Quoted Lead Time Research Articles

In This Issue

In This Issue

TECHNICAL NOTE—An Optimal Policy for Joint Dynamic Price and Lead-Time Quotation

For a dynamic joint price and lead-time quotation problem with a fairly general demand function, we show that the policy consisting of a threshold and a reward-maximizing lead-time is optimal. This policy offers some interesting managerial insights. Under this policy, finding the exact optimal quotation can be accomplished by single-variable policy iterations of unimodal value functions.

Setting planned lead times for a make-to-order production system with master schedule smoothing

This article considers a make-to-order manufacturing environment with fixed guaranteed delivery lead times and multiple product families, each with a stochastic demand process. The primary challenge in this environment is how to meet the quoted delivery times subject to fluctuating workload and capacity limits. The tactical planning parameters are considered, namely, the planning windows and planned lead times. The planning process that is modeled is the one in which the demand represents a dynamic input into the master production schedule. A planning window for each product family controls how the schedule of each product family is translated into a job release. It can be thought of as the slack that exists when the fixed quoted delivery lead time is longer than the total planned production lead time. Furthermore, the planned lead time of each station regulates the workflow within a multi-station shop. The model has underlying discrete time periods to allow the modeling of the planning process that is typically defined in time buckets; within each time period, the intra-period workflow that permits multiple job movements within the time period is modeled. The presented model characterizes key performance measures for the shop as functions of the planning windows and planned lead times. An optimization model is formulated that is able to determine the values of these planning parameters that minimize the relevant production-related costs. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for additional results of the simulation study in Section 6 of this manuscript.]

Optimal and heuristic lead-time quotation for an integrated steel mill with a minimum batch size

This paper presents a model of lead-time policies for a production system, such as an integrated steel mill, in which the bottleneck process requires a minimum batch size. An accurate understanding of internal lead-time quotations is necessary for making good customer delivery-date promises, which must take into account processing time, queueing time and time for arrival of the requisite volume of orders to complete the minimum batch size requirement. The problem is modeled as a stochastic dynamic program with a large state space. A computational study demonstrates that lead time for an arriving order should generally be a decreasing function of the amount of that product already on order (and waiting for minimum batch size to accumulate), which leads to a very fast and accurate heuristic. The computational study also provides insights into the relationship between lead-time quotation, arrival rate, and the sensitivity of customers to the length of delivery promises.

Contracting with an urgent supplier under cost information asymmetry

We investigate a contract setting problem faced by a manufacturer who can procure major modules from an overseas supplier, as well as a local supplier. The overseas supplier is prime and offers quality products, whereas the local supplier is viewed only as a backup, and its products are inferior in quality. As the local supplier needs to put in additional effort to fulfill the urgent orders, it is difficult for the manufacturer to estimate this urgent supplier’s production cost. This asymmetric cost information becomes an obstacle for the manufacturer in managing the urgent supplier. In this paper, we study two types of contingent contracts. One is the common price-only contract, and the other is a contract menu consisting of a transfer payment and a lead time quotation. We construct a Stackelberg game model and evaluate how the involvement of an urgent supplier with private cost information affects performances of the prime supplier and the manufacturer in different scenarios (with or without the urgent supplier, under different contingent contracts). We also conduct numerical experiments to show how the parameters of the contracts affect profits of the manufacturer.

Quoting Lead Times and Prices to Customers

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).

Dynamic Lead-Time Quotation for an M/M/1 Base-Stock Inventory Queue

We study a dynamic lead-time quotation problem in a base-stock inventory system characterized by lead-time sensitive Poisson demand and exponentially distributed service times. We show that the optimal profit is unimodal in the base-stock level. We compare the base-stock system with a make-to-order (MTO) system and show that the lead-time quotes are lower in an MTO system and that increasing the base-stock level does not necessarily decrease the expected number of customers waiting. Numerical results show that when customers are less sensitive to lead-time quotes, the benefit of quoting lead times with a higher precision is significant, whereas when customers are more sensitive to lead-time quotes, the benefit of holding inventory is significant.

Combined make-to-order/make-to-stock supply chains

A multi-item manufacturer served by a single supplier in a stochastic environment is considered. The manufacturer and the supplier have to decide which items to produce to stock and which to produce to order. The manufacturer also has to quote due dates to arriving customers for make-to-order products. The manufacturer is penalized for long lead times, missing the quoted lead times and high inventory levels. Several variations of this problem are considered and effective heuristics for the make-to-order/make-to stock decision are designed to find the appropriate inventory levels for make-to-stock items. Scheduling and lead time quotation algorithms for centralized and decentralized versions of the model are also developed. Extensive computational testing is performed to assess the effectiveness of the proposed algorithms, and the centralized and decentralized models are compared in order to quantify the value of centralized control in this supply chain. As centralized control is not always practical or cost-effective, the value of limited information exchange for this system is explored. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource(s): Online appendix including additional computational analysis and proofs.]

