The impact of priority sequencing decisions on the customer-related performance of a make-to-order (MTO) production system was investigated. The priority se-quencing problem was modeled as a Markov decision process (MDP). The objective function was defined as the sum of a fixed and a variable cost of tardiness, which allowed the investigation of the two commonly used performance criteria “on-time probability” and “expected tardiness”. With the MDP model, it is possible to compare simple priority rules with the optimal policy while it is only possible to compare different rules with each other when the optimal policy is unknown.
The numerical results show that it is possible to achieve near optimal system perfor-mance by employing simple due-date-based rules. Nevertheless, the optimal policy, as well as the simple rule with the closest performance, heavily depend on the rel-ative value of the fixed cost in tardiness penalty. As the value of the fixed cost increases, the performance of EDD deteriorates. When the fixed cost plays a role and the due-dates are difficult to meet, adhering to processing based on the EDD discipline results in a percentage cost gap of more than 56%. On the other hand,
K Tightness F CF S EDD EDDP Aotp EDDotpDC LDD
10 TL 1 η 0.744 0.748 0.769 0.846 0.792
(±0.000) (±0.001) (±0.000) (±0.000) (±0.000)
E[T] 1.441 1.106 1.258 1.860 2.567
(±0.005) (±0.004) (±0.005) (±0.007) (±0.008)
Cost 0.865 0.742 0.765 0.869 1.193
(±0.003) (±0.002) (±0.002) (±0.003) (±0.003)
10 TL 2 η 0.859 0.874 0.878 0.927 0.867
(±0.000) (±0.000) (±0.000) (±0.000) (±0.000)
E[T] 0.747 0.505 0.551 1.046 2.006
(±0.003) (±0.003) (±0.003) (±0.005) (±0.007)
Cost 0.460 0.353 0.364 0.469 0.889
±0.002) (±0.002) (±0.002) (±0.002) (±0.003)
10 TL 3 η 0.927 0.940 0.940 0.967 0.910∗
(±0.000) (±0.000) (±0.000) (±0.000) (±0.000)
E[T] 0.351 0.235 0.243 0.551 1.595
(±0.002) (±0.002) (±0.002) (±0.004) (±0.007)
Cost 0.226 0.167 0.169 0.240 0.685
(±0.001) (±0.001) (±0.001) (±0.002) (±0.003)
20 TL 1 η 0.728 0.731 0.754 0.842 0.788
(±0.001) (±0.001) (±0.001) (±0.000) (±0.000)
E[T] 1.801 1.496 1.641 2.284 3.046
(±0.010) (±0.009) (±0.011) (±0.012) (±0.013)
Cost 1.014 0.903 0.921 1.023 1.366
(±0.005) (±0.004) (±0.005) (±0.005) (±0.005)
20 TL 2 η 0.838 0.853 0.858 0.923 0.864
(±0.001) (±0.001) (±0.001) (±0.000) (±0.000)
E[T] 1.065 0.825 0.864 1.438 2.457
(±0.009) (±0.009) (±0.009) (±0.012) (±0.013)
Cost 0.601 0.496 0.502 0.613 1.053
(±0.004) (±0.004) (±0.004) (±0.005) (±0.005)
20 TL 3 η 0.906 0.916 0.917 0.962 0.907
(±0.001) (±0.001) (±0.001) (±0.000) (±0.000)
E[T] 0.610 0.504 0.517 0.905 2.021
(±0.006) (±0.006) (±0.006) (±0.009) (±0.011)
Cost 0.346 0.294 0.298 0.371 0.840
(±0.003) (±0.003) (±0.003) (±0.003) (±0.004) Values after±give the half-width of a 95% confidence interval.
Table 3.13Effect ofKon the performance of simple rules in larger problem sizes (CRLmax= 20)
the proposed EDDotp rule performs close to optimal, which also works well when the due-dates are easier to meet. Moreover, when there is a fixed cost, delaying the priority sequencing decisions to the next order completion instead of deciding upon arrival provides further improvement potential.
Due to the nature of priority sequencing decisions, the size of the state space in-creases exponentially in the problem size. The major limitation of an exact analysis is therefore the fact that required computational times easily become prohibitive for larger sized problems.
4. Dynamic Pricing, Leadtime Quotation and Due-Date-Based Priority Dispatching
We model the marketing-operations collaboration problem as a Markov decision process (MDP) to obtain the optimal quotation and dispatching policy numeri-cally. 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 penalized with a fixed cost and the customers differ significantly in their sensitivity to price and leadtime. By joint optimization, 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 optimization can also suggest the lowering of a firm’s service level in order to achieve higher profits by serving more customers.
4.1. Introduction
This chapter considers a firm that provides service to a market of price- and leadtime-sensitive customers and processes orders following a make-to-order fash-ion (MTO). The customer arrivals and order completfash-ions evolve according to a stochastic process. The firm makes individual price/leadtime quotes to dynami-cally arriving prospective customers, who then make the decision whether or not to place an order by trading off these two aspects of service. The customers are not homogeneous in their sensitivity to price and leadtime. If a customer accepts the quote, his order along with its promised leadtime, becomes an input to manufactur-ing. If completing an order takes longer than the promised leadtime, the firm may suffer a loss of goodwill or future business, may incur extra shipping costs or lose revenue if it has been offering price discounts in case of tardiness. The firm’s ob-jective is to maximize the expected profit, which is the margin earned from placed orders minus tardiness penalties. By quoting prices and leadtimes, the firm con-trols its demand, i.e., makes an order selection decision by influencing which of the prospective customers finally places an order. By dispatching orders accordingly, the firm aims at decreasing tardiness penalties. In such a business environment, it is necessary for the firm to consider interdependencies between marketing- and operations- (manufacturing) related decisions.
We compare two scenarios regarding the firm’s approach to taking such interde-pendencies into account. In the first scenario (sequential approach), marketing
quotes price/leadtime pairs in coordination with manufacturing, which then dis-patches obtained orders with given leadtimes. In the second scenario, marketing and manufacturing fully collaborate and make these decisions jointly (simultane-ous optimization approach). The decisions in the first scenario are made as follows.
Marketing considers the firm’s profit maximization as the objective, i.e., it takes the consequences of its decisions for manufacturing into account. Thus, it manages the trade-off between quoting shorter leadtimes to attract more customers and increase their willingness to pay and incurring higher tardiness penalties. Upon arrival of a prospective customer, marketing knows which type of customer he is. However, it has incomplete information regarding the current state of manufacturing. Although the current number of orders in the manufacturing system and the maximum num-ber of pending orders it allows are known to marketing, it has no information about the sequence in which they are going to be processed. Marketing therefore assumes a first-come-first-served (FCFS) discipline in processing. However, manufacturing may follow alternative policies for dispatching.
We answer the following research questions: (1) How much can the profitability be increased? (2) How are the system utilization, the service level of the firm and the selection of different customer types affected when the simultaneous optimization approach, rather than one of the sequential approaches, is considered? (3) How do the tardiness penalty structure and the market-related characteristics affect the answers to the first two questions?
The chapter is structured as follows: the model is presented in Section 4.2. Section 4.3 introduces the investigated KPI’s and describes their computation. Section 4.4 presents numerical results and Section 4.5 summarizes findings.