Lead-time setting, capacity utilization, and pricing decisions under lead-time dependent demand

This research examines the lead-time setting, capacity utilization, and pricing decisions facing a firm serving customers that are sensitive to quoted lead-times. We model the firm's operations as an M/M/1 queue and treat the demand as being linear in price and quoted lead-time. We analyze the quoted lead-time, capacity utilization, and price that maximize revenues less total variable production costs, WIP holding costs, and lateness penalty costs. We use this analysis to show that the capacity utilization should be lower when (1) customers are more sensitive to lead-times and/or (2) the firm incurs higher congestion related costs and/or (3) the penalty for lateness is higher. Further, we study the robustness of optimal profit contributions when the model parameters are mis-estimated.     

Monopoly pricing when customers queue

It takes time to process purchases and as a result a queue of customers may form. The pricing and capacity (service rate) decision of a monopolist who must take this into account are characterized. We find that an increase in the average number of customers arriving in the market either has no effect on the price, or else causes the firm to reduce the price in the short run. In the long run the firm will increase capacity and raise the price. When customer preferences are linear, the equilibrium is socially efficient. When preferences are not linear, the equilibrium will not normally be socially efficient.     

Coordination of marketing and production for price and leadtime decisions

We study a firm which serves customers that are sensitive to quoted price and leadtime, with pricing and leadtime decisions being made by the marketing and production departments, respectively. We analyze the inefficiencies created by the decentralization of the price and leadtime decisions. In the decentralized setting, the total demand generated is larger, leadtimes are longer, quoted prices are lower, and the firm's profits are lower as compared to the centralized setting. We show that coordination can be achieved using a transfer price contract with bonus payments. We also provide insights on the sensitivity of the optimal decisions with respect to market characteristics, sequence of decisions and the firm's capacity level.     

Pricing competition on innovative product between innovator and entrant imitator facing strategic customers

When an innovative product is introduced into the market, innovators always face competition from entrant imitators. Strategic customers may also anticipate this and can design their purchase plans accordingly. In this study, we develop a dynamic game model to formulate the problem associated with competitive product pricing between an innovator and an imitator for obtaining a pricing equilibrium. The influence of various factors on pricing policies, market sales and profits are analysed. We argue that when anticipating forthcoming competitors, innovators should not price too highly in the monopoly stage. The optimal monopoly price decreases with the quality ratio and forms a U shape along with the dimension of customers’ strategic level; however, the right tail of the U is mitigated when the quality ratio increases. In the duopoly phase, the markdown for the innovator and the difference in product cost performance between the innovator and imitator are investigated. We then analyse the value of demand information. The numerical analysis indicates that the value decreases with customers’ strategic level and increases with the quality ratio. The revealing behaviour of the innovator influences the imitator marginally in pricing and considerably in profit. Finally, a medium level is always preferred when the imitator chooses the product quality level.     

Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty

In this article, we investigate the newsvendor problem in a joint ordering and pricing setting in the presence of option contracts under demand uncertainty. At the beginning of a single selling season, the newsvendor who faces additive stochastic demand can obtain goods through two ways: ordering from a firm or purchasing and exercising call options. Single ordering (ordering from a firm only or purchasing and exercising call options only) and mixed ordering (ordering from a firm and purchasing and exercising call options simultaneously) cases are investigated. We find that the newsvendor’s optimal pricing and ordering strategies exist and are unique for both cases, respectively. In addition, when both cases are available, mixed ordering is the newsvendor’s optimal ordering policy. If only single ordering is available, the newsvendor prefers ordering from a firm when demand risk is low, while enjoys purchasing and exercising call options when demand risk is high. We also find that with option contracts, the newsvendor’s optimal order quantity and maximum expected profit are all decreasing in the option price and exercise price of product, while the optimal retail price in terms of option price and exercise price of product are intricate. Moreover, we show that, mixed ordering is more capable to deal with supply price volatility risk.     

