breed [ arrow ] breed [ customer ] customer-own [reqd-items items state express check-out tagged face-to] patches-own [wall invisible-barrier] globals [time-to-next-customer revenue store-cost customer-cost average-wait defectors wage profit waiting-time customers-served checkout-x checkout-y offset door-x door-y checkout-inc first-till-y ;; y coord of first till below exit tills queues shelves ] to setup ca set-current-plot "Revenue and Cost" clear-plot set-current-plot "Average Waiting Time" clear-plot set time-to-next-customer 0 set revenue 0 set store-cost 0 set customer-cost 0 set average-wait 0 set waiting-time 0 set customers-served 0 set defectors 0 set checkout-x -10 set checkout-y -14 set door-x -17 set door-y 14 set first-till-y 12 set checkout-inc (world-height + min-pycor + first-till-y) / num-checkouts set wage 1 set profit 5 random-seed 47823 set-default-shape turtles "person" ;; setup the patches ask patches [set pcolor white] draw-walls end to draw-walls ask patches [set wall false] ;; draw left and right walls ask patches with [abs pxcor = max-pxcor] [ set pcolor blue ] ;; draw top and bottom walls ask patches with [abs pycor = max-pycor] [ set pcolor blue ] ;; paint the checkout line blue ask patches [ if ((abs (pxcor - checkout-x) < 2) and (pycor != door-y)) ;; patches on the checkout line [ set pcolor blue ] ] ;; put the supermarket entry door in ask patch-at door-x door-y [ set pcolor white ] ;; put the supermarket exity door in ask patch-at door-x (- door-y) [ set pcolor white ] ;; debug statements ;type "checkout-inc " ;print checkout-inc ;type "screen-edge-y " ;print screen-edge-y ;type "screen-size-y " ;print screen-size-y ;; put num-checkout grey till lanes into the patches set tills patches with [(floor((pycor + max-pycor) mod checkout-inc) - 1 = 0) and (pycor < first-till-y ) and (abs (pxcor - checkout-x) < 2) ] ask tills [ set pcolor 7 ] ;; set color grey ;; put num-checkout queues into the patches set queues patches with [(floor((pycor + max-pycor) mod checkout-inc) - 1 = 0) and (pycor < first-till-y ) and (pxcor = checkout-x + 2) ] ask queues [ set pcolor 75 ] ;; set color teal ;; draw shelves set shelves patches with [(floor((pycor + max-pycor + 1) mod 5) <= 1) and abs (pycor) < max-pycor - 3 and pxcor < max-pxcor - 5 and pxcor > (- 4)] ask shelves [ set pcolor 35 ;; set color brown set wall true] ;; shelves are walls ask patches with [pcolor = blue] [set wall true] ;; blue walls are now identified ask patches with [pxcor <= -9] [set invisible-barrier true] ;; this invisible barrier keeps shoppers inside the shops ;; draw arrows in and out of supermarket create-custom-arrow 1 [set color green set shape "default" setxy door-x door-y set heading 90] create-custom-arrow 1 [set color red set shape "default" setxy door-x (- door-y) set heading 270] ;; draw Target logo create-custom-arrow 1 [set color white set shape "target2" set size 3 setxy -14 14] ;; draw Express lane if (express-lane) [ create-custom-arrow 1 [ set color black set shape "x" set size 1.5 setxy -9.5 10.1 ] ] end to go ;; turtle procedure if (time-to-next-customer <= 0) [spawn] move-queues ask customer [customer-move] set time-to-next-customer (time-to-next-customer - 1) ;print time-to-next-customer remove-customer set store-cost (store-cost + wage * num-checkouts) do-plot end to spawn create-custom-customer 1 ;; create 1 new customer [ set state 1 ;; state 1 = going shopping set items 0 set check-out 0 setxy door-x door-y set heading 90 set size 1.7 ;set tagged false ifelse (random 100 < 70) ;; only 30% of shoppers are express [ set express false set reqd-items (floor(random-normal 10 2)) set color 136 ] [ set express true ; set reqd-items (random 4) set reqd-items (random 2) set color 16 ] ;; chance of defecting if all queues are full or average wait longer than the time it takes to process shopping (= reqd-items) if (reqd-items < average-wait) or (not any? patches with [pcolor = 75 and (count customer-here = 0)]) [ ifelse (express and Express-lane) [] ;; if there is an express lane then express shoppers will not defect. [ ;; defect with probability 0.9 if (random 100 < 90) [ fd 2 set state 5 set defectors (defectors + 1) ] ] ] ] set time-to-next-customer (random-exponential 5) end to customer-move locals [dest] if (state = 5) ;; leaving the shop now [ ifelse (patch-here = patch door-x (- door-y)) [ ; remove-customer ] [ facexy-nowrap door-x (- door-y) fd 1 ;customer-collision-movement ] ] if (state = 4) [ ifelse (pcolor = 7) [ set check-out (check-out + 1) set revenue (revenue + profit) if (check-out >= reqd-items) [ set state 5 ;; state