An integrated inventory–transportation system with modified periodic policy for multiple products

Efficient management of a distribution system requires an integrated approach towards various logistical functions. In particular, the fundamental areas of inventory control and transportation planning need to be closely coordinated. Our model deals with an inbound material-collection problem. An integrated inventory–transportation system is developed with a modified periodic-review inventory policy and a travelling-salesman component. This is a multi-item joint replenishment problem, in a stochastic setting, with simultaneous decisions made on inventory and transportation policies. We propose a heuristic decomposition method to solve the problem, minimizing the long-run total average costs (major- and minor-ordering, holding, backlogging, stopover and travel). The decomposition algorithm works by using separate calculations for inventory and routing decisions, and then coordinating them appropriately. A lower bound is constructed and computational experience is reported.     

Sensitivity analysis of the newsvendor model

Quality of decisions in inventory management models depends on the accuracy of parameter estimates used for decision making. In many situations, error in decision making is unavoidable. In such cases, sensitivity analysis is necessary for better implementation of the model. Though the newsvendor model is one of the most researched inventory models, little is known about its robustness. In this paper, we perform sensitivity analysis of the classical newsvendor model. Conditions for symmetry/skewness of cost deviation (i.e., deviation of expected demand–supply mismatch cost from its minimum) have been identified. These conditions are closely linked with symmetry/skewness of the demand density function. A lower bound of cost deviation is established for symmetric unimodal demand distributions. Based on demonstrations of the lower bound, we found the newsvendor model to be sensitive to sub-optimal ordering decisions, more sensitive than the economic order quantity model. Order quantity deviation (i.e., deviation of order quantity from its optimum) is explored briefly. We found the magnitude of order quantity deviation to be comparable with that of parameter estimation error. Mean demand is identified as the most influential parameter in deciding order quantity deviation.     

Fuzzy profit measures for a fuzzy economic order quantity model

Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the fuzzy profit of the inventory model when the demand quantity and unit cost are fuzzy numbers. Since the parameters contained in the inventory model are fuzzy, the profit value calculated from the model should be fuzzy as well. Based on the extension principle, the fuzzy inventory problem is transformed into a pair of two-level mathematical programs to derive the upper bound and lower bound of the fuzzy profit at possibility level α. According to the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs to solve. By enumerating different α values, the upper bound and lower bound of the fuzzy profit are collected to approximate the membership function. Since the profit of the inventory problem is expressed by the membership function rather than by a crisp value, more information is provided for making decisions.     

Separation results for multi-product inventory hedging problems

We analyze financial hedging tools for inventory management in a risk-averse corporation. We consider the problem of optimizing simultaneously over both the operational policy and the hedging policy of the corporation in a multi-product model. Our main contribution is a separation result such that for a corporation with multiple products and inventory departments, the inventory decisions of each department can be made independently of the other departments’ decisions. That is, no interaction needs to be considered among different products.     

Joint spare parts inventory and reliability decisions under a service constraint

Reliability and inventory levels of spare parts are major factors that determine the service level for the maintenance of machines provided by original equipment manufacturers (OEMs). In general, decisions on reliability and stock levels are made separately in practice, and academic literature offers little guidance on how to jointly make these two decisions. In order to fill in the gap in the literature and provide guidance to OEMs, we jointly model reliability and inventory problems. We consider three different service measures: aggregate fill rate, average downtime per system per year and expected total number of long downs in a year. Our models minimize the sum of holding and emergency shipment costs subject to a limited reliability improvement budget and a target service level. We develop an algorithm that considers reliability and inventory decisions simultaneously, test our solution approach on real-life and randomly generated data sets and compare the results with an approach that considers reliability and inventory decisions sequentially. Numerical results show substantial benefits of integrating reliability and inventory decisions.     

An integrated model for warehouse and inventory planning

The purpose of this article is to evaluate the value of integrating tactical warehouse and inventory decisions. Therefore, a global warehouse and inventory model is presented and solved. In order to solve this mathematical model, two solution methodologies are developed which offer different level of integration of warehouse and inventory decisions. Computational tests are performed on a real world database using multiple scenarios differing by the warehouse capacity limits and the warehouse and inventory costs. Our observation is that the total cost of the inventory and warehouse systems can be reduced drastically by taking into account the warehouse capacity restrictions in the inventory planning decisions, in an aggregate way. Moreover additional inventory and warehouse savings can be achieved by using more sophisticated integration methods for inventory and warehouse decisions.     

