Analysis of the impact of simultaneous optimization on KPI’s 68

In order to answer the second research question, we observe the levels of related KPI’s. Table 4.3 gives the system utilization (ρ), the percentage of LS (φLS) and PS (φP S) customers that accept the quote under a sequential approach (Seq) and the simultaneous approach (Sim). Since in all three sequential approaches the (p, L) quotes are made by marketing in the same way, ρ, φ_LS and φ_{P S} are the same for all. The on-time probability of orders (η) differs between three approaches that differ in the dispatching policy manufacturing follows. Table 4.4 gives η under the sequential approaches (Seq, i, i = 1,2,3) and the simultaneous approach (Sim).

The tables present the results for the base case (ξL= 0.75 andξ_p = 0.75) in which ζ and κ are varied in the respective order. The arrows on the right of the values in column Sim indicate the direction of change compared to the values in columns Seq and Seq,3 in Tables 4.3 and 4.4 respectively. Tables for cases 2, 3 and 4 are not provided in the manuscript, however our conclusions hold for all.

For a profit maximizing MTO firm, the typical trade-off is between obtaining more orders to increase revenue and being able to attain the promised leadtimes to avoid tardiness costs. A joint optimization enables the evaluation of this trade-off in the most informed way. In other words, it enables accurate judgment whether the benefits due to obtaining more orders outweighs the loss due to more frequently failing to complete them within leadtimes or vice versa.

(6,0) (3,1) (0,2)

Table 4.3 shows that the simultaneous approach increases the system utilization typically by increasing both φ_{P S} and φ_LS or either one of them without decreasing the other. In some cases where the system receives equally likely arrivals of two dissimilar customer types, e.g. sub-case 5, the simultaneous optimization enables the firm to attract more customers, as well as to improve its service level (see Tables 4.3 and 4.4).

Similar results are observed in cases 2.5, 3.8 and 4.8. One can notice that, in all of these cases, the simultaneous approach prefers PS customers, i.e. either increases φ_{P S} more than it increasesφ_LS or increasesφ_{P S}while decreasingφ_LS. Although the number of cases where the simultaneous approach prefers LS customers is higher, this clearly indicates that higher profits are not necessarily a result of being able to attract more high margin customers. In most of the cases, on the other hand, the simultaneous approach suggests that lowering firm’s service level (η) is a better way towards achieving higher profits.

Typically, the highest service levels are obtained when the order processing sequence is optimized in a second step after (p, L) quotes are made by marketing under the FCFS assumption (Seq,3 in Table 4.4). This can be explained as follows. Although

(6,0) (3,1) (0,2)

Sub-case κ ζ Seq,1Seq,2Seq,3 Sim Seq,1Seq,2Seq,3 Sim Seq,1Seq,2Seq,3 Sim 1 0.2 0.05 0.738 0.738 0.742 0.735↓ 0.771 0.771 0.772 0.772↓ 0.774 0.774 0.774 0.774↓ 2 0.2 0.5 0.699 0.699 0.705 0.674↓ 0.710 0.710 0.712 0.708↓ 0.734 0.734 0.734 0.734↓ 3 0.2 0.95 0.632 0.632 0.644 0.617↓ 0.690 0.690 0.693 0.688↓ 0.695 0.695 0.695 0.695↓ 4 0.6 0.05 0.874 0.873 0.882 0.862↓ 0.885 0.885 0.888 0.883↓ 0.888 0.888 0.888 0.883↓ 5 0.6 0.5 0.644 0.642 0.681 0.678↓ 0.712 0.712 0.723 0.729↑ 0.732 0.732 0.733 0.737↑ 6 0.6 0.95 0.561 0.561 0.598 0.511↓ 0.603 0.603 0.613 0.612↓ 0.614 0.614 0.615 0.614↓ 7 1 0.05 0.902 0.902 0.914 0.896↓ 0.912 0.914 0.918 0.916↓ 0.932 0.933 0.933 0.927↓ 8 1 0.5 0.686 0.691 0.730 0.623↓ 0.758 0.761 0.770 0.759↓ 0.786 0.786 0.787 0.772↓ 9 1 0.95 0.616 0.616 0.650 0.553↓ 0.659 0.659 0.666 0.666↓ 0.660 0.660 0.661 0.659↓

Table 4.4On-time probability of orders (η) under the sequential approaches and the simultaneous approach (Case 1: ξL= 0.75,ξp= 0.75)

the firm has the flexibility to prioritize orders optimally, e.g. to give a higher priority to processing an order of a high margin customer, this is not taken into account when making quotes to customers. This leads to making cautious leadtime quotes and to a lower percentage of acceptances than it can potentially be. The failure to efficiently use the potential of extracting a higher revenue from (e.g. LS) customers by making lower leadtime quotes might also lead to more cautious price quotes (e.g.

to PS customers). A lower success in obtaining customers makes it less challenging to achieve high service levels.

4.5. Conclusions

The joint optimization problem of a profit maximizing firm that quotes price/leadtime pairs to two types of prospective customers who differ in their sensitivities to price and leadtime and dispatches placed orders based on the due-dates was investi-gated. The problem was modeled as a Markov decision process (MDP) and the optimal pricing, leadtime quotation and dispatching policy was numerically ob-tained. The optimal policy was compared with different sequential optimization approaches. The results showed that it is close to optimal to process orders based on FCFS when customers are similar in their sensitivity to price and leadtime and the tardiness penalty is proportional to the tardiness. On the other hand, when the tardiness penalty is a fixed cost and the customers are dissimilar in their sensitivity to price and leadtime, considerable inefficiencies result from not harmonizing the price/leadtime quotation decisions with dispatching. We showed that, by consider-ing a joint decision-makconsider-ing approach, the firm can make better (p, L) quotes, i.e.

quotes with a higher acceptance rate, to both customer types and attain higher service levels. The results also highlighted the value of dispatching orders, even if

the flexibility to dispatch orders is not initially taken into account when making (p, L) quotes.

5. Efficiency of Paced and Unpaced Assembly Lines under Consideration of Worker

Variability – A Simulation Study

Incorporating recent findings from behavioral operations, we compare paced and unpaced assembly lines with respect to their steady-state efficiency via simulation.

In particular, workers can speed-up their service times when needed to feed down-stream workers or to unblock updown-stream workers. It is found that unpaced lines are superior to paced lines for many real-world settings, i.e. in mixed-model produc-tion environments with a long line length. However, the benefit they provide has been overestimated in previous studies because of simplifying assumptions such as the disregarding of state-dependent behavior or worker fatigue. With an inhomo-geneous workforce, the efficiency is also sensitive to worker placement. In unpaced conditions, an inexperienced worker should be placed in the middle of the line, while in paced conditions, he should be placed to the first workstation. Workers capable of speed-up should be placed in the middle of the line in both line types.

5.1. Introduction

This chapter compares two types of assembly lines that are widely found in cus-tomization industries such as the automobile industry, a paced line with an auto-mated transportation system and an unpaced line with a manual transportation system. It is motivated by the question: what type is superior in which production environment and how do human characteristics influence this comparison? The pro-posed simulation model extends mathematical approaches for analyzing the impact of human behavior on assembly lines. It also enables the generation of insights into the management of an inhomogeneous workforce.

The chapter is organized as follows. In Section 5.2, the simulation models are introduced, while Section 5.3 presents the results of the simulation study. Section 5.4 concludes and lists directions for further research.