is now heading for the exit facexy-nowrap door-x (- door-y) ] ] ;; customer must be standing in the queue [ set waiting-time (waiting-time + 1) ] ] if (state = 3) [ ifelse (pcolor = 75 or pcolor = 7) [ ;type "in the queue, agent " print who set state 4 ;; state is now in the queue set heading 270 ] [ ;fd 1 customer-collision-movement ] ] if (state = 2) [ ;check to see if the customer has reached to ;one of the target goal squares then pick up the item set dest face-to if any? neighbors with [pxcor = (pxcor-of dest) and pycor = (pycor-of dest)] [ set items (items + 1) set face-to (one-of patches with [pcolor = 35]) facexy-nowrap pxcor-of face-to pycor-of face-to ] if (items >= reqd-items) [ set state 3 ;; state is now checking out set face-to (min-one-of patches with [pcolor = 75] [count turtles-here]) ;randomly select a checkout with the shortest length queue facexy-nowrap pxcor-of face-to pycor-of face-to ] customer-collision-movement ; Alex's dodgy old code for state = 2 ; if any? neighbors with [pcolor = 35] ; [ ; set items (items + 1) ; set face-to (random-one-of patches with [pcolor = 35]) ; facexy-nowrap pxcor-of face-to pycor-of face-to ; ] ; if (items >= reqd-items) ; [ ; set state 3 ;; state is now checking out ; set face-to (min-one-of patches with [pcolor = 75] [count turtles-here]) ; facexy-nowrap pxcor-of face-to pycor-of face-to ; ] ; fd 1 ] if (state = 1) ;; agent going into the shops [ ifelse (patch-here = patch (- 6) 14) [ set state 2 ;; change to collecting items set face-to (one-of patches with [pcolor = 35]) facexy-nowrap pxcor-of face-to pycor-of face-to ] [ facexy-nowrap -6 14 ] fd 1 ] end to bounce ;; turtle procedure to rebound off the blue patches...a bit hacky for the reflecting of the x-axis since we never bounce off the -ve x-axis ; check: hitting left or right wall? if (abs pxcor-of patch-ahead 1 = max-pxcor) ; if so, reflect heading around x axis [ set heading (- heading) ] ; check: hitting top or bottom wall? if (abs pycor-of patch-ahead 1 = max-pycor) ; if so, reflect heading around y axis [ set heading (180 - heading) ] end to customer-collision-movement locals[forward-patch willCollide doneCollisionMovement goleft num degrees] set willCollide false set doneCollisionMovement false set goLeft false set num 0 set degrees 2 ;check to see if the customer is about to collide with a patch that is a ;shelf or the wall set forward-patch patch-ahead 1 ;we just rebound off a blue patch ifelse pcolor-of forward-patch = blue [ bounce ] ;for shelves we use our AutoMagical(TM) collision avoidance algorithm [ if forward-patch = nobody or wall-of forward-patch = true [ set willCollide true ] ;if I'm going to collide with the shelf patch ahead of me if (willCollide) [ ;then rotate left or right depending on which patch is free if (wall-of (patch-left-and-ahead degrees 1) = true) [ set goleft false ] ;while we are going to collide rotate until we find a direction we can move ;unobstructed while[(wall-of patch-ahead 1) = true and num <= (360 / degrees)] [ ifelse goleft [ left degrees ] [ right degrees ] set num (num + 1) ;this num is so that we don't go into an infinite loop ;this line just makes it so that it picks a random direction if it gets really stuck if num > (360 / degrees) [ left (random 360) ] ] set doneCollisionMovement true ] if any? neighbors with [wall = true] [ set doneCollisionMovement true ] if not doneCollisionMovement [ if not (face-to = 0.0) [ facexy-nowrap pxcor-of face-to pycor-of face-to ] ] ] fd 1 end to move-queues locals [till-occupied] set till-occupied false ask patches with [pcolor = 75] [ ask patch-at -3 0 [ if (any? turtles-here) [set till-occupied true] ] if((not till-occupied) and (any? turtles-here)) [ ask n-of 1 customer-here [ set heading 270 fd 3 ] set customers-served (customers-served + 1) ;set waiting-time (waiting-time - 1) ] ] end to remove-customer ask customer with [abs(xcor - door-x) <= 1 and abs(ycor - (- door-y)) <= 1] [die] end to do-plot set-current-plot "Revenue and Cost" set-current-plot-pen "cost" plot store-cost set-current-plot-pen "revenue" plot revenue ;set-current-plot-pen "profit" ;plot revenue - store-cost ifelse (customers-served = 0) [ set average-wait 0 ] [ set average-wait (waiting-time / customers-served) ] set-current-plot "Average Waiting Time" set-current-plot-pen "waiting time" plot average-wait set-current-plot-pen "defectors" if (customers-served != 0) [ plot (defectors / customers-served * 100) ] end @#$#@#$#@ GRAPHICS-WINDOW 303 10 733 461 17 17 12.0 1 10 1 1 1 0 1 1 1 -17 17 -17 17 CC-WINDOW 5 616 1197 711 Command Center 0 BUTTON 29 55 100 88 Setup