Characterization of facility assignment costs for a location-inventory model under truckload distribution

We consider a two-stage distribution system, where the first stage consists of potential distribution centres (DCs) and the second stage consists of geographically dispersed existing retailers. Our goal is to determine the set of open DCs and assignment of open DCs to retailers simultaneously with inventory decisions of retailers. In addition to the DC-specific fixed facility location costs, we explicitly model the inventory replenishment and holding costs at the retailers and truckload transportation costs between the DCs and the retailers. The transportation costs are subject to truck/cargo capacity, leading to an integrated location-inventory problem with explicit cargo costs. We develop a mixed-integer nonlinear model and analyse its structural properties leading to exact expressions for the so-called implied facility assignment costs and imputed per-unit per-mile transportation costs. These expressions analytically demonstrate the interplay between strategic location and tactical inventory/transportation decisions in terms of resulting operational costs. Although both the theory and practice of integrated logistics have recognized the fact that strategic and tactical decisions are interrelated, to the best of our knowledge, our paper is the first to offer closed-form results demonstrating the relationship explicitly. We propose an efficient solution approach utilizing the implied facility assignment costs and we demonstrate that significant savings are realizable when the inventory decisions and cargo costs are modelled explicitly for facility location purposes.     

Integrating operations and marketing decisions using delayed differentiation of products and guaranteed delivery time under stochastic demand

In this research, we integrate the issues related to operations and marketing strategy of firms characterized by large product variety, short lead times, and demand variability in an assemble-to-order environment. The operations decisions are the inventory level of components and semi-finished goods, and configuration of semi-finished goods. The marketing decisions are the products price and a lead time guarantee which is uniform for all products. We develop an integrated mathematical model that captures trade-offs related to inventory of semi-finished goods, inventory of components, outsourcing costs, and customer demand based on guaranteed lead time and price.The mathematical model is a two-stage, stochastic, integer, and non-linear programming problem. In the first stage, prior to demand realization, the operation and marketing decisions are determined. In the second stage, inventory is allocated to meet the demand. The objective is to maximize the expected profit per-unit time. The computational results on the test problems provide managerial insights for firms faced with the conflicting needs of offering: (i) low prices, (ii) guaranteed and short lead time, and (iii) a large product variety by leveraging operations decisions.     

替代产品的动态库存决策与控制

考虑了替代产品的动态库存决策与控制问题,建立了替代产品的多周期动态库存决策与控制模型.得到了目标函数的一些重要性质,给出了系统最优参数的求解算法,利用动态规划方法对系统的库存参数进行了优化求解.     

Project-driven supply chains: integrating safety-stock and crashing decisions for recurrent projects

We study a new class of problems—recurrent projects with random material delays, at the interface between project and supply chain management. Recurrent projects are those similar in schedule and material requirements. We present the model of project-driven supply chain (PDSC) to jointly optimize the safety-stock decisions in material supply chains and the crashing decisions in projects. We prove certain convexity properties which allow us to characterize the optimal crashing policy. We study the interaction between supply chain inventory decisions and project crashing decisions, and demonstrate the impact of the PDSC model using examples based on real-world practice.     

Optimizing Supply Shortage Decisions in Base Stock Distribution Operations

This paper addresses policies and agreements between suppliers and customers for handling supply shortages in base-stock systems under uncertain demand. We investigate the impacts that backlogging and expediting decisions have on inventory and transportation costs in these systems and develop a model for deciding whether a supplier should completely backlog, completely expedite, or employ some combination of backlogging and expediting shortages. Our results indicate that practical cases exist where some combination of both expediting and backlogging supply shortages outperforms either completely expediting or backlogging all shortages. Including transportation costs in our model provides incentive to employ `hybrid' policies that partially expedite and partially backlog excess demands within a given period. Our model demonstrates how inventory policy decisions directly impact transportation costs and provides a heuristic approach for jointly minimizing expected inventory and transportation costs.     

A column generation-based heuristic algorithm for an inventory routing problem with perishable goods

An inventory routing problem is a variation of the vehicle routing problem in which inventory and routing decisions are determined simultaneously over a given time horizon. The objective is to minimize the sum of transportation and inventory costs. In this paper, we study a specific inventory routing problem in which goods are perishable (PIRP). We develop a mathematical model for PIRP and exploit its structure to develop a column generation-based solution approach. Cutting planes are added to improve the formulation. We present computational experiments to demonstrate that our methodology is effective, and that the integration of routing and inventory can yield significant cost savings.     

Inventory model of deteriorating items on non-periodic discrete-time domains

In this paper, we demonstrate how to model a discrete-time dynamic process on a non-periodic time domain with applications to operations research. We introduce a discrete-time model of inventory with deterioration on domains where time points may be unevenly spaced over a time interval. We formalize the average cost function composed of storage, depreciation and back-ordering costs. The optimal condition is given to locate the optimal point that minimizes the average cost function. Finally, we present simulations to demonstrate how a manager can use this model to make inventory decisions.     

Coordinating inventory control and pricing strategies: The continuous review model

We analyze an infinite horizon, single product, continuous review model in which pricing and inventory decisions are made simultaneously and ordering cost includes a fixed cost. We show that there exists a stationary (s,S) inventory policy maximizing the expected discounted or expected average profit under general conditions.     

