Quoted Lead Time Research Articles

Lead-time quotation in presence of ex-ante and ex-post reference effects of quotes on customers

Lead-time quotation in presence of ex-ante and ex-post reference effects of quotes on customers

Online Lead Time Quotation with Predictions

Online Lead Time Quotation with Predictions

Single versus dynamic lead-time quotations in make-to-order systems with delay-averse customers

Single versus dynamic lead-time quotations in make-to-order systems with delay-averse customers

When do firms benefit from joint price and lead-time competition?

Motivated by the observation that more and more firms are now using lead-time guarantee as a new competitive weapon to attract customers, we study firms’ optimal decisions in prices and lead-time quotations when they compete in these two dimensions for demand. We formulate a simultaneous game between multiple firms that sell substitutable products to the same market, and customer demand is determined by both prices and lead-time quotations of all firms. We fully characterize the existence and uniqueness of the Nash equilibrium, and use analytical results supplemented by comprehensive numerical examples to understand the impact of competition. Our research yields two key counterintuitive findings. First, although on the surface price and lead-time shape the demand function in a similar fashion, competition in these two dimensions drives equilibrium price and lead-time quotation in opposite directions. In particular, price competition decreases price but increases lead-time quotation, whereas lead-time competition increases price but decreases lead-time quotation. Second, under joint price and lead-time competition, if the relative price and lead-time competition intensities are disparate, firms can benefit from increased competition in the weaker dimension. The intuition is that increased competition in the weaker dimension diffuses the tensions between the firms in the stronger competition dimension, mitigating its negative impact on profit. To the best of our knowledge, we are among the first to identify conditions under which firms can gain from intensified competition.

Fair and profitable: How pricing and lead-time quotation policies can help

In this paper, we propose four policies to serve price and lead-time sensitive customers with a single type of product produced in an M/GI/1 type make-to-stock queueing system. The policies are developed to observe certain principles of fairness: if a customer is quoted a longer lead-time, she/he must be charged a lower price and a significant proportion of the deliveries has to be made during the quoted lead times. Although handling non-exponential service times in this setting presents difficulties, our analysis of the proposed policies is exact. Two of the policies operate with static prices, while one of the two dynamic pricing policies also quotes dynamic lead times. By construction of the policies, we show that the dynamic pricing policies are more profitable. Numerical examples bring additional light by showing that in small markets with oversensitive customers, dynamic policies can be profitable while static pricing policies can fail. In a larger market, a simple dynamic policy charging two prices depending on the stock availability can be a reasonable compromise. Dynamic policies tend to suffer less against high production time variability as well.

Lead-time quotation and hedging coordination in make-to-order supply chain

In the Make-To-Order (MTO) supply chain, for enticing the retailer to choose a shorter delivery lead-time, which improves the manufacturer's wholesale prices, the manufacturer adopts the Production Time Hedging (PTH) strategy as an incentive. Since the profit of the retailer depends not only on the Quoted Delivery Lead-Time (QDLT) but also on the Realized Delivery Lead-Time (RDLT), effectively hedging production time uncertainty reduces tardy delivery. We build an analytical model to investigate how PTH affects the retailer's QDLT decision and the supply chain performance. We consider models for four scenarios, namely (I) the centralized model, (II) the Nash model, (III) the manufacturer-led Stackelberg model, and (IV) the retailer-led Stackelberg model. We derive close-form results on the optimal hedging and QDLT decisions. In models II and III, PTH reduces the QDLT under all the conditions. However, in model IV, PTH can only coordinate the retailer when the hedging cost is low, or the holding cost/tardiness penalty is high. Besides, we find that model III is the dominant scenario for both players. Extending model IV to consider the case where the retailer sources from multiple manufacturers, we show that multiple sourcing is the dominant strategy when a manufacturer's hedging cost is high, or its holding cost/lead-time sensitivity factor is small. From the numerical study, we are interesting to find that the retailer's profit increases with the manufacturer's holding cost/lead-time sensitivity factor.

Lead-time quotations in unobservable make-to-order systems with strategic customers: Risk aversion, load control and profit maximization

We develop a model for pricing, lead-time quotation and delay compensation in a Markovian make-to-order production or service system with strategic customers who exhibit risk aversion. Based on a concave utility function of their net benefit, customers make individual decisions to join the system or balk without observing the state of the queue. The decisions of arriving customers result in a symmetric join/balk game. Regarding the firm’s strategy, the provider announces a fixed entrance fee, a lead-time quotation and a compensation rate for the part of a customer delay which exceeds the quoted lead-time.We analyze the effect of customer risk aversion and the compensation policy on the equilibrium join/balk strategies and the resulting input rates, and assess the flexibility of the provider in inducing a range of possible input rates under various constraints on the pricing/compensation policy. In numerical experiments we explore the behavior of pricing curves that reflect the provider’s choices in inducing specific input rates. A key insight obtained from the analysis is that a main benefit of the lead-time and compensation option is to allow the entrance fee to remain high and the provider prefers strategies that lead to this direction.

