We now use the closed-form expression to compare alternative planning systems.
Throughout this section, we make use of a “baseline case” which is based on a real-istic humanitarian context. Our parameter estimates, presented in Table 2.1, were obtained through a questionnaire and a subsequent interview with a logistics expert from one of the humanitarian organizations involved in this study. The question-naire asks for several key metrics describing a “typical program”, and can be found in Appendix 2.E.
Parameter Value Remark
τ 0.544 days Calibrated
η 0.0128
δ 0.25
N 40 Assumption
K 2
C 22 Assumption
λH, λL 10 per day, 10 per day qij 0.75 if i = j, 0.25 otherwise
κH, κL 1/10, 5/70 Not unique
γH, γL 1, 1 Not unique
λR, λP 1/1.5 per day, 1/2 per day
µS 1/0.648 per day Calibrated
Table 2.1: Baseline case parameters.
Our questionnaire results do not yield unique disutility functions. Instead, as suffices for the purpose of our analyses, the questionnaire aims to reveal a realistic quantification of the relative disutility of higher and lower urgency requests. Param-eter τ was chosen such that the average travel time from depot to destination equals the reported value. Mean time on site was estimated by deducting the estimated travel time per request from the reported field delay per request. The reported num-ber of vehicles C was slightly adjusted to obtain a stable queuing system. Finally, our experiments involve solving thousands of VRP instances, for which computa-tion times grow exponentially with N . We therefore restricted ourselves to instances involving up to 40 nodes (i.e., demand points).
The functions Tϕ(N, K, η, δ) we use in our analyses are defined in Table 2.2 and were obtained through least squares fitting (see Appendix 2.C). VRP problem in-stances were solved by applying CPLEX 12.63 to the two-commodity flow formula-tion from Baldacci et al. (2004) combined with rounded capacity inequalities from Lysgaard (2003) and (if applicable) precedence constraints. The solver was pro-grammed in C++ and validated against standard instances from Christofides and Eilon (1969). Our overall experiments were programmed in Matlab R2015a.
Parameter Value # Instances R2
βCV RP [0.782; 21.263; 0.336; 1.451] 12100 0.98
βP C−CV RP [0.809; 21.271; 0.172; 1.803] 12100 0.95 βCL−P C−CV RP [0.840; 20.812; 0.159; 1.607] 12100 0.94
TCV RP(40, 2, 1, 0) 0.237 100
TP C−CV RP(40, 2, 1, 0) 0.251 100
TCL−P C−CV RP(40, 2, 1, 0) 0.247 100
Table 2.2: Fitted travel time functions.
2.4.1 Effectiveness of Systems that Pursue Proxy Objectives
Private sector planning approaches and many planning approaches proposed in the humanitarian logistics literature employ objective functions that are not necessarily in line with humanitarian objectives (Holguín-Veras et al., 2013). This might partly explain the low uptake of such approaches in the humanitarian sector. This section
addresses this hypothesis. Specifically, we compare a system that (to some extent) incorporates perceived urgency levels of requests with a system that makes planning decisions so as to minimize travel times. Travel delay in the first system is estimated using the function TP C−CV RP and queuing delay is estimated based on a priority queuing system (see Section 2.3). Hence, travel times are affected by priority con-straints, and expected queuing delay is smaller in the high priority queue. For the travel time-based system, travel delay is estimated using the function TCV RP and queuing delay is estimated based on a first-come-first-served queuing system. For this system, travel times are not hindered by precedence constraints, which comes at the expense of every request having the same queuing delay distribution.
Two important contextual determinants of the effectiveness of both systems are the travel burden and the observable variation in urgency levels. The larger the travel delay compared to the time on site, the larger the impact of travel time improvements on total delay can be. Similarly, the larger the variations in urgency levels and the better these urgency levels are assessed, the larger the impact of priority-based plan-ning can be. Figure 2.4 depicts how relative effectiveness is affected when observable variation in urgency levels moves from low (qii = 0.5, κH/κL= 1) to high (qii= 1.0, κH/κL = 1.8) and when adapting scaling factor τ and µS such that, in the baseline case, the fraction of field delay spent traveling moves from 1% to 50%. All other parameters remain as described in Tables 2.1 and 2.2. The highlighted point in the figure represents the baseline case.
The results are intuitive yet interesting: (relative) effectiveness is highly context-specific, standard (private sector) objective functions can underperform in some con-texts, but tend to perform comparatively well in many others. For example, our results suggest that the program under consideration would be 9.0% more effective with a travel time-based system than with a priority level-based system. This stresses the importance of carefully analyzing the context before designing a planning system.