Dynamic pricing for perishable items with costly price adjustments

Dynamic pricing is widely adopted in inventory management for perishable items, and the corresponding price adjustment cost should be taken into account. This work assumes that the price adjustment cost comprises of a fixed component and a variable one, and attempts to search for the optimal dynamic pricing strategy to maximize the firm’s profit. However, considering the fixed price adjustment cost turns this dynamic pricing problem to a non-smooth optimal control problem which cannot be solved directly by Pontryagin’s maximum principle. Hence, we first degenerate the original problem into a standard optimal control problem and calculate the corresponding solution. On the basis of this solution, we further propose a suboptimal pricing strategy which simultaneously combines static pricing and dynamic pricing strategies. The upper bound of profit gap between the suboptimal solution and the optimal one is obtained. Numerical simulation indicates that the suboptimal pricing strategy enjoys an efficient performance.     

A statistical Markov chain approximation of transient hospital inpatient inventory

Inventory levels are critical to the operations, management, and capacity decisions of inventory systems but can be difficult to model in heterogeneous, non-stationary throughput systems. The inpatient hospital is a complicated throughput system and, like most inventory systems, hospitals dynamically make managerial decisions based on short term subjective demand predictions. Specifically, short term hospital staffing, resource capacity, and finance decisions are made according to hospital inpatient inventory predictions. Inpatient inventory systems have non-stationary patient arrival and service processes. Previously developed models present poor inventory predictions due to model subjectivity, high model complexity, solely expected value predictions, and assumed stationary arrival and service processes. Also, no models present statistical testing for model significance and quality-of-fit. This paper presents a Markov chain probability model that uses maximum likelihood regression to predict the expectations and discrete distributions of transient inpatient inventories. The approach has a foundation in throughput theory, has low model complexity, and provides statistical significance and quality-of-fit tests unique to this Markov chain. The Markov chain is shown to have superior predictability over Seasonal ARIMA models.     

Impacts of inventory shortage policies on transportation requirements in two-stage distribution systems

This paper investigates the impacts inventory shortage policies have on transportation costs in base-stock distribution systems under uncertain demand. The model proposed demonstrates how backlogging arrangements can serve to decrease the variability of transportation capacity requirements, and hence the magnitude of transportation costs, when compared with policies that expedite demand shortages. The model shows how inventory policy decisions directly impact expected transportation costs and provides a new method for setting stock levels that jointly minimizes inventory and transportation costs. The model and solution method provide insights into the relationship between inventory decisions and transportation costs and can serve to support delivery policy negotiations between a supplier and customer that must choose between expediting and backlogging demand shortages.     

Integrated capacity and inventory management with capacity acquisition lead times

We model a make-to-stock production system that utilizes permanent and contingent capacity to meet non-stationary stochastic demand, where a constant lead time is associated with the acquisition of contingent capacity. We determine the structure of the optimal solution concerning both the operational decisions of integrated inventory and flexible capacity management, and the tactical decision of determining the optimal permanent capacity level. Furthermore, we show that the inventory (either before or after production), the pipeline contingent capacity, the contingent capacity to be ordered, and the permanent capacity are economic substitutes. We also show that the stochastic demand variable and the optimal contingent capacity acquisition decisions are economic complements. Finally, we perform numerical experiments to evaluate the value of utilizing contingent capacity and to study the effects of capacity acquisition lead time, providing useful managerial insights.     

A static-dynamic strategy for spare part inventory systems with nonstationary stochastic demand

Inventory control is especially difficult when demand is stochastic and nonstationary. We consider a spare part inventory control problem with multiple-period replenishment lead time, and describe a static-dynamic strategy for the problem. By solving a static-dynamic uncertainty model, the strategy first makes decisions on the replenishment periods and order-up-to-levels over the planning horizon, but implements only the decisions of the first period. It then uses the rolling horizon approach in the next period when the inventory status is revised, and the multi-period problem is updated as better forecasts become available. In light of structural property of the developed static-dynamic uncertainty model, the optimal solution to the model can be obtained without much computational effort and thus the strategy can be easily implemented. Computational experiments and result of a case study verify the efficacy of the proposed strategy.     

第三方库存-路线问题的模型及混合遗传算法设计

根据第三方库存-路线问题的特点,以车辆租赁费用和运行费用之和为目标函数,不限制客户每次的配送量小于车辆容量,建立了满载运输和非满载运输混合的整数规划模型.针对第三方库存-路线问题的复杂性,本文设计嵌入禁忌搜索的遗传算法来同时决策库存和路线问题.首先对配送间隔进行编码,然后用禁忌搜索法计算每天需要配送的车辆路线问题.最后与其下界值进行比较,结果表明该算法是一个有效的算法,不但第三方能取得较低的运营总成本和较高的车辆利用率,而且也能为客户节约库存空间.