A Particle Swarm Optimization Algorithm for Solving Pricing and Lead Time Quotation in a Dual-Channel Supply Chain with Multiple Customer Classes

The combination of traditional retail channel with direct channel adds a new dimension of competition to manufacturers’ distribution system. In this paper, we consider a make-to-order manufacturer with two channels of sale, sale through retailers and online direct sale. The customers are classified into different classes, based on their sensitivity to price and due date. The orders of traditional retail channel customers are fulfilled in the same period of ordering. However, price and due date are quoted to the online customers based on the available capacity as well as the other orders in the pipeline. We develop two different structures of the supply chain: centralized and decentralized dual-channel supply chain which are formulated as bilevel binary nonlinear models. The Particle Swarm Optimization algorithm is also developed to obtain a satisfactory near-optimal solution and compared to a genetic algorithm. Through various numerical analyses, we investigate the effects of the customers’ preference of a direct channel on the model’s variables.

Customer rejection to guide lead time quotation and pricing decisions

The lead time (LT) quotation and pricing models in make-to-order environments usually assume that all arriving orders are accepted. Hence, despite the loss of demand, the firm must quote a relatively long LT to tackle the situations where there are too many waiting orders. This paper investigates the policy of accepting orders based on the state of the system and, consequently, rejecting customers when the number of waiting orders is larger than a given threshold value. Indeed, if there are less than K jobs in the system (K fixed), then the new order is accepted and a pair of LT and price are quoted to the customer. Otherwise, the order is rejected. Thus, we model the firm’s operations as a M/M/1/K queue instead of the commonly-used M/M/1 queue. We determine the optimal solution for K = 1 and solve the problem numerically for K ≥ 2. We show that our policy can be more profitable than the all-orders acceptance policy. We provide insights into when should a K be imposed and how such a K should be chosen. We find that the higher the sensitivity of demand to price or to LT is, the lower the optimal value of K.

Outsourcing contracts and ordering decisions of a supply chain under multi-dimensional uncertainties

We consider a supply chain in which a manufacturer with random yield sells the product through a retailer, where the overflowed order of the retailer may be fulfilled by the manufacturer’s outsourcing product. The inherent uncertainties include demand uncertainty, yield uncertainty, and outsourcing information asymmetry. Two contingent outsourcing contracts are studied based on whether the delivery lead-time quotation is adopted or not. We study how the two outsourcing contracts affect supply chain decision-makings and profits by introducing a backup supplier with private cost information. By employing backward induction technique, we obtain a closed-form analytical solution for backup supplier selection and ordering decisions. The manufacturer can outsource the retailer’s overflowed order to a backup supplier when the actual yield is low. In the presence of multi-dimensional uncertainties, there exists robustness for both outsourcing contracts. Depending on both the yield and the backup supplier’s cost type, the manufacturer makes one of three choices to outsource production: choosing both types of the backup supplier, choosing only the low-cost backup supplier, or choosing neither. The outsourcing quantity may be a part or all of the retailer’s overflowed order. Unlike the contract without constraint on lead-time, the quotation of the delivery lead-time endows the manufacturer with the ability of revealing the true cost information, thus it can improve the manufacturer’s outsourcing profit. However, the quotation of delivery lead-time may make the whole supply chain less efficient.

Optimization of a condition-based duration-varying preventive maintenance policy for the stockless production system based on queueing model

A stockless production system is considered, in which the products are not produced until the orders are accepted. Due to this character, the duration of the preventive maintenance has an influence on the lead time. In addition, in this stockless production system, the cost of the preventive maintenance depends on its duration; if the lead time exceeds to the quoted lead time, some penalty cost should be considered; and the non-conforming products can still be sold by a discount. A condition-based duration-varying preventive maintenance policy is designed for the stockless production system, by making a tradeoff among the duration of the preventive maintenance, the time for the machine continuously producing, and the lead time of the order. According to the characters of the stockless production system with the designed preventive maintenance policy, it can be modeled by a BMAP/G/1 infinite-buffer queueing model with gated service and queue-length dependent vacation. Based on this queueing model, the stationary probability distributions of four performance measures for the stockless production system are analyzed, including, the number of the products produced in a production cycle, the number of the unfulfilled orders at arbitrary time, the time required to fulfill the tasks present at arbitrary time, and the lead time of the order accepted at arbitrary time. Moreover, based on some information of these performance measures, a profit function, which represents the average profit of the manufacture in a production cycle, is constructed to optimize the designed preventive maintenance policy according to specific conditions. Finally, given an example with the purchasers having different sensitivities to the lead time, some numerical experiments are carried out; and from the numerical experiments, some general results can be inferred for the stockless production system with the designed preventive maintenance policy.

