Asymptotic analysis of periodic policies for the inventory routing problem

In this article, a distribution system is studied where the sum of transportation and inventory costs is to be minimized. The inventory holding cost is assumed to be the same for all retailers. A fixed partition (FP) periodic policy is proposed with tight asymptotic worst‐case performance of 3/2 with respect to the best possible policy. This bound cannot be improved in the class of FP periodic policies. In partition‐based PB policies, the retailers are first partitioned into sets and then the sets are grouped in such a way that sets of retailers within a group are served together at selected times. A PB periodic, policy is presented with tight worst‐case asymptotic performance of with respect to the best possible policy. This latter performance improves the worst‐case asymptotic performance of of the previously best known policy for this problem. We also show that the proposed PB periodic policy has the best worst‐case asymptotic performance within the class of PB policies. Finally, practical heuristics inspired by the analyzed policies are designed and tested. The asymptotic worst–case performances of the heuristics are shown to be the same of those of the analyzed policies. Computational results show that the heuristics suggested are less than 6.4% on average from a lower bound on the optimal cost when 50 or more retailers are involved. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013     

Joint inventory and pricing decisions for perishable products with two‐period lifetime

We consider a periodic review model over a finite horizon for a perishable product with fixed lifetime equal to two review periods. The excess demand in a period is backlogged. The optimal replenishment and demand management (using price) decisions for such a product depend on the relative order of consumption of fresh and old units. We obtain insights on the structure of these decisions when the order of consumption is first‐in, first‐out and last‐in, first‐out. For the FIFO system, we also obtain bounds on both the optimal replenishment quantity as well as expected demand. We compare the FIFO system to two widely analyzed inventory systems that correspond to nonperishable and one‐period lifetime products to understand if demand management would modify our understanding of the relationship among the three systems. In a counterintuitive result, we find that it is more likely that bigger orders are placed in the FIFO system than for a nonperishable product when demand is managed. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Production/distribution system design with inventory considerations

This study addresses the design of a three‐stage production/distribution system where the first stage includes the set of established retailers and the second and third stages include the sets of potential distribution centers (DCs) and potential capacitated suppliers, respectively. In this problem, in addition to the fixed location/operating costs associated with locating DCs and suppliers, we consider the coordinated inventory replenishment decisions at the located DCs and retailers along with the appropriate inventory costs explicitly. In particular, we account for the replenishment and holding costs at the retailers and selected DCs, and the fixed plus distance‐based transportation costs between the selected plants and their assigned DCs, and between the selected DCs and their respective retailers, explicitly. The resulting formulation is a challenging mixed‐integer nonlinear programming model for which we propose efficient heuristic solution approaches. Our computational results demonstrate the performance of the heuristic approaches as well as the value of integrated decision‐making by verifying that significant cost savings are realizable when the inventory decisions and costs are incorporated in the production distribution system design. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 172–195, 2012     

一种装甲装备摩托小时梯次储备的生成与控制方法

针对成建制列装新装备部队如何使教练车形成规定的摩托小时梯次储备并尽早产生送中修装备问题,运用改进的模拟退火算法辅助制定年度装备使用送修计划,构造了以重点用车、一般用车、控制用车平均摩托小时储备为自变量的目标函数,用以量化表示教练车形成摩托小时梯次储备的程度,通过对任务分配的不断调整,找出使目标函数值最大的解,得到最优的使用送修计划安排,并利用Matlab软件在算法上实现了这一过程。     

Selecting T for a periodic review inventory model with staggered deliveries

Consider a single‐item, periodic review, infinite‐horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T periods, one audits the current stock level and decides on deliveries for the next T periods, thus incurring a fixed audit cost and—when one schedules deliveries—a fixed order cost. The problem is to find a review period T and an ordering policy that satisfy the average cost criterion. The current article extends an earlier treatment of this problem, which assumed that the fixed order cost is automatically incurred once every T periods. We characterize an optimal ordering policy when T is fixed, prove that an optimal review period T** exists, and develop a global search algorithm for its computation. We also study the behavior of four approximations to T** based on the assumption that the fixed order cost is incurred during every cycle. Analytic results from a companion article (where μ/σ is large) and extensive computational experiments with normal and gamma demand test problems suggest these approximations and associated heuristic policies perform well when μ/σ ≥ 2. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 329–352, 2000     

A computationally efficient approach for determining inventory levels in a capacitated multiechelon production‐distribution system

The system under study is a single item, two‐echelon production‐inventory system consisting of a capacitated production facility, a central warehouse, and M regional distribution centers that satisfy stochastic demand. Our objective is to determine a system base‐stock level which minimizes the long run average system cost per period. Central to the approach are (1) an inventory allocation model and associated convex cost function designed to allocate a given amount of system inventory across locations, and (2) a characterization of the amount of available system inventory using the inventory shortfall random variable. An exact model must consider the possibility that inventories may be imbalanced in a given period. By assuming inventory imbalances cannot occur, we develop an approximation model from which we obtain a lower bound on the per period expected cost. Through an extensive simulation study, we analyze the quality of our approximation, which on average performed within 0.50% of the lower bound. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 377–398, 2000     

Volume discount decisions: Wealth maximization or EOQ approach?