Near-Optimal Dynamic Lead-Time Quotation and Scheduling Under Convex-Concave Customer Delay Costs

We consider a make-to-order system where customers are dynamically quoted lead times (and prices). Customers are homogenous but have general (nonlinear) disutility for delay. Because the firm is a monopolist, the pricing problem is trivial and the dynamic problem reduces to one of lead-time quotation and order sequencing. We also consider the (static) problem of up-front capacity installation. We use a large-capacity asymptotic regime to make the problem tractable. We provide recommended policies for convex, concave, and convex-concave lead-time cost functions and prove that these policies are asymptotically optimal. The policies are both highly intuitive and readily implementable. Moreover, they provide delay guarantees for all served customers. They are tested numerically; we find that significant benefits can accrue by using the prescribed dynamic policies instead of first-come-first-served type policies.

Competitive Algorithms for Due Date Scheduling

We consider several online scheduling problems that arise when customers request make-to-order products from a company. At the time of the order, the company must quote a due date to the customer. To satisfy the customer, the company must produce the good by the due date. The company must have an online algorithm with two components: The first component sets the due dates, and the second component schedules the resulting jobs with the goal of meeting the due dates. The most basic quality of service measure for a job is the quoted lead time, which is the difference between the due date and the release time. We first consider the basic problem of minimizing the average quoted lead time. We show that there is a (1+e)-speed $O(\frac{\log k}{\epsilon})$ -competitive algorithm for this problem (here k is the ratio of the maximum work of a job to the minimum work of a job), and that this algorithm is essentially optimally competitive. This result extends to the case that each job has a weight and the objective is weighted quoted lead time. We then introduce the following general setting: there is a non-increasing profit function p i (t) associated with each job J i . If the customer for job J i is quoted a due date of d i , then the profit obtained from completing this job by its due date is p i (d i ). We consider the objective of maximizing profits. We show that if the company must finish each job by its due date, then there is no O(1)-speed poly-log-competitive algorithm. However, if the company can miss the due date of a job, at the cost of forgoing the profits from that job, then we show that there is a (1+e)-speed O(1+1/e)-competitive algorithm, and that this algorithm is essentially optimally competitive.

Production control with backlog-dependent demand

A manufacturing firm that builds a product to stock to meet a random demand is studied. Production time is deterministic, so that if there is a backlog, customers are quoted a lead time that is proportional to the backlog. In order to represent the customers' response to waiting, a defection function—the fraction of customers who choose not to order as a function of the quoted lead time—is introduced. Unlike models with backorder costs, the defection function is related to customer behavior. Using a continuous flow control model with linear holding cost and Markov modulated demand, it is shown that the optimal production policy has a hedging point form. The performance of the system under this policy is evaluated, allowing the optimal hedging point to be found. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix]

Optimal control of a high-volume assemble-to-order system with maximum leadtime quotation and expediting

For an assemble-to-order system with a high volume of prospective customers arriving per unit time, we show how to set nominal component production rates, quote prices and maximum leadtimes for products, and then, dynamically, sequence orders for assembly and expedite components. (Components must be expedited if necessary to fill an order within the maximum leadtime.) We allow for updating of the prices, maximum leadtimes, and nominal component production rates in response to periodic, random shifts in demand and supply conditions. Assuming expediting costs are large, we prove that our proposed policy maximizes infinite-horizon expected discounted profit in the high-volume limit. For a more general assemble-to-order system with arbitrary cost of expediting and the option to salvage excess components, we show how to solve an approximating Brownian control problem and translate its solution into an effective control policy.

Dynamic Pricing and Lead-Time Quotation for a Multiclass Make-to-Order Queue

This paper considers a profit-maximizing make-to-order manufacturer that offers multiple products to a market of price and delay sensitive users, using a model that captures three aspects of particular interest: first, the joint use of dynamic pricing and lead-time quotation controls to manage demand; second, the presence of a dual sourcing mode that can expedite orders at a cost; and third, the interaction of the aforementioned demand controls with the operational decisions of sequencing and expediting that the firm must employ to optimize revenues and satisfy the quoted lead times. Using an approximating diffusion control problem we derive near-optimal dynamic pricing, lead-time quotation, sequencing, and expediting policies that provide structural insights and lead to practically implementable recommendations. A set of numerical results illustrates the value of joint pricing and lead-time control policies.

