Further counterexamples to the monotonicity property of t-step maintainable structures

Abstract

Until Guerry's (1990) counterexample to a conjecture of Davies about three-state hierarchical organisations kept at constant size via annual promotion, wastage and recruitment, it was easy to believe that such structures maintainable in t steps would also be maintainable in t + 1 steps. Here we present further counterexamples, which show that t-step maintainability does not imply (t + 1)-step maintainability, for astonishingly large values of t.

Evaluating Recruitment Strategies Using Fuzzy Set Theory in Stochastic Manpower Planning

“…In order to attain a desired stock vector it is important to deal with the problem of controlling parameters. In previous work attainability is studied in a deterministic approach, among under other conditions, under control by promotion and control by recruitment [2,12,13,14,15,16,17,18,19,20].…”

“…This enables organizations to investigate the impact of a recruitment and/or promotion policy on the future personnel stocks and if necessary, to adapt it in order to reach or approach the desired class sizes in the future. A lot of research is done on the so called attainability and maintainability problem of a desired personnel stock vector under control by recruitment and control by promotion [12,13,14,15,16,17,18,19,20]. This discussion in most research is restricted to an embedded Markov chain model, implying that the total number of individuals in the system is known (e.g.…”