Inventory Management for Customers with Alternative Lead Times

It is common for suppliers operating in batch‐production mode to deal with patient and impatient customers. This paper considers inventory models in which a supplier provides alternative lead times to its customers: a short or a long lead time. Orders from patient customers can be taken by the supplier and included in the next production cycle, while orders from impatient customers have to be satisfied from the on‐hand inventory. We denote the action to commit one unit of on‐hand inventory to patient or impatient customers as the inventory‐commitment decision, and the initial inventory stocking as the inventory‐replenishment decision. We first characterize the optimal inventory‐commitment policy as a threshold type, and then prove that the optimal inventory‐replenishment policy is a base‐stock type. Then, we extend our analysis to models to consider cases of a multi‐cycle setting, a supply‐capacity constraint, and the on‐line charged inventory‐holding cost. We also evaluate and compare the performances of the optimal inventory‐commitment policy and the inventory‐rationing policy. Finally, to further investigate the benefits and pitfalls of introducing an alternative lead‐time choice, we use the customer‐choice model to study the demand gains and losses, known as demand‐induction and demand‐cannibalization effects, respectively.     

On Optimal Expediting Policy for Supply Systems with Uncertain Lead‐Times

We examine the role of expediting in dealing with lead‐time uncertainties associated with global supply chains of “functional products” (high volume, low demand uncertainty goods). In our developed stylized model, a retailer sources from a supplier with uncertain lead‐time to meet his stable and known demand, and the supply lead‐time is composed of two random duration stages. At the completion time of the first stage, the retailer has the option to expedite a portion of the replenishment order via an alternative faster supply mode. We characterize the optimal expediting policy in terms of if and how much of the order to expedite and explore comparative statics on the optimal policy to better understand the effects of changes in the cost parameters and lead‐time properties. We also study how the expediting option affects the retailer's decisions on the replenishment order (time and size of order placement). We observe that with the expediting option the retailer places larger orders closer to the start of the selling season, thus having this option serve as a substitute for the safety lead‐time and allowing him to take increased advantages of economies of scale. Finally we extend the basic model by looking at correlated lead‐time stages and more than two random lead‐time stages.     

Lead Time and Price Quotation Mode Selection: Uniform or Differentiated?

Firms in service and make‐to‐order manufacturing industries often quote lead times and prices to customers. We define uniform quotation mode (UQM) as the strategy where a firm offers a single lead time and price quotation, and differentiated quotation mode (DQM) is where a firm offers a menu of lead times and prices for customers to choose from. Both modes are followed in practice. Firms should determine which is more profitable. We classify customers into two groups: lead time sensitive (LS) and price sensitive (PS). LS customers value lead time reduction more than PS customers. We develop mathematical models of both quotation modes and analyze them to determine the most profitable mode under specified situations as well as the best lead time and price quotations within each mode. We find that DQM is dominated by UQM whenever PS customers have positive utilities from UQM or LS customers have positive utilities from DQM. Otherwise, which quotation mode is better depends on multiple factors, such as customer characteristics (including lead time reduction valuation and product valuation of a customer, and the proportion of LS customers) and production characteristics (including the desired service level and service or production cost).     

Optimal Sourcing and Lead‐Time Reduction under Evolutionary Demand Risk

We develop a real‐options model for optimizing production and sourcing choices under evolutionary supply‐chain risk. We model lead time as an endogenous decision and calculate the cost differential required to compensate for the risk exposure coming from lead time. The shape of the resulting cost‐differential frontier reveals the term structure of supply‐chain risk premiums and provides guidance as to the potential value of lead‐time reduction. Under constant demand volatility, the break‐even cost differential increases in volatility and lead time at a decreasing rate, making incremental lead‐time reduction less valuable than full lead‐time reduction. Stochastic demand volatility increases the relative value of incremental lead‐time reduction. When demand has a heavy right tail, the value of lead‐time reduction depends on how extreme values of demand are incorporated into the forecasting process. The cost‐differential frontier is invariant to discount rates, making the cost of capital irrelevant for choosing between lead times. We demonstrate the managerial implications of the model by applying it first to the classic Sport‐Obermeyer case and then to a supplier‐selection problem faced by a global manufacturer.     