Effect of a lead time-dependent cost on lead time quotation, pricing, and capacity decisions in a stochastic make-to-order system with endogenous demand

The research on lead time quotation in make-to-order stochastic systems with an endogenous demand generally considers a system modelled as an M/M/1 queue with a linear demand that is sensitive to lead time and price, and always assume a constant unit operating cost. It is known that firms can reduce the operating cost by quoting a longer lead time. The idea of this paper stems from this observation. Indeed, we extend the existing works by modelling the unit operating cost, not as a constant, but as a convex decreasing function of the quoted lead time, which significantly rises the analytical difficulty but offers opportunities for many insights. We study three settings: (i) lead time quotation model, (ii) lead time quotation and pricing model, and (iii) lead time quotation, pricing, and capacity decision model. For each setting, we provide the optimal policy and conduct experiments to derive insights. In particular, we analyze the new trade-offs raised by the consideration of a lead time-sensitive cost. Some of our results are not intuitive.

Capacity optimization and competition with cyclical and lead-time-dependent demands

Capacity acquisition is often capital- and time-consuming for a business, and capacity investment is often partially or fully irreversible and difficult to change in the short term. Moreover, capacity determines the action space for service/production scheduling and lead-time quotation decisions. The quoted lead-time affects the customer’s perceived service quality. Thus, capacity acquisition level and lead-time quotation affect a firm’s revenue/profit directly or indirectly. In this paper, we investigate a joint optimization problem of capacity acquisition, delivery lead-time quotation and service-production scheduling with cyclical and lead-time-dependent demands. We first explore the structural properties of the optimal schedule given any capacity and lead-time. Then, the piecewise concave relationship between the delay penalty cost and the capacity acquisition level is found. Thereby, an efficient and effective polynomial time algorithm is provided to determine the optimal capacity acquisition level, delivery lead-time quotation and service/production schedule simultaneously. Furthermore, a capacity competition game among multiple firms is addressed. The numerical studies show that capacity equilibrium often exists and converges to a unique solution.

Dynamic pricing, leadtime quotation and due date based priority dispatching

This study considers a profit-maximising make-to-order manufacturing firm that (i) dynamically quotes a price/leadtime pair to arriving prospective customers who then decide whether or not to place an order by trading off the price and leadtime and (ii) dispatches placed orders. We model the marketing–operations collaboration problem as a Markov decision process to obtain the optimal quotation and dispatching policy numerically. We further investigate the sub-optimality of several sequential approaches. Our numerical results show that sub-optimality is negligible when the tardiness penalty is proportional to tardiness and the customer sensitivities to price and leadtime quotes are similar. However, it is considerable when tardiness of orders is penalised with a fixed cost and the customers differ significantly in their sensitivity to price and leadtime. By joint optimisation, it is possible to make more appealing price/leadtime quotes to customers and at the same time reach a better service level. On the other hand, the joint optimisation can also suggest the lowering of a firm’s service level in order to achieve higher profits.

Optimization and Customer Utilities under Dynamic Lead Time Quotation in an M/M Type Base Stock System

In a manufacturing and inventory system, information on production and order lead time helps consumers’ decision whether they receive finished products or not by considering their own impatience on waiting time. In Savaşaneril et al. (2010), the optimal dynamic lead time quotation policy in a one-stage production and inventory system with a base stock policy for maximizing the system’s profit and its properties are discussed. In this system, each arriving customer decides whether he/she enters the system based on the quoted lead time informed by the system. On the other hand, the customer’s utility may be small under the optimal quoted lead time policy because the actual lead time may be longer than the quoted lead time. We use a utility function with respect to benefit of receiving products and waiting time and propose several kinds of heuristic lead time quotation policies. These are compared with optimal policies with respect to both profits and customer’s utilities. Through numerical examples some kinds of heuristic policies have better expected utilities of customers than the optimal quoted lead time policy maximizing system’s profits.

