may or may not work by identifying the cases where the vendor can increase his/her profits either by increasing or decreasing the buyer's order quantity. We prove useful properties of the expected profit functions in the centralized and decentralized models of the problem, and we utilize these properties to develop alternative incentive schemes for win–win solutions. Our analysis allows us to quantify the value of coordination and, hence, to identify additional opportunities for the vendor to improve his/her profits by potentially turning a nonprofitable transaction into a profitable one through the use of an appropriate tariff schedule or a vendor‐managed delivery contract. We demonstrate that financial gain associated with these opportunities is truly tangible under a vendor‐managed delivery arrangement that potentially improves the centralized solution. Although we take the viewpoint of supply chain coordination and our goal is to provide insights about the effect of transportation considerations on the channel coordination objective and contractual agreements, the paper also contributes to the literature by analyzing and developing efficient approaches for solving the centralized problem with stepwise freight costs in the single‐period setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The stochastic joint replenishment problem: A new policy,analysis, and insights

In this study, we propose a new parsimonious policy for the stochastic joint replenishment problem in a single‐location, N‐item setting. The replenishment decisions are based on both group reorder point‐group order quantity and the time since the last decision epoch. We derive the expressions for the key operating characteristics of the inventory system for both unit and compound Poisson demands. In a comprehensive numerical study, we compare the performance of the proposed policy with that of existing ones over a standard test bed. Our numerical results indicate that the proposed policy dominates the existing ones in 100 of 139 instances with comparably significant savings for unit demands. With batch demands, the savings increase as the stochasticity of demand size gets larger. We also observe that it performs well in environments with low demand diversity across items. The inventory system herein also models a two‐echelon setting with a single item, multiple retailers, and cross docking at the upper echelon. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Approximate dynamic programming methods for an inventory allocation problem under uncertainty

We propose two approximate dynamic programming methods to optimize the distribution operations of a company manufacturing a certain product at multiple production plants and shipping it to different customer locations for sale. We begin by formulating the problem as a dynamic program. Our first approximate dynamic programming method uses a linear approximation of the value function and computes the parameters of this approximation by using the linear programming representation of the dynamic program. Our second method relaxes the constraints that link the decisions for different production plants. Consequently, the dynamic program decomposes by the production plants. Computational experiments show that the proposed methods are computationally attractive, and in particular, the second method performs significantly better than standard benchmarks. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

两个单周期的备件存储模型

在工作寿命和修理时间之一服从一般的连续型分布,另一个服从指数分布的情形下讨论了单周期的备件存储问题,通过适当地划分系统的状态,利用Markov更新过程的理论进行了分析,建立了概率型模型,并由模型得到了最佳备件数的求法。     

戴维南等效电路的广义求解

根据重构类网络定理在相量模型电路中应用的时域充要条件,本文提出了一种戴维南等效电路的广义求解方法。     

Disruption management in production planning

We study the problem of recovering a production plan after a disruption, where the disruption may be caused by incidents such as power failure, market change, machine breakdown, supply shortage, worker no‐show, and others. The new recovery plan we seek after has to not only suit the changed environment brought about by the disruption, but also be close to the initial plan so as not to cause too much customer unsatisfaction or inconvenience for current‐stage and downstream operations. For the general‐cost case, we propose a dynamic programming method for the problem. For the convex‐cost case, a general problem which involves both cost and demand disruptions can be solved by considering the cost disruption first and then the demand disruption. We find that a pure demand disruption is easy to handle; and for a pure cost disruption, we propose a greedy method which is provably efficient. Our computational studies also reveal insights that will be helpful to managing disruptions in production planning. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

In this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797–809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log‐concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log‐concavity properties of compound distributions. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 345–356, 2015     

The (s,Q) inventory model with Erlang lead time and deterministic demand

We develop a simple, approximately optimal solution to a model with Erlang lead time and deterministic demand. The method is robust to misspecification of the lead time and has good accuracy. We compare our approximate solution to the optimal for the case where we have prior information on the lead‐time distribution, and another where we have no information, except for computer‐generated sample data. It turns out that our solution is as easy as the EOQ's, with an accuracy rate of 99.41% when prior information on the lead‐time distribution is available and 97.54–99.09% when only computer‐generated sample information is available. Apart from supplying the inventory practitioner with an easy heuristic, we gain insights into the efficacy of stochastic lead time models and how these could be used to find the cost and a near‐optimal policy for the general model, where both demand rate and lead time are stochastic. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004