ACTIVITY ANALYSIS

Activity analysis - This is an approach to micro-economics, where a system is composed of elementary functions, called activities, which influenced the early growth of linear programming . When using the LP form: Min(cx: x >= 0, Ax >= b), an insightful way to view an activity is that negative coefficients represent input requirements and positive coefficients represent outputs:

 _____ | c_j | <--- cost or revenue |-----| | - | <--- input to activity j | | |-----| | + | <--- output from activity j |_____| 

In general, the reduced cost   then represents the net worth of the activity for the prices , p:   This leads to an economic interpretation not only of LP, but also of the simplex method : agents (activity owners) respond instantaneously to changes in prices, and the activity with the greatest net revenue wins a bid to become active (basic), thus changing the prices for the next time (iteration). In this context, activities can be regarded as transformations, from inputs to outputs. Three prevalent transformations are: form, place and time. Here are examples:

 blend transport inventory _____ _____ _____ | c | | c | | c | |-----| |-----| |-----| |-.4 | apples | -1 | Chicago | -1 | t |-.6 | cranberries |-----| |-----| |-----| | .6 | Denver | 1 | t+1 | 1 | cranapple | .4 | Seattle | | |_____| |_____| |_____| Transformation Transformation Transformation of form of place of time