Optimum use of air tankers in initial attack: selection, basing, and transfer rules

X(12 I JI,K2;1,JH) X(K2;I,JH) Z Expect payment for flight time during one day Total annual budget for air tanker operations Guaranteed annual minimum payment for flight time Expect payment for the air tanker through one day Integer variable: I if used as a home base; 0 otherwise Integer variable: I if the air tanker uses the base as home base; 0 otherwise Home base set-up cost Guaranteed, fixed, seasonal payment for air tanker availability Probability that a randomly selected day has the indicated fire day condition Conditional probability of the current fire day condition given the fire day condition of the previous day Index for the air tankers in the system. I = I. .. IMAX Index number for a particular air base in the system Air base at which an air tanker is stationed on the morning when atransfer/use decision is to be made Air base to which an air tanker is transferred following a transfer/use decision Home base number(JH always occurs with I as (I,JH). For example (1,3) indicates that aircraft I has base 3 as its home base) Fire day condition for a particular day Fire day condition on the day preceding the transfer/use decision Fire day condition on the day of the transfer/use decision Expected output of air tanker I transferred to J2 on a day of type K2 A fraction, less than one Expected number of days in the fire season Number of air tankers assigned to a particular air base on any given day Expected number of air tankers assigned to a particular base on any given day Limit on the number of air tankers assigned to a particular base on any given day Total budget available to cover home base set-up costs Joint probability that air tanker I, which has home base JH, will be at air base J I on sarue randomly selected day, that fire condition K2 is observed early the next day and air tanker I is sent to base J2 Conditional probability; transfer rules for the air tanker I Fire day condition probability; equivalent to g(K2) Expected total daily output of the air tanker system Un'lted States Department of Agriculture