Mixed-Integer Linear Programming Model by Linear Approximation for a Strike Package-to-Target Assignment Problem

Table 2

Notations for the mathematical model.

Indices	Description sets
	Set of strike package types;
	Set of weapon types;
	Set of target nodes
	Set of base and target nodes;
	Set of aircraft types;
Parameters
	Value of target i
	Probability of survival against enemy threat between nodes i and j
	Probability of destroying target i with weapon
	Distance between nodes i and j
	Flight speed of strike package s
	Maximum flight time of strike package type s
	Offensive mission time for target i of strike package s
	Number of aircraft type k joining in strike package type s
	Maximum sorties of aircraft type k
	Maximum number of weapons for attacking target i
	Amount of loaded weapon on strike package s
	Total number of weapons for the air operation
	Sufficiently large number (Big-M)
Decision variables
	Amount of used weapon for attacking target
	Cumulative usage of weapon of strike package at target
	Time that strike package arrived at target
	Cumulative survival probability until reaching target ;
	Decision variable for the subtour elimination constraints (SECs)