Inventory positioning, scheduling and lead-time quotation in supply chains

We consider supply chain networks composed of several centrally managed production facilities as well as external suppliers. We design effective heuristics for inventory positioning, order sequencing, and short and reliable due-date quotation for this supply chain. We perform extensive computational testing to assess the effectiveness of our algorithms, and we explore the impact of supply chain topology on inventory costs and effective due-date quotation.

Effective on-line algorithms for reliable due date quotation and large-scale scheduling

We consider the sequencing of a series of jobs that arrive at a single processor over time. At each job’s arrival time, a due date must be quoted for the job, and the job must complete processing before its quoted due date. The objective is to minimize the sum (or average) of quoted due dates, or equivalently, the average quoted lead time. In this paper, we propose on-line heuristics for this problem and characterize the conditions under which these heuristics are asymptotically optimal. Computational testing further demonstrates the relative effectiveness of these heuristics under various conditions.

Manufacturing lead-time rules: Customer retention versus tardiness costs

Inaccurate production backlog information is a major cause of late deliveries, which can result in penalty fees and loss of reputation. We identify conditions when it is particularly worthwhile to improve an information system to provide good lead-time information. We first analyze a sequential decision process model of lead-time decisions at a firm which manufactures standard products to order, and has complete backlog information. There are Poisson arrivals, stochastic processing times, customers may balk in response to quoted delivery dates, and revenues are offset by tardiness penalties. We characterize an optimal policy and show how to accelerate computations. The second part of the paper is a computational comparison of this optimum (with full backlog information) with a lead-time quotation rule that is optimal with statistical shop-status information. This reveals when the partial-information method does well and when it is worth implementing measures to improve information transfer between operations and sales.

Production and Subcontracting Strategies for Manufacturers with Limited Capacity and Volatile Demand

We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system, when it is managed according to this policy, is evaluated.

Scheduling and Reliable Lead-Time Quotation for Orders with Availability Intervals and Lead-Time Sensitive Revenues

Motivated by applications in the manufacturing and service industries, we consider two models for coordinating scheduling with lead-time quotation: a basic model with a single customer type, and an enhanced model where an additional second customer type expects immediate service or production. In both models, revenues obtained from the customers are sensitive to the lead time, there is a threshold of lead time above which the customer does not place an order, and the quoted lead times are 100% reliable. These models are related to well-known scheduling problems, which have been studied in both offline and online settings. We introduce the immediate quotation case and study it with the (traditional) online version. We provide complexity results for the offline case, and perform competitive analysis for the online cases. A natural question of bridging the gap between the online and quotation models leads us to the delayed quotation model, which we study briefly. The analysis of these models provides useful qualitative insights as well.

The choice of dispatching rules in a shop using internally set due-dates with quoted leadtime and tardiness costs

Setting due-dates poses a dilemma for the manufacturing manager. If the duedates extend the quoted leadtimes to ensure delivery reliability, the shop incurs the customer's ire for having such long leadtimes. If they shorten its quoted leadtimes, it faces the prospect of incurring the customer's wrath for poor delivery reliability. This study examines the trade-offs involved in choosing a dispatching rule in a shop that can set due-dates subject to penalties for the length of the quoted leadtime and tardiness. The results of this study indicate that the shortest processing time rule works well for modest tardiness penalties. As the penalty for tardiness increases, dispatching rules such as first-come, first-serve and first-in-system first-serve, work well. The earliest due-date rule generally does not perform well in this study because of the interaction between the earliest duedate rule and the parameters of the due-date assignment rule. The paper concludes with the discussion of possible extensions of this work.

Customer order lead times for production based on lead time and tardiness costs

In practice decisions regarding customer order lead time and customer order processing are taken in different parts of the organization. Definite lead times are quoted by the sales department and job flow decisions are taken by the production department. This split up of decision responsibilities is in accordance with the differences in scope and control areas in complex organizations like job-shops or engineer-to-order firms. In this paper we present a simple economic model of sales and production in a job shop. Production aims at realizing the jobs by using its capacity to perform the operations of the jobs. Sales, using a model of the performance of production, aimes at maximizing expected profit by quoting lead times to customer orders, given that penalties are put on quoting long lead times and on tardy deliveries. Analysis of the model shows that for any combination of penalties on lead times and tardiness, there exist job flow times distributions for which it is optimal for sales to quote unrealistically short customer order lead times. Specifically if the job flow time has a high mean value and/or a high variance sales tends to quote a lead time with zero lead time penalty. In practice we often observe that the job flow times are long and have a high variance. The research presented in this paper shows why this may stimulate sales to neglect flow time information and to quote unrealistically short lead times. Our model shows that under a wide range of economic conditions a job flow time distribution with a small mean and a small variance seems to be a necessary condition for sales to quote realistic customer order lead times.