Dynamic pricing for multiple class deterministic demand fulfillment

We consider how a firm should allocate inventory to multiple customer classes that differ based on the price they pay and their willingness to incur delay in fulfillment of their demand. The problem is set in a deterministic demand, economic-order-quantity-like environment with holding, backorder, lost demand and setup costs. The firm either fulfills demand or offers a price discount to induce the demand to wait for fulfillment from the next reorder. We determine the optimal policy and discuss how changes in various parameters affect profitability, customer service, and operational measures such as order frequency and base stock levels. We compare the results to a policy that only rations inventory without dynamic discounting and to a policy that only provides discounts. Through the comparison, we observe that dynamic pricing can be seen as a combination of a pricing mechanism which determines demand and an allocation mechanism that differentiates between customer classes, serving each ones needs. We show that if lower-value customers are distinguished by accepting reduced service, it is possible that both high and low-value customer classes see better levels of service under the optimal policy than under a discounting only policy. In addition we demonstrate the applicability of the results to a stochastic version of the problem.     

Optimal pricing and core acquisition strategy for a hybrid manufacturing/remanufacturing system

Remanufacturing is one of the product recovery options where the quality of used products (cores) is upgraded to ‘as-good-as-new’ conditions. In this article, we consider a monopolist firm selling new and remanufactured products to quality-conscious primary customers and price-sensitive secondary customers, respectively, with one-way substitution, i.e. some primary customers may substitute new products by remanufactured products while secondary customers can never afford to buy new products. We develop economic models under two scenarios – when the supply of cores is unconstrained and when manufacturers have to procure cores at an acquisition price. The major observations of the article are as follows. A firm is better off when there is no constraint on the supply of cores. Even when cores have to be acquired at an acquisition price, the profitability is higher than that when the firm does not engage in remanufacturing activities. When a larger number of primary customers replace new products with remanufactured products, there is partial cannibalization of new product sales; however, the combined market share and profitability of the firm increase. When core supply is constrained and customers are less sensitive to core prices, the limited supply of cores may render remanufacturing an infeasible option for the firm. Therefore, firms should not only generate awareness among primary customers to buy remanufactured products, but also step up efforts to ensure a steady supply of cores. We conclude the article with managerial implications and directions for future research.     

Optimal pricing for cloud service providers in a competitive setting

Cloud services are transforming business and government at an ever-increasing rate. As a form of cloud service, software as a service (SaaS) is one of the fast growing segments of the information technology and has become an attractive alternative to the on-premises software. In this paper, we study the optimal pricing strategies of a cloud service provider in an incumbent-entrant setting under user upgrade cost and switching cost. Our results show that in equilibrium the market structure is not unique. The specific market segmentation depends on the incumbent’s pricing strategy whether to provide discounted price to its old customers and the levels of user upgrade cost and switching cost. When faced with customers who are heterogeneous in the sensitivity to the related costs, the incumbent firm may need to offer a discount to the new customers rather than to those who have purchased from it. This implies that the entry of a SaaS firm into the market is a potential threat to the incumbent on-premises software firm, especially in capturing new customers from the untapped market.     

Control of a manufacturing system with random product yield and downward substitutability

We consider a manufacturing system where the quality of the end product is uncertain and is graded into one of several quality levels after production. We assume stochastic demand for each quality level, stochastic production times, and random quality yields. We also assume downward substitutability (i.e., customers who require a given product will be satisfied by a higher quality product at the same price). The firm produces to stock and has the option to refuse satisfying customers even when it has items in stock. We formulate this problem as a Markov Decision Process in the context of a simple M/M/1 make-to-stock queue with multiple customer classes to gain insight into the following questions: (i) how does the firm decide when to produce more units (i.e., what is the optimal production policy?) and (ii) how does the firm decide when to accept/reject orders and when to satisfy customers demanding lower quality products using higher quality products? In the case of two product classes, we completely characterize the structure of the optimal production and acceptance/substitution policies. However, the structure of the optimal policy is complicated and we therefore develop a simple heuristic policy for any number of classes which performs very well. We finally extend our heuristic to the system where production occurs in batches of size of larger than one, the system where there is a setup cost for initiating production, and the case where processing time distribution is Erlang.     