A recent paper finds that when volume discounts are available, in some cases, reliance on the Economic Order Quantity (EOQ) model can induce purchasers to make wealth reducing decisions, and the Present Value (PV) approach should be preferred. While this finding is theoretically correct, the magnitudes of wealth reductions suggested by the paper's numerical examples seem to be questionable. Furthermore, the paper also finds that, in some other cases, a purchaser using the EOQ approach realizes a net increase in current wealth compared to a purchaser using the PV approach. Logic suggests that such a finding cannot be correct, since by its very definition, it is the PV approach that seeks to maximize the current wealth. We offer an alternative frame of comparison and a modified model to show that, under the paper's assumptions, the EOQ approach can never realize a net increase in current wealth compared to the current wealth generated by the PV approach. On the other hand, we also show that when typical values of the relevant parameters prevail, the additional costs imposed by the EOQ approach are not significant. Finally, we suggest that insofar as the PV approach requires greater administrative costs to implement, it may even be counterproductive to the goal of wealth maximization. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 377–389, 1998     

Scheduling multiple products on parallel machines with setup costs

We consider a class of production scheduling models with m identical machines in parallel and k different product types. It takes a time p_i to produce one unit of product type i on any one of the machines. There is a demand stream for product type i consisting of n_i units with each unit having a given due date. Before a machine starts with the production of a batch of products of type i a setup cost c is incurred. We consider several different objective functions. Each one of the objective functions has three components, namely a total setup cost, a total earliness cost, and a total tardiness cost. In our class of problems we find a relatively large number of problems that can be solved either in polynomial time or in pseudo‐polynomial time. The polynomiality or pseudo‐polynomiality is achieved under certain special conditions that may be of practical interest; for example, a regularity pattern in the string of due dates combined with earliness and tardiness costs that are similar for different types of products. The class of models we consider includes as special cases discrete counterparts of a number of inventory models that have been considered in the literature before, e.g., Wagner and Whitin (Manage Sci 5 (1958), 89–96) and Zangwill (Oper Res 14 (1966), 486–507; Manage Sci 15 (1969), 506–527). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Optimal capacity in a coordinated supply chain

We consider a supply chain in which a retailer faces a stochastic demand, incurs backorder and inventory holding costs and uses a periodic review system to place orders from a manufacturer. The manufacturer must fill the entire order. The manufacturer incurs costs of overtime and undertime if the order deviates from the planned production capacity. We determine the optimal capacity for the manufacturer in case there is no coordination with the retailer as well as in case there is full coordination with the retailer. When there is no coordination the optimal capacity for the manufacturer is found by solving a newsvendor problem. When there is coordination, we present a dynamic programming formulation and establish that the optimal ordering policy for the retailer is characterized by two parameters. The optimal coordinated capacity for the manufacturer can then be obtained by solving a nonlinear programming problem. We present an efficient exact algorithm and a heuristic algorithm for computing the manufacturer's capacity. We discuss the impact of coordination on the supply chain cost as well as on the manufacturer's capacity. We also identify the situations in which coordination is most beneficial. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

The value of information sharing in a two‐stage supply chain with production capacity constraints

We consider a simple two‐stage supply chain with a single retailer facing i.i.d. demand and a single manufacturer with finite production capacity. We analyze the value of information sharing between the retailer and the manufacturer over a finite time horizon. In our model, the manufacturer receives demand information from the retailer even during time periods in which the retailer does not order. To analyze the impact of information sharing, we consider the following three strategies: (1) the retailer does not share demand information with the manufacturer; (2) the retailer does share demand information with the manufacturer and the manufacturer uses the optimal policy to schedule production; (3) the retailer shares demand information with the manufacturer and the manufacturer uses a greedy policy to schedule production. These strategies allow us to study the impact of information sharing on the manufacturer as a function of the production capacity, and the frequency and timing in which demand information is shared. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003