Contingency Strategies in Managing Supply Systems with Uncertain Lead‐Times

The globalization of markets and geographic dispersion of production facilities, combined with a heavy outsourcing of supply chain processes, have substantially increased the exposure of supply chains to supply lead‐times of long and uncertain nature. In this paper, we study the potential use of two contingency strategies on top of the conventionally used time buffer—statically planned safety lead‐time (SL)—approach to deal with the lead‐time uncertainty. These are (1) the ex‐ante planning for disruption safety stock (DSS) to be released when a “disruption” (in this case, late delivery of the order) occurs; and (2) the ex‐post dynamic emergency response (DER), which dynamically decides on the timing and size of an emergency order to be placed. Our work elaborates on the optimal parameter setting for these strategies, compares their added values when used to complement the traditional SL approach, and examines how the use of the contingency strategies affects the SL and corresponding cycle length of a periodic review system. Our research finds that: (1) the above contingency strategies reduce the reliance on the SL and are cost effective when the coefficient of variation (CV) of the uncertain lead‐time is high; (2) it is important to re‐optimize the SL to account for the contingency plans; and (3) re‐optimization of the cycle length to account for the presence of the contingency responses, as opposed to using an EOQ‐determined cycle length, does not significantly improve the cost performance. However, such re‐optimization does well in the SL approach when the CV of the uncertain lead‐time is high.     

Equilibrium Joining Strategies and Optimal Control of a Make‐to‐Stock Queue

We consider a make‐to‐stock, finite‐capacity production system with setup cost and delay‐sensitive customers. To balance the setup and inventory related costs, the production manager adopts a two‐critical‐number control policy, where the production starts when the number of waiting customers reaches a certain level and shuts down when a certain quantity of inventory has accumulated. Once the production is set up, the unit production time follows an exponential distribution. Potential customers arrive according to a Poisson process. Customers are strategic, i.e., they make decisions on whether to stay for the product or to leave without purchase based on their utility values, which depend on the production manager's control decisions. We formulate the problem as a Stackelberg game between the production manager and the customers, where the former is the game leader. We first derive the equilibrium customer purchasing strategy and system performance. We then formulate the expected cost rate function for the production system and present a search algorithm for obtaining the optimal values of the two control variables. We further analyze the characteristics of the optimal solution numerically and compare them with the situation where the customers are non‐strategic.     

Ordering,Pricing, and Lead‐Time Quotation Under Lead‐Time and Demand Uncertainty

In this article, we study the newsvendor problem with endogenous setting of price and quoted lead‐time. This problem can be observed in situations where a firm orders semi‐finished product prior to the selling season and customizes the product in response to customer orders during the selling season. The total demand during the selling season and the lead‐time required for customization are uncertain. The demand for the product depends not only on the selling price but also on the quoted lead‐time. To set the quoted lead‐time, the firm has to carefully balance the benefit of increasing demand as the quoted lead‐time is reduced against the cost of increased tardiness. Our model enables the firm to determine the optimal selling price, quoted lead‐time, and order quantity simultaneously, and provides a new set of insights to managers.     

