Pij probability customers from area i travel to store

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Unformatted text preview: rs, we calculate the probability that customers from area i will visit a particular store j Huff Location Model • Annual customer expenditures for item k at store j can now be calculated. • Pij = Probability customers from area i travel to store j • Ci = Number of customers in area i (e.g. census track) • Bik = Annual budget for product k for customers in area i • m = Number of customer areas in the market region Huff Location Model • Market share of product k purchased at store j can now be calculated Part 6: Queueing System Simplest Possible System • M/M/1 Queue • inter arrival time ~ exp(λ), iid • service time ~ exp(µ), iid • buffer has infinite capacity • every customer get served (FIFO) Formulas More General Systems • G/G/1 Queue ! ! E(Wq ) ⇥ 1 • G/G/N Queue E(Wq ) ⇡ c2 + c2 a s E(S ) 2 ⇢ p 2(N +1) 1 1 ⇢ c2 + c2 E(S ) a s 2 N Calculation of coefficient of variation, formulas Formulae for M/M/n queues ⇢= P0 = /µ (0 < ⇢ < n) 1 ⇣P ⌘ n 1 ⇢i ⇢n + n!(1 ⇢/n) i=0 i! n+1 ⇢ Lq = (n 1)!(n L = Lq + ⇢ W = L/ Wq = Lq / P0 ⇢)2 Nominal load/expected # of busy servers Kill me! Intuitive Little’s law Little’s Law • Formulae ! ! • • Lq = Wq L= W Conditions and Caveats Steady state, ...... (I) Inventory = (R)Flow Rate × (T)Flow Time Part 7: Call Center Management Long Term Planning • # of CSRs to hire and train • r monthly turnover rate • τ time to train an employee (month) • yt # of employees on hand at time t • yj # of employees who finish training at the beginning of month t • ηt # of employees...
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