Back to basics: fundamental principles of system dynamics and queueing theory

Ghaffarzadegan and Larson (2018) contend that “many traditional operations research (OR) models can be improved by including feedback processes, as is commonly done in system dynamics (SD) p. 327” modelers build better combining the strengths of both modeling schools. Focusing mainly on queueing theory a fundamental building block Operations Research, they provide compelling examples supporting their claim. Similarly, Lane (1994) argued dialog between soft would mutually beneficial. In this note, I argue principles do not even have to include processes generate useful insights. To achieve this, distill six principles, associated with understanding stocks-and-flows queueing, help managers (and modelers) important insights real settings. The may educators, managers, researchers’ stock-and-flow structures implications practice. For each principle, note describes practical examples, connecting previous literature increasing potential for use teaching modeling. Experimental shows people struggle understand behavior simple systems (Cronin et al., 2009; Sterman, 2010; Sweeney 2000). aspiration broaden cases simple, insightful, easy communicate, impactful dynamic systems. Before considering how appropriately combine we recognize differences. Queueing emerged from need telephone traffic congestion early 1900s. soon expanded study other where random arrivals were processed server (Shortle 2018). interested predicting queue length waiting time queue. Applications range telecommunication engineering industrial hospital service management. While typically focuses long-run stationary (i.e. steady state) systems, transient dynamics, stocks flows represent blocks. However, while are treated similarly differently. (or rates) assumed fixed but probabilistic, variable, deterministic. Stochastic rates critical queuing because sophisticated only emerge input (λ) smaller than (μ)i, when stochastic. deterministic, capturing expected values Interesting deterministic due delays (Barlas Özgün, 2018), i.e. complexity. Little's Law, cornerstone result queuing, dictates relationship Stock (L) flow (e.g. inflow outflow) passing through system. When state, Law establishes long term average value equal product long-term arrival rate residence time, or wait (w) items stock. That is, proportional (λ). also applied infer instantaneous Figure 1 formulations theory. Below, real-world consultancy project, derived knowledge queueing. first two feedback, remaining four do. From these different contexts. draw collaboration Henk Akkermans joint work at Etel, an incumbent mid-sized telecommunications provider. At our engagement, Etel was upgrading its existing copper landline infrastructure fiber, which enabled it offer voice-over internet protocol (VOIP) services installed customer base. Part focused Etel's back-office operations: customers contracted new VOIP services, process activate them. Because automated handle activation (100% quality), allocated minimal capacity (Figure 2a). some contracts had problems literally fall out processing, requiring rework before ready 2b). 2 captures basic structure (adapted Akkermans, 2018; 2016). assumes inflows outflows constant frequently analyses). practice, rarely case. those assumptions allow mathematical tractability, mismatches common place practice lead interesting managerial challenges capture derive mismatch order fallout processing incoming orders) outflow corrections faulty helped determine amount resources capacity) required allocate rework. regular meetings compare list orders been resolved. Still, service-capacity adjustments made mostly reactive mode: hiring firing) based perceived work. 20 weeks operations, high volume fallouts justify decision increase number staff dedicated Afterwards, low justified significantly reduce nature provided estimate human requirements guided managers' firing decisions. 3a data outflows. reduced over felt able address root causes problem. Principle: Proper allows identify behaviors inform specific organizational requirements. Failure comprehend state inadequate A typical insight elementary calculus captured aptly queueing) accumulate imbalance outflows, generating disequilibrium dynamics. systematically, did readily major stocks. asked stock rework, took assisted team consultants, several collect it. track monitor oblivious buildup after week 40 3b). Stocks source information policy Queue influence decisions should taken into consideration. Failing account such shortsighted unanticipated consequences. simplest possible 2000), reasoning error caused poor accumulation known stock–flow failure. An respect rate, higher amounts stock.ii Under proper conditions, management faced changes eventually act stabilize it, raising bringing equilibrium. equilibrium, (L = λw) equilibrium decrease) proportionally affect (L), (w), both. if observe 10% contracting (λ), might backlog contracts) (see 5). Without fallouts, (Lγ). change fractioniii (γ) Hence, rate) fraction quality) outflow). This proportionality deceiving especially (measured absolutes) quality levels percentages). (HR) expectation rates, failure assess impact HR types quality. increased actual dropped (from 90% 80%), total 20%. So, adjusted capacity, They wrongly 20% suffice rate. Focused quality, struggled more double influx problems. Management (due Law) fractional affecting Mistaking multiplicity fractions challenging Previous 2000) resort correlational explain flows, adopting correlation heuristic, conclude “that system's output positively correlated inputs 316” (Sterman, 2010). All else same outflows), results takes hiring, training) make additional available levels, short experience could keep computing ratio (R) resolution Information them evaluate intervention. By keeping inflows, times units Residence measure performance discouraged (Kleinrock, 1975), affects arrivals. state-dependent reinforcing mechanism operate vicious virtuous way, depending level Typically, increases, leads fractions, spiral makes problem very manage. has previously Oliva Sterman (2001). still represents sizable challenge managers. mechanism, fail maintain get control. persistent downstream call complaint handling. realize prevented anticipating calls complaints. directly influences solve But depends whose reworked resulting workload wait. (in primary activation) cascade volumes, secondary handling). further generates Multiplicative effects occur persistence rework). Consider former effect. Customers must company try resolve them, center. As center communicates back office, put pressure rate), workload. effect closes Rework Volume Loop (R2) next latter Orders resolved stay longer prolonged periods multiple so does frequency and, call-center escalate workload, closing Wait (R3) loop. loops multiplicative processes. decision-making heavily compartmentalized, cascades exacerbated. addition, departments communicated shared monthly basis, compounded case, internal company, spill outside partner companies. 7 formulation Due functional boundaries, difficult plan effects. High-level mapping interconnections organizations areas It consider nonlinear parameters time) others addressing complaints). cascading across companies Gonçalves (2018), supplier-delivery cause retailers aggressively beyond demand. distills suggests often “employ heuristics intuitively appealing erroneous 117” 2009), heuristic stock-flow Training help. albeit devoid valuable insight. recognizing state), linkages second principle highlights informational cumulative integrate improve models. critical, interesting, counterintuitive mistaking flows), appropriate dealing levels. times) combines performance) feed presence manage way. Finally, processes), cascade, impacting capacity), prepare preventively avoid situations. industry models, bridging seek generalize illustrated example, applicable operating Overall, resonates Homer (1997) “potent structure” flawed making hope motivate discussion ways am grateful invitation support his Etel. thank Andreas Größler Markus Schwaninger constructive comments suggestions manuscript. errors mine. Open Access Funding Universita della Svizzera Italiana. Paulo Professor Director Humanitarian Group Università italiana (USI), Switzerland. He Research Fellow University Cambridge Judge Business School (CJBS). His simulation, behavioral experiments, optimization, econometrics, strategic, tactical operational humanitarian holds Ph.D. Science System Dynamics MIT Sloan M.Sc. Massachusetts Institute Technology (MIT).