An Application of Master Schedule Smoothing and Planned Lead Time Control

Make‐to‐order (MTO) manufacturers must ensure concurrent availability of all parts required for production, as any unavailability may cause a delay in completion time. A major challenge for MTO manufacturers operating under high demand variability is to produce customized parts in time to meet internal production schedules. We present a case study of a producer of MTO offshore oil rigs that highlights the key aspects of the problem. The producer was faced with an increase in both demand and demand variability. Consequently, it had to rely heavily on subcontracting to handle production requirements that were in excess of its capacity. We focused on the manufacture of customized steel panels, which represent the main sub‐assemblies for building an oil rig. We considered two key tactical parameters: the planning window of the master production schedule and the planned lead time of each workstation. Under the constraint of a fixed internal delivery lead time, we determined the optimal planning parameters. This improvement effort reduced the subcontracting cost by implementing several actions: the creation of a master schedule for each sub‐assembly family of the steel panels, the smoothing of the master schedule over its planning window, and the controlling of production at each workstation by its planned lead time. We report our experience in applying the analytical model, the managerial insights gained, and how the application benefits the oil‐rig producer.     

The Impact of Complexity on Knowledge Transfer in Manufacturing Networks

Coordinating knowledge transfer within multi‐plant manufacturing networks is a challenging task. Using a computational model, we examine when it is beneficial to create production knowledge within a central unit, the “lead factory,” and transfer it to geographically dispersed plants. We demonstrate that the knowledge transfer generates a trade‐off between a positive cost‐saving effect due to fewer adaptations in each plant, and a negative transfer cost effect due to the costly knowledge transfer itself. The complexity of the production process moderates the performance implications of the knowledge transfer because it determines the relative strength of these two effects. For production processes with low complexity, knowledge transfer can engender superior network performance. Here, an optimal extent of knowledge transfer exists, and thus, a complete knowledge transfer is not performance maximizing. For production processes with medium and high levels of complexity, performance is reduced rather than enhanced through knowledge transfer so that it is optimal not to transfer any knowledge from the lead factory to the plants. While we analyze knowledge transfer within a manufacturing network, our results are transferable to other settings that consist of a knowledge sending and receiving unit.     

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.     

Approximations to Optimal k‐Unit Cycles for Single‐Gripper and Dual‐Gripper Robotic Cells

We consider the problem of scheduling operations in bufferless robotic cells that produce identical parts using either single‐gripper or dual‐gripper robots. The objective is to find a cyclic sequence of robot moves that minimizes the long‐run average time to produce a part or, equivalently, maximizes the throughput. Obtaining an efficient algorithm for an optimum k‐unit cyclic solution (k ≥ 1) has been a longstanding open problem. For both single‐gripper and dual‐gripper cells, the approximation algorithms in this paper provide the best‐known performance guarantees (obtainable in polynomial time) for an optimal cyclic solution. We provide two algorithms that have a running time linear in the number of machines: for single‐gripper cells (respectively, dual‐gripper cells), the performance guarantee is 9/7 (respectively, 3/2). The domain considered is free‐pickup cells with constant intermachine travel time. Our structural analysis is an important step toward resolving the complexity status of finding an optimal cyclic solution in either a single‐gripper or a dual‐gripper cell. We also identify optimal cyclic solutions for a variety of special cases. Our analysis provides production managers valuable insights into the schedules that maximize productivity for both single‐gripper and dual‐gripper cells for any combination of processing requirements and physical parameters.     

Flexible Backup Supply and the Management of Lead‐Time Uncertainty

We consider replenishment decisions for a constant rate demand environment from a supplier with uncertain lead times. We study the potential use of a flexible backup supplier as an emergency response to accurate lead‐time information arriving at (or close after) the beginning of the demand interval and well after an original order with the stochastic lead‐time supplier has been placed. The emergency response decisions involve whether to order and how much from the flexible backup supplier, with the objective of minimizing the cost of meeting demand. We derive the optimal emergency‐response policy and clearly outline its implications on the optimized safety lead time of the original order placement and on the cost of meeting demand. We examine the impact on the use of the flexible backup supplier of factors like the arrival time of accurate lead‐time information and the response lead time of the backup supplier. We further study the potential benefits of the use of the flexible backup supplier in a dual role: as one of the two suppliers in a redundant supply system assigned to originally meet the demand and as an emergency response to later‐arriving lead‐time information. Our numerical studies illustrate the benefits from the use of the flexible backup supplier as an emergency response, but for reasonable purchase premiums and short lead times of flexible backup supply options, their use in a dual (regular and emergency response) role often leads to improved performance over safety lead‐time single and uncertain lead‐time supplier‐replenishment strategies. The benefits of the backup supply options are accentuated the higher the lead‐time uncertainty of the stochastic lead‐time supplier is.     