Pricing and effort decisions for a supply chain with uncertain information

This paper analyses the pricing and effort decisions of a supply chain with single manufacturer and single retailer. The manufacturer produces a kind of product and then wholesales the product to the retailer, who in turn retails it to customers over a single selling season. The retailer can influence demand through her sales effort. This research depicts the consumer demand, the manufacturing cost and the sales effort cost as uncertain variables. Considering the demand expansion effectiveness of sales effort, one centralised and three decentralised game models are built on the basis of the expected value criterion, and the equilibrium solutions are obtained. We investigate the effects of the parameters’ uncertainty degrees on the pricing and effort decisions. The results indicate that the manufacturer benefits from improvement in demand and cost uncertainties when he has at least bargaining power in the supply chain. The results also imply that the uncertainty degree of sales effort elasticity has an outstanding influence on the pricing and effort decisions, whereas the uncertainty degree of price elasticity has a modest impact on these decisions. We also study the effects of the parameters’ uncertainty degrees on the supply chain from the consumers’ perspective. The results suggest that with a power retailer, the retail price should always be on the high end. Consequently, consumers do not necessarily benefit from a power retailer. When the manufacturer and the retailer have equal bargaining power, consumers do not necessarily benefit from the supply chain, either.     

On the effect of demand randomness on a price/quantity setting firm

Replenishment and pricing decisions are of great importance to firms. Traditionally replenishment and pricing strategies are determined by separate units of a firm, the former by production and the latter by marketing. In determining these two strategies, firms frequently have to face two challenges. One stems from a lack of coordination between production and marketing, which leads to revenue loss or excess inventory. The other is caused by lack of information when making these two decisions. That is, firms usually have to make decisions when market information is poor. We consider the joint effects of coordination and information when market demand becomes more variable in the sense of a specific mean preserving transformation. We have three main findings. First, when these two strategies are coordinated by the Headquarters (HQ) of the firm, the HQ uses pricing and inventory as two instruments to manage uncertainty. How exactly increasing demand variability affects the decisions depends on the type of demand uncertainty faced. In particular, for additive demand uncertainty, both price and service level decrease in demand variability, whereas for multiplicative demand uncertainty, they both increase in demand variability. Second, the value of information increases with the level of demand variability, suggesting that it is more beneficial to have information when demand is more variable. The impact of demand variability on the value of coordination, however, is indeterminate. Furthermore, perfect information has more value than perfect coordination if and only if demand variability is high. Third, coordinating these two decisions reduces the value of obtaining the demand information and similarly coordination is more valuable when the demand information is unavailable than otherwise.     

Advance booking discount in the presence of spot market

We consider a risk-neutral firm that can procure raw material via long-term contract as well as in spot market, using the material as a one-to-one input to produce a seasonal product and selling it in the customer market. The firm can use the advance booking discount (ABD) program to entice customers to place their orders prior to the selling season. The ABD program provides an opportunity for the firm to update its understanding of the regular demand and spot price. We separately analyse two cases: (NI) no information updating and (IU) information updating cases. In each case, we derive the optimal discount pricing strategy and corresponding expected profit of the firm. By comparing them, we investigate the value of information updating obtained from the pre-committed order. Among others, our study finds that if the product has a relatively high profit margin, or a low profit margin where the raw material spot price is more sensitive to the trading volume, it is optimal for the firm to implement the discount strategy. The optimal discount coefficient in the IU case is never lower than in the NI case. We further find that the optimal discount coefficient in the NI case decreases in spot market volatility; however, it increases in spot market volatility if and only if the firm’s market share is larger than half of the total market demand in the IU case.     

The value of sharing lead time information

The widespread adoption of Enterprise Resource Planning (ERP) systems has, among many other benefits, increased the ability of a firm to share operational data with customers. In this paper we analyze the factors that determine whether or not sharing a specific type of information, namely state-dependent lead time information, can benefit a firm. We develop a stochastic model of a custom-production environment, in which customers are handled on a first-come first-served basis but have differing tolerances for waiting. The firm has the option to share different amounts of information about the lead time a potential customer may incur. Although the information differs across scenarios, the reliability of that information in terms of the probability that a stated lead time is met is equal in the eyes of the customers. We derive conditions under which sharing more information with customers improves the firm's profits and the customers' experiences. We show that it is not always the case that sharing information improves the lot of the firm. We show that when customers' tolerances for waiting are more heterogeneous then the benefit to the firm from sharing lead time information increases. Our conclusion is that management should only authorize sharing detailed lead time information, be it through information system integration or frontline sales people, after a careful analysis of a customer's sensitivity to delay.     

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.     