setup NIL 1 T OBSERVER T NIL BUTTON 35 120 98 153 Go go T 1 T OBSERVER T NIL SLIDER 39 199 211 232 num-checkouts num-checkouts 1 10 4 1 1 NIL SWITCH 38 261 181 294 Express-lane Express-lane 1 1 -1000 BUTTON 121 119 184 152 Step go NIL 1 T OBSERVER T NIL PLOT 776 26 1188 323 Revenue and Cost time dollars 0.0 10.0 0.0 10.0 true false PENS "profit" 1.0 0 -13345367 true "cost" 1.0 0 -2674135 true "revenue" 1.0 0 -10899396 true PLOT 783 356 1164 602 Average Waiting Time NIL NIL 0.0 10.0 0.0 10.0 true false PENS "waiting time" 1.0 0 -16777216 true "defectors" 1.0 0 -2674135 true @#$#@#$#@ WHAT IS IT? ----------- This model simulates a supermarket in order to assess the revenue and costs when different numbers of checkouts are open. If too few checkouts are open, then the queues fill up, the waiting times become excessive and customers defect rather than entering the store. If too many checkouts are open, then the revenue will never offset the wage costs of all the checkout chicks. HOW IT WORKS ------------ Shoppers arrive according to an exponential distribution. They may be one of two types: express shoppers, who only have a few items to collect; or normal shoppers, who intend to do a full shop. The number of items express shoppers collect is drawn from a uniform distribution, while normal shoppers use a normal distribution with a significantly larger mean. Once they are in the store, shoppers randomly select a square on the shelves. This represents an item they must collect. They must then navigate between the shelves to collect that item. This uses a collision aviodance algorithm to avoid the shelves and the walls, although no attempt is made to avoid other customers. Once they have the item, they cross it off their list and select another square of shelving at random. This simulates the way Martin shops. Once they have collected the desired number of items, the proceed to the checkout. They select the checkout with the shortest queue, measured by the number of shoppers. The rate of processing at the checkout is proportional to the number of items. Once the checkout is complete the agents walk to the door, at which point they are killed off. HOW TO USE IT ------------- The control parameter is the number of available checkouts. Slide this between 1 and 10 to see the effect on revenue, cost and waiting time. THINGS TO NOTICE ---------------- Observe the nonlinear behaviour when the number of checkouts = 1. Initially, revenue increases very steeply, but soon the queue expands, waiting times grow and almost all the customers defect. The supermarket becomes very empty and revenues stagnate, until the waiting times fall and some of the customers return. Analytic results from queuing theory cannot capture this kind of behaviour. THINGS TO TRY ------------- Try a behaviour space exploration over the control parameter. Graph the revenue and cost to find the number of checkouts that maximises profit. Graph the waiting times against the number of checkouts. Try commenting out the set random seed line in the code, so the model gives different results each run. EXTENDING THE MODEL ------------------- The express lane has not been fully implemented in this model. If the button is set to on, this does mean that express shoppers are less likely to defect. However, it would be nice to set aside one aisle as express only. Then see if the optimum solution is to have an express aisle to reduce the waiting time for express shoppers. There is no feedback between customer experience and new arrival times. If customers had to wait a long time, they would be expected to be less likely to return. Try making the arrival rate depend on customer experience to see if the supermarket should keep more checkouts open in this scenario. CREDITS AND REFERENCES ---------------------- Model developed by Alex Ryan and Martin Wong. The problem was conceived by Simon Angus for the Beyond the Metaphor course on the mathematics of complex systems, held at the University of New South Wales in February 2007. http://www.maths.unsw.edu.au/news/2006/complexcourse.html @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 link true 0 Line -7500403 true 150 0 150 300 link direction true 0 Line -7500403 true 150 150 30 225 Line -7500403 true 150 150 270 225 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line 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210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 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150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon 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