The Impact of Outsourced Manufacturing on Timing of Entry in Uncertain Markets

Several firms are interested in manufacturing and selling new products based on a new process technology. Before manufacturing can begin, either these Original Equipment Manufacturers (OEMs), or a Contract Manufacturer (CM) needs to adopt the process technology, i. e., make a capacity investment in it. Due to market uncertainty, the timing of capacity investment is crucial. In such a setting, we investigate how the timing of process adoption, an important determinant of time‐to‐market, is impacted by the make/buy decision. We first characterize the optimal time for process adoption and show that this delay depends on competitive intensity, cost structure and the rate of forecast improvement. Due to differing cost structures, incentives and risks, an OEM and a CM may invest in a new process technology at different times. We show that while there are conditions where outsourced manufacturing can be advantageous for the OEM from a time‐to‐market perspective, there are also cases where the OEM would be disadvantaged. In these cases, the OEM can accelerate process adoption by risk sharing through joint investment. Finally, the right choice of CM is extremely important for an OEM that faces a short time window for product introduction: An efficient CM not only provides low costs but also rapid access to new process technologies, and therefore higher revenues.     

End‐of‐Life Inventory Problem with Phaseout Returns

We consider the service parts end‐of‐life inventory problem of a capital goods manufacturer in the final phase of its life cycle. The final phase starts as soon as the production of parts terminates and continues until the last service contract expires. Final order quantities are considered a popular tactic to sustain service fulfillment obligations and to mitigate the effect of obsolescence. In addition to the final order quantity, other sources to obtain serviceable parts are repairing returned defective items and retrieving parts from phaseout returns. Phaseout returns happen when a customer replaces an old system platform with a next‐generation one and returns the old product to the original equipment manufacturer (OEM). These returns can well serve the demand for service parts of other customers still using the old generation of the product. In this study, we study the decision‐making complications as well as cost‐saving opportunities stemming from phaseout occurrence. We use a finite‐horizon Markov decision process to characterize the structure of the optimal inventory control policy. We show that the optimal policy consists of a time‐varying threshold level for item repair. Furthermore, we study the value of phaseout information by extending the results to cases with an uncertain phaseout quantity or an uncertain schedule. Numerical analysis sheds light on the advantages of the optimal policy compared to some heuristic policies.     

A Capacitated Multi‐echelon Inventory Placement Model under Lead Time Constraints

We develop an inventory placement model in the context of general multi‐echelon supply chains where the delivery lead time promised to the customer must be respected. The delivery lead time is calculated based on the available stocks of the different input and output products in the different facilities and takes into account the purchasing lead times, the manufacturing lead times, and the transportation lead times. We assume finite manufacturing capacities and consider the interactions of manufacturing orders between time periods. Each facility manages the stocks of its input and output products. The size of customer orders and their arrival dates and due dates are assumed to be known as in many B2B situations. We perform extensive computational experiments to derive managerial insights. We also derive analytical insights regarding the manufacturing capacities to be installed and the impacts of the frequency of orders on the system cost.     