Joint pricing and advertising strategy with reference price effect

Consumers are susceptible to reference price effects when they make purchase decisions for a certain product. Meanwhile, the sales price and advertisement are the determinable factors that have impact on consumers’ reference price which are also fundamental marketing strategies. Therefore, how to determine an appropriate sales price and advertising effort level to maximise firms’ profits is an essential task. A joint pricing and advertising problem for a monopolistic firm with consideration of reference price effect is investigated, where consumer demand rate is price-sensitivity and depends on the gap between the sales price and the reference price in consumers’ mind. An optimisation model is established to maximise the firm’s total profit by making a joint pricing and advertising strategy. The static and dynamic joint strategies are obtained by applying Pontryagin’s maximum principle. Results show that the dynamic strategies dominate the static ones. Furthermore, the dynamic pricing and dynamic advertising strategies are strategic complements. Additionally, the length of the sales period plays a key role in determining the superiority of the two dynamic strategies. Specifically, a relatively short sales period highlights the value of the dynamic advertising while a long sales period strengthens the function of the dynamic pricing.     

A manufacturer’s production and pricing strategies with a salvage channel

We study a manufacturer’s production quantity and pricing decisions when the manufacturer has an opportunity to sell surplus inventory through a salvage channel. Before sales begin, the manufacturer determines the production quantity without knowing customer demand. After demand is realised, the manufacturer first satisfies the demand through primary channel while charging a fixed price or adjusting price to maximise profit. At the end of the selling season, the manufacturer resells surplus inventory through the salvage channel, which can be either integrated with or independent of the manufacturer. The manufacturer’s optimal production quantity and expected profit are investigated under different salvage channel structures. We show that the salvage channel improves the manufacturer’s profitability as well as the availability of the product to potential customers through both primary and salvage channels.     

Optimal Price-Inventory Decisions: Profit vs. ROII

Making optimal price-inventory decisions in the face of alternate criteria is studied for a monopoly firm. When the firm's demand function belongs to the logarithmic concave class, necessary and sufficient optimality conditions are obtained for profit and return on inventory investment criteria. It is shown that decentralized price-inventory decision-making is optimal when the return criterion is used. The theoretical developments are elucidated with a detailed study of linear demand and a comprehensive numerical example.     

Supply chain capacity and outsourcing decisions: the dynamic interplay of demand and supply uncertainty

We study the interplay of demand and supply uncertainty in capacity and outsourcing decisions in multi-stage supply chains. We consider a firm's investment in two stages of a supply chain (Stage 1 models the “core” activities of the firm, while Stage 2 are the “non-core” activities). The firm invests in these two stages in order to maximize the multi-period, discounted profit. We consider how non-stationary stochastic demand affects the outsourcing decisions. We also consider how investment levels are affected by non-stationary stochastic supply when the market responds to the firm's investments. We characterize the optimal capacity investment decisions Tor the single- and multi-period versions of our model and focus on how changes in supply and demand uncertainly affect the extent of outsourcing. We find that as the responsiveness of the market to investments made by the firm increases, the reliance on outsourcing generally increases. While greater supply and greater demand have the expected effect on investments, decreases in variability are not as straightforward. Greater supply uncertainty increases the need for vertical integration while greater demand uncertainty increases the reliance on outsourcing. In the multi-period model, we find that the nature of adjustments in capacity based on changes in demand or supply follows from the comparative statics of the single-period model, although whether outsourcing increases or decreases depends on the costs of adjusting capacity.     

Review of supplier diversification and pricing strategies under random supply and demand

Uncertainties of supply and demand are two major sources of risk in any supply chain. As a result, the companies are implementing different strategies to mitigate the effects of these risks. Supplier diversification and responsive pricing are two of the main strategies that are used to mitigate the supply and demand risks. In supplier diversification, a firm uses multiple channels of sourcing while in responsive pricing, a firm manipulates demand through pricing to mitigate supply and demand risks. In this paper, we review lot-sizing problems when supply and demand are random. We focus on studies that have considered supplier diversification or responsive pricing as a mitigation strategy. We classify the studies based on their main assumptions and summarise their major findings. Finally, we present some directions for future research. Part of what we have found is that most studies that use multiple decision makers have focused on cases where information is complete and non-cooperative. There is a need to consider more realistic situations when there is information asymmetry between the decision makers. In addition, we have found that there is a lack of studies that look at the impact of joint ordering and pricing in the existence of multiple suppliers.