Coordination of pricing and leadtime quotation under leadtime uncertainty

In many service and make-to-order manufacturing firms, pricing and leadtime quotation are two of the most important decisions. We consider a firm that serves customers who are sensitive to both price and quoted leadtime, with pricing and leadtime decisions being delegated to the marketing and production departments, respectively. According to the power structure within the firm, we model the problem as a Nash game, production Stackelberg game, and marketing Stackelberg game. For each game, the unique equilibrium is derived. In addition, for each decentralized setting, we design a mechanism that can be used by the firm to coordinate the decisions of the production and marketing departments. It is observed that the coordination schemes in the different games are of the same form. In particular, we find that the detailed values of the coordinating transfer prices under different power structures are the same. Moreover, we demonstrate that under some mild conditions on the level of the potential demand, the marketing Stackelberg game Pareto-dominates the Nash game in terms of expected profits.

Supply chain design to guarantee quoted lead time and inventory replenishment: model and insights

Do lead time constraints only lead to re-think and re-optimise the inventory positioning along the supply chain or can they impact on the design of the supply chain itself? To answer such a question, we integrate the lead time constraints in a multi-echelon supply chain design model and challenge the difficulty of combining in the same model the long-term decisions (facility location, supplier selection) with the midterm decisions (inventory placement and replenishment, delivery lead time). The model guarantees the respect of the quoted lead time associated with each customer order and the replenishment of the different stocks (raw materials, intermediate and final products) in the different stages of the supply chain between any pair of consecutive orders. We use the model to investigate the impact of the quoted lead time and customer’s order frequency on supply chain design decisions and costs. Some of our results indicate that the lead time constraints can lead to bringing the sites of manufacturing and distribution close to the demand zone and to select local suppliers in spite of their higher cost.

Dynamic lead time quotation under responsive inventory and multiple customer classes

We address the lead time quotation problem of a manufacturer serving multiple customer classes. Customers are sensitive to the quoted lead times and the manufacturer has the flexibility to keep inventory to improve responsiveness. We model the problem as a Markov decision process and characterize the optimal lead time quotation, rationing, and production policies. We then define internal and external service level measures and analyze the impact of inventory keeping decision on these measures. Before analyzing the impact, we first derive the relation between inventory level and lead time quotes. We then show that the effect of inventory level on the service levels may not follow the intuition. We also study alternative lead time quotation and production schemes. We contrast the performance of these alternative policies with that of the optimal policy. Specifically, through a numerical study, we quantify the value of controlled arrivals and customer rejection, the value of information on customer status, and the value of a far-sighted policy. Through the numerical study, we also identify the effect of revenue mix and demand mix on the inventory keeping decisions and the performance measures. Finally, we measure the impact of lead time quotation on resource pooling (i.e., inventory and capacity pooling). We show that the value of resource pooling is limited under the optimal policy, since lead time quotation is already effective in balancing the demand with capacity, and in allocating the resources among different customer classes.

Price and Lead Time Quotation for Contract and Spot Customers

We study price and lead time quotation decisions in a make-to-order system with two customer classes: (1) contract customers whose orders are practically always accepted and fulfilled based on a contract price and lead time agreed on at the beginning of the time horizon, and (2) spot purchasers who arrive over time and are quoted a price and lead time pair dynamically. The objective is to maximize the long-run expected average profit per unit time, where profit from a customer is defined as revenues minus lateness penalties incurred because of lead time violations. We model the dynamic quotation problem of the spot purchasers as an infinite horizon Markov decision process, given a fixed price and lead time for contract customers. We analyze the impact of customer preferences (e.g., price and lead time sensitivity) on the optimal price and lead time decisions for spot purchasers and characterize the optimal policy. We explore the benefits of dynamic quotation compared to the use of fixed price and lead times, and provide recommendations for firms. Finally, we analyze the optimal contract terms given the dynamic quotation strategy for spot purchasers and discuss the profit improvements offered by the optimal mix of spot and contract customers.

Designing supply networks under maximum customer order lead times

ABSTRACTWe consider the problem of designing supply networks for producing and distributing goods under restricted customer order lead times. Companies apply various instruments for fulfilling orders within preset lead times, such as locating facilities close to markets, producing products to stock, choosing fast modes of transportation, or delivering products directly from plants to customers without the use of distribution centers. We provide two alternative models that consider these options to a different extent, when designing multi-layer, multi-product facility networks that guarantee meeting restricted lead times. A computational evaluation compares both models with respect to solvability and the quality of the obtained networks. We find that formulating the problem as a time–space network flow model considerably helps to design high-quality networks. Furthermore, the lead times quoted to customers affect the design of all layers in the supply network. In turn, this shows that when service requirements are applied, the strategic planning of the network should be adapted accordingly. Concerning the instruments considered for meeting quoted lead times, the choice between make-to-order and make-to-stock production is found to be of utmost importance, whereas transportation decisions have a minor impact.