More generally, we hypothesize that impact-based planning, which is to make deci-sions so as to minimize expected disutility, only tends to have substantial added value when both the travel burden and the need for prioritization are large. When travel times are small, routing will have little effect on field delays, so focusing on prioritiza-tion solely will yield close to optimal decisions. Similarly, when variaprioritiza-tions in urgency
levels are very small or cannot be observed, there is little a priori need for prioriti-zation, and travel time-based planning will be close to optimal. When both travel times and observable variations in urgency levels are small, routing and prioritization will both have little impact on effectiveness, and a simple heuristic planning policy, e.g. assigning vehicles to requests in the order of requisition, will be close to optimal.
We hypothesize that substantial effectiveness gains could be achieved by jointly op-timizing routing and prioritization only when both travel delays and urgency level variations are large. Furthermore, we hypothesize that software requirements and the need to build specialized software vs. using off-the-shelf software makes impact-based planning substantially more costly than travel time-impact-based planning and priority level-based planning, which will in turn be substantially more costly than heuristic planning. Based on these considerations, we arrive at the context-specific optimal planning approaches hypothesized in Figure 2.5.
Observable variation
Figure 2.4: Disutility increase (%) when im-plementing priority-based planning instead of travel time-based planning. The highlighted point repre-sents the baseline case.
Section 2.2 stresses that information about the operational context is often lacking at a central level. Data-intensive systems might therefore be ineffective in certain
humanitarian contexts. In what follows, we investigate how the quality of travel time data and urgency assessments affects the effectiveness of data-intensive centralized planning systems. We compare a basic travel time-based system that has real-time information about travel times with a system that makes decisions based on expected travel times and prioritizes requests based on assessments of quality qii = q. The first could represent the case when local information from staff and/or drivers is incorporated during planning sessions. For a given stochasticity level δ, travel delay in this system is estimated using the function TCV RP and queuing delay is estimated based on a first-come-first-served queuing system. For the data-intensive system, travel delays are estimated by the function TP C−CV RP with δ = 0 and queuing delays are calculated based on a priority queuing system. Hence, in contrast with the basic system, the data-intensive system is able to incorporate urgency levels into planning decisions. It may, however, encounter increased travel delays due to precedence constraints and due to a gap in information about travel times.
Figure 2.6 depicts the expected increase in disutility when implementing the data-intensive system instead of the basic system, as a function of the quality of informa-tion. Specifically, we let assessment quality and operational uncertainty vary from low (q = 0.5, δ = 0.0) to high (q = 1.0, δ = 1.0). All other parameters remain equal.
Operational uncertainty
Assessment quality 0
High
Low 10
20
Low High
10 15 20
Figure 2.6: Disutility increase (%) when implementing advanced, data-intensive planning in-stead of basic travel time-based planning. The highlighted point represents the baseline case.
The figure shows that data-intensive systems underperform in any of the settings considered, and that the optimality gap can be rather substantial when quality of data
worsens. For example, under current levels of assessment quality and stochasticity, disutility would be 11.6% larger for the data-intensive system. The performance gaps might be smaller when there is more variation in urgency levels and when the basic system also deals with information gaps. Yet, our results point at an important general issue: centralizing decisions and incorporating more information does not necessarily lead to better decisions, particularly when data are imprecise and when local staff is already quite good at making routing decisions. Again, this stresses the importance of context-specific decision making. The next section further investigates optimal planning system hierarchies.
2.4.3 Optimal Level of Centralization
As argued, centralized systems lend themselves well to prioritization but may suf-fer from substantial information gaps and hence suboptimal routing. Decentralized systems are less suited to prioritization, but may have more accurate information.
Hybrid systems combine the strengths of both systems by making routing decisions at the field level, where most information is available, while also incorporate priori-tization. A weakness of this system is that field staff may not be able to optimally incorporate both travel time information and urgency levels. Hence, the planning problem may either need to be simplified, e.g. by taking cluster-based routing deci-sions, or not be solved to optimality.
