Featured Story November 2020 – January 2021
Make-to-order systems with delay-averse strategic customers: Load control policies

By Dr. Myron Benioudakis, Research Fellow.

Nowadays, more and more companies adopt MTO strategies and create competitive advantages (Cachon, G. and Terwiesch, C. (2009)), because under this approach: (i) waste resources are minimized, since the processes related to production do not start before receiving a customer order, (ii) the risk of inefficiency is minimized as long as all manufacturing takes place after receiving the customer’s order, thus company operations are focused on the manufacturing of the specific products as efficiently as possible, and (iii) the customers place orders whenever they require a product or service, enjoying a more personalized service compared to companies that adopt more mass production-oriented strategies.

In firms that produce products on a make-to-order basis or provide a service, customer delay is a crucial factor that affects both the demand and the profitability, directly or indirectly. Customers may react to delay, real or anticipated, in a variety of ways ranging from mild to very extreme, depending on the effect it has on their own operation. Therefore, production or service providers must be able to effectively address customers' concerns about delays in order for the demand not to be adversely affected.

In considering the effects of delay on the customers and the firm, several interacting factors must be taken into account. First, in many cases customer behavior is strategic, in the sense that customers also consider the reaction of other customers when they make their decision to place the order for the product or service, i.e., whether to join the system or balk. This creates externalities, since the decision of a customer affects and is affected by the behavior of the other customers, and it may have unexpected consequences in the formation of demand patterns. In addition, customers are often affected disproportionately by long delays, since they may lead to defaults or extreme losses. In such cases customers exhibit a risk-averse behavior, which must also be considered as its effect on the demand may be quite adverse.

The implications of strategic customer behavior on the performance of a queueing system have been studied extensively in the recent years. Early works on the M/M/1 queue include Naor (1969) and Edelson and Hilderbrand (1975) for the observable and unobservable models, respectively. Many variations of the original models have been studied since, and a comprehensive review of the literature is provided in Hassin (2016).

Furthermore, in terms of the firm's objectives, the standard approach is to determine the parameters of the pricing/compensation policy that maximize the provider's profit, and accept the demand resulting from this policy as optimal. However in many cases firms are interested in controlling the customer flow from a more general viewpoint, not necessarily tied to short-term profit maximization. The provider may want to determine a pricing/compensation policy that will shape a particular demand pattern over time, which may not be profit maximizing in the short-run but aim to increasing market share, product reputation etc. Such concerns and objectives are especially relevant for startup companies or new products introduced to the market. In such situations it is useful to know the policy flexibility in inducing a desired input rate to the system, especially in the presence of limitations as discussed above.

The problem of adjusting the input rate, the traffic and generally the load of a system has been studied extensively, although there are not many works that focus on the variability of the input rate with respect to policy parameters. This question has been explored in deterministic network flow problems under a Wardrop equilibrium framework, where it is desired to arrange the flow patterns so that no user has an incentive to change his/her route (Dafermos and Nagurney (1984), Tobin and Friesz (1988)). Another way to adjust the input rate is the admission control using pricing policies (Low (1974), Ata and Shneorson (2006)).

For this problem, recent research results (Benioudakis et. Al (2021)) show that when the provider has full flexibility in a pricing/compensation policy, he or she can mitigate the adverse effects of risk aversion almost entirely, by employing a policy that compensates fully for the excess delay and sets the entrance fee close to the customer service benefit. However in this case there is no strictly optimal policy. A key insight obtained from this research is that the main benefit of the lead-time and compensation option is to allow the entrance fee to remain high and the provider always prefers strategies that lead to that direction. Furthermore, as risk aversion increases, the range of achievable input rates may decrease substantially, depending on the policy constraints. In this case the provider has the highest flexibility when he or she is free to set the compensation rate, even when he or she is forced to keep the entrance fee and/or the lead-time at fixed values.

Summary and applications: Load control policies may be very useful in situations where in addition to profits the provider must also consider additional factors. For example, startup companies that introduce new products or services may need a pricing strategy that generates a given demand pattern, not necessarily optimal during the introduction phase. This is usually done for achieving the most appropriate market penetration rate in the long term, depending on recognition of the company or the brand name, the intensity of competition, the available resources to ensure the desirable service levels, etc.


Ata, B. and Shneorson, S. (2006). Dynamic Control of an M/M/1 Service System with Adjustable Arrival and Service Rates. Management Science, 52(11):1778– 1791.

Benioudakis, M., Burnetas, A., and Ioannou, G. (2021). Lead-time quotations in unobservable make-to-order systems with strategic customers: Risk aversion, load control and profit maximization. European Journal of Operational Research, 289(1):165–176.

Cachon, G. and Terwiesch, C. (2009). Matching supply with demand, volume 2. McGraw-Hill Singapore.

Dafermos, S. and Nagurney, A. (1984). Sensitivity analysis for the asymmetric network equilibrium problem. Mathematical Programming, 28(2):174–184.

Edelson, N. M. and Hilderbrand, D. K. (1975). Congestion Tolls for Poisson Queuing Processes. Econometrica, 43(1):81–92.

Hassin, R. (2016). Rational Queueing. Chapman and Hall/CRC.

Low, D. W. (1974). Optimal Dynamic Pricing Policies for an M/M/s Queue. Operations Research, 22(3):545–561.

Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica: journal of the Econometric Society, 37(1):15–24.

Tobin, R. L. and Friesz, T. L. (1988). Sensitivity Analysis for Equilibrium Network Flow. Transportation Science, 22(4):242–250.
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