Two Backorder Compensation Mechanisms in Inventory Systems with Impatient Customers

We study a compensation mechanism design problem with customer‐choice behavior in a continuous review setting where the production and demand processes are stochastic. When a stockout occurs, the firm controls backorders on the basis of certain compensation policies. Customers make decisions to maximize their utility, which is decreasing in the price, the waiting time, and the customer's impatience factor. We assume that the impatience factor is private information held by the customer only. Two compensation mechanisms are designed to control backorders, namely uniform compensation and priority auction with an admission price. Under uniform compensation, the firm offers the same discount to all customers, whereas under auction compensation, priority is granted according to the customers' bid prices. We obtain the optimal stockout price and base stock level under each mechanism, and analyze the properties of the respective optimal policies. Assuming linear waiting costs with uniformly distributed impatience factor, we find that the auction mechanism (1) maintains a lower base stock level and results in greater profit and (2) benefits customers with relatively lower or higher impatience factors, but customers with a medium impatience factor may be rendered worse off. We further show that both compensation mechanisms are suitable for products with a high unit profit, a high lost sales penalty cost, and a high holding cost.     

TIME‐BASED PRICING AND LEADTIME POLICIES FOR A BUILD‐TO‐ORDER MANUFACTURER

We studied time‐based policies on pricing and leadtime for a build‐to‐order and direct sales manufacturer. It is assumed that the utility of the product varies among potential customers and decreases over time, and that a potential customer will place an order if his or her utility is higher than the manufacturer's posted price. Once an order is placed, it will be delivered to the customer after a length of time called “leadtime.” Because of the decrease in a customer's utility during leadtime, a customer will cancel the order if the utility falls below the ordering price before the order is received. The manufacturer may choose to offer discounted prices to customers who would otherwise cancel their orders. We discuss two price policies: common discounted price and customized discounted price. In the common discounted price policy, the manufacturer offers a single lower price to the customers; in the customized discounted price policy, the manufacturer offers the customers separately for individual new prices. Our analytical and numerical studies show that the discounted price policies results in higher revenue and that the customized discounted price policy significantly outperforms the common discounted price policy when product utility decreases rapidly. We also study two leadtime policies when production cost decreases over time. The first uses a fixed leadtime, and the second allows the leadtime to vary dynamically over time. We find that the dynamic leadtime policy significantly outperforms the fixed leadtime policy when the product cost decreases rapidly.     

基于可控提前期的随机寄售库存模型

本文通过假定需求提前期为随机且可控的,将寄售库存（Consignment Stock,CS）模型拓展到随机情形。本文首先将库存成本分为与财务相关的成本和与储存相关的成本两部分,得出CS方式下买卖双方的联合期望总成本公式,然后将订货量、订货点、提前期、运送次数作为决策变量,求得系统的最优参数设置及最小总成本。文章最后提出一个算法,并通过仿真的形式表明无论在确定还是随机环境中,CS方式的总成本都可能优于集成化库存方式。     

DELIVERY GUARANTEES AND THE INTERDEPENDENCE OF MARKETING AND OPERATIONS

Delivery guarantees are an important element in a customer satisfaction program. When setting delivery guarantees, a firm must consider customer expectations as well as operational constraints. We develop a profit‐maximization model in which a firm's sales organization, with incomplete information on operations' status, solicits orders and quotes delivery dates. If obtained, orders are processed in a make‐to‐order facility, after which revenue is received, minus tardiness penalty if the delivery was later than quoted. We specify conditions for an optimal log‐linear decision rule and provide exact expressions for its effect on arrival rate, mean processing time, and mean cycle time.     

Using Frontier Portfolios to Improve Make‐to‐Order Operations

Make‐to‐order (MTO) manufacturers face a common problem of maintaining a desired service level for delivery at a reasonable cost while dealing with irregular customer orders. This research considers a MTO manufacturer who produces a product consisting of several custom parts to be ordered from multiple suppliers. We develop procedures to allocate orders to each supplier for each custom part and calculate the associated replenishment cost as well as the probability of meeting the delivery date, based on the suppliers' jobs on hand, availability, process speed, and defective rate. For a given delivery due date, a frontier of service level and a replenishment cost frontier are created to provide a range of options to meet customer requirements. This method can be further extended to the case when the delivery due date is not fixed and the manufacturer must “crash” its delivery time to compete for customers.