Single Stage (r,Q) Inventory Policy

;; Single stage model, EOQ model

globals [
  setup-price
  unit-price
  unit-holding-cost
  unit-backorder-penalty               ;; These are the given cost parameters
  demand-today
  ]



turtles-own [
  r 
  q 
  on-hand-stock 
  back-order
  inventory-position                   ;; The storage unit follows the (r,Q) policy
  alpha-service-level
  beta-service-level
  pipeline
  
  fixed-order-cost
  variable-order-cost
  inventory-holding-cost
  back-order-penalty
  total-cost
  
  num-filled
  num-missed
  quantity-filled
  quantity-missed
]

to setup
  ca
  
  set setup-price 100
  set unit-price 1
  set unit-holding-cost 0.05
  set unit-backorder-penalty 2
  
  
  set-default-shape turtles "circle"
  crt 1 [
    set color red 
  ]
  ask turtles [
    set on-hand-stock 100
    set back-order 0
    set inventory-position (on-hand-stock - back-order)
    set total-cost 0
    set r re-order-point
    set q order-quantity
    set pipeline n-values lead-time [0]
    set fixed-order-cost 0
    set variable-order-cost 0 
    
    resize-shape
  ]
  reset-ticks
end 

to go
  if ticks >= 1000 [stop]
  update-policy
  set demand-today daily-demand            ;; demand for every day is different
  ask turtles [
    receive
    sell
    replenish
    calculate-service-level
    resize-shape
  ]
  update-plot
  tick
end 

to update-policy
  ask turtles [
    set r re-order-point                 ;; inventory policy can be adjusted on the fly
    set q order-quantity 
  ]  
end 

to-report should-order?
  report inventory-position <= r                     ;; If the inventory position is below reorder point r, we should place an order
end                                                   

to receive
  let amount-received first pipeline                         ;; amount-received equals to the first item in "pipeline" list 
  ifelse back-order > 0                                      
  [
    ifelse back-order >= amount-received                     ;; after receiving the order, update on-hand stock and back-orders
    [
      set back-order (back-order - amount-received)
    ]
    [
      set back-order 0
      set on-hand-stock (amount-received - back-order)
    ]
    
  ]
  [
    set on-hand-stock (on-hand-stock + amount-received)
  ]
end 

to sell
  ifelse on-hand-stock >= demand-today
  [
    set on-hand-stock (on-hand-stock - demand-today)
    set num-filled num-filled + 1
    set quantity-filled (quantity-filled + demand-today)               ;; according to today's demand, update the on-hand stock and back-orders
  ]
  [
    set num-missed num-missed + 1                                      ;; if a demand is not fully met, num-missed + 1
    ifelse on-hand-stock > 0                                           ;; filled demand goes to quantity-filled, unfilled demand goes to quantity-missed
    [
      set quantity-filled (quantity-filled + on-hand-stock)
      set quantity-missed (quantity-missed + demand-today - on-hand-stock)
      
      set on-hand-stock 0
      set back-order (demand-today - on-hand-stock)
    ]
    [
      set quantity-missed (quantity-missed + demand-today)
      
      set back-order (back-order + demand-today)
    ]
  ]
end 

to replenish
  ifelse should-order? [
    set pipeline lput q pipeline                                       
    set fixed-order-cost fixed-order-cost + setup-price
    set variable-order-cost variable-order-cost + unit-price * q
  ]
  [
    set pipeline lput 0 pipeline                                      ;; if place an order, put the order quantity q into pipeline list
  ]
  set pipeline but-first pipeline
  set inventory-position sum pipeline + on-hand-stock - back-order                 ;; note that inventory position = on-hand stock - back-orders + inventory in-transit
  
  set inventory-holding-cost inventory-holding-cost + on-hand-stock * unit-holding-cost
  set back-order-penalty back-order-penalty + back-order * unit-backorder-penalty
  set total-cost (fixed-order-cost + variable-order-cost + inventory-holding-cost + back-order-penalty)
end 

to update-plot
  set-current-plot-pen "on-hand"
  plot sum [on-hand-stock] of turtles              ;; draw inventory profile on the plot
  
  set-current-plot-pen "back-ordered"
  plot sum [back-order] of turtles
end 

to calculate-service-level
  set alpha-service-level num-filled / (num-filled + num-missed)                   ;; alpha-service level is based on times filled
  set beta-service-level quantity-filled / (quantity-filled + quantity-missed)     ;; beta-service level is based on quantity filled
end 

to resize-shape
  set size 0.5 * (sqrt on-hand-stock)          ;; visualize the on-hand stock via size of the turtle
end 

to-report truncated-normal [mean-value std-value min-value max-value]
  let random-num random-normal mean-value std-value
  ifelse random-num > max-value or random-num < min-value
  [report min-value + random-float (max-value - min-value)]
  [report random-num]
end 

to-report daily-demand
;;  report 10
;;  report random-poisson mean-for-poisson             ;; Here we assume that the daily demand follows the Poisson distribution
                                                     ;; with mean specified by the user
                                                     
  report truncated-normal mean-for-normal std-for-normal lower-bound-for-normal upper-bound-for-normal
end