Again, contextual factors largely determine the relative effectiveness of these sys-tems. Uncertainty determines the size of the information gap centralized systems encounter, urgency levels determine the need for prioritization, and the travel bur-den determines the need for routing optimization. Let us assess how these factors relate to the optimal planning system. As before, we model a centralized system as a priority queuing system basing decisions on expected travel times (i.e., TP C−CV RP for δ = 0.0). A decentralized system is represented by a first-come-first-served queu-ing system with travel time function TCV RP. In the hybrid system, travel delays are based on the function TCL−P C−CV RP and queuing delays are estimated based on a priority queuing system. This system hence represents the case where the cen-tral planner divides destinations into four clusters and lists their priorities whereas
field staff optimizes routes based on actual travel times, clustering, and precedence constraints.
Figure 2.7 depicts how the optimal system changes when the information gap on a centralized level moves from low (δ = 0.0) to high (δ = 1.0) and when the importance of prioritization versus the importance of routing moves from low (qii= 0.5, κH/κL= 1, τ = τ0.50) to high (qii= 1.0, κH/κL = 25, τ = τ0.01). The three areas depicted in the figure will change, e.g., when also the decentralized and hybrid systems deal with information gaps or are incapable of optimizing routes. Yet, the figure supports the general insights drawn before: the optimal planning system is heavily context-specific and centralization does not necessarily lead to better decisions. Given that available decision support models typically assume high levels of centralization (Ortuño et al., 2013; De la Torre et al., 2012), this resonates with our second hypothesis that many of the tools proposed in the literature are not well-suited to the humanitarian context.
Our results more generally hint at the relationship hypothesized in Figure 2.8.
Centralized systems outperform others when information gaps are small and when prioritization is very important. This may well represent the context of emergency medical service provisioning in developed countries, where centralized planning sys-tems are common (Andersson and Värbrand, 2007). When uncertainty increases, hybrid systems are to be preferred, as they both incorporate adequate travel time information and account for urgency levels. This may well reflect disaster relief settings, where both uncertainty and urgency levels are high (Holguín-Veras et al., 2012). Decentralized systems maximize effectiveness when prioritization is relatively unimportant and uncertainty is large, which occurs in development assistance set-tings (Holguín-Veras et al., 2012). Finally, differences in effectiveness will be minor when both uncertainty and the need for prioritization is small, since each system has access to accurate information and yields near-optimal decisions by minimizing travel delays only.
Low High Importance of prioritization vs. routing Low
High
Operational uncertainty
Figure 2.7: Contexts in which centralized (white), hybrid (light grey), and decentralized (dark grey) systems maximize effectiveness.
As follows from the framework depicted in Figure 2.2, optimizing planning and rout-ing decisions is not the only way to increase the effectiveness of a plannrout-ing system.
Alternatives are to reduce request delays, to improve car sharing, and to increase mission lengths (i.e., the number of destinations visited per trip). For decision mak-ers, it is relevant to know the relative potential impact of such adaptations, as this enables them to optimize their project portfolio. Assessment of these alternatives can help up assess our third hypothesis: that innovations other than optimizing planning and routing can yield greater benefit.
In what follows, we assess the impact of the different adaptations by calculating effectiveness of several systems. The first represents a simple travel time-based plan-ning system, which we consider as a default system. The second is a system that makes optimized planning decisions. To obtain a rough estimate of the potential improvement, we consider the case where one can prioritize without losing routing efficiency. That is, we estimate travel times using the function TCV RP and we es-timate queuing delays based on a priority queuing system. In the third system, we adapt mission lengths by increasing the number of destinations per trip from two to three. The fourth is a dedicated system, which splits up the default system into two
parts having C/2 vehicles and arrival rates λi/2. In the fourth system, request delays have been decreased by 50%. Figure 2.9 depicts the expected delays for each of the systems. Note that queuing delays are queue-specific in the optimized scheduling case.
Figure 2.9: Expected delays (days) encountered between generation and fulfillment of a request for different planning systems. Q1 and Q2 denote the high and low priority queue, respectively.
The results indicate that minimizing request delays and optimizing car pooling (i.e., going from a dedicated to a pooled system) are by far the most promising strategies. Compared to the default system, effectiveness increases by 22.82% when reducing request delays and decreases by 17.04% when accounting for the assignment constraints coming with the dedicated system. Increasing mission lengths is beneficial as well, improving effectiveness by 8.28%. Optimized planning, in contrast, increases effectiveness by a mere 0.36%.
Again, one should be careful with generalizing these results to other contexts.
The relative impact of different adaptations will be largely affected by contextual factors like the importance of prioritization. Yet, the order of magnitude of the effects suggests that there are a substantial number of contexts in which issues other than optimizing planning decisions deserve most attention. This also resonates with responses from several of the interviewees, who suggested that the major problems encountered on an operational level are behavioral rather than technical.