This paper provides insights into assessing customer relationships in a revenue management environment and depicts methodological problems that may arise in this context. For this purpose, we formulate a multi-period deterministic linear programing model, which accounts for customers’ future demand behavior being dependent on the provider’s previous availability decisions. Moreover, on the basi...

We present an extension of the Simplex method for solving problems with piecewise-linear functions of individual variables within the constrains of otherwise linear problems. This work generalizes a previous work of Fourer that accommodate piecewise-linear terms in objective functions. The notion of nonbasic variable is extended to a variable fixed at a breakpoint. This new algorithm was implem...

Prescription charts are not designed with the task of programing medical devices in mind [cf. 1]. This is surprising because we know that charts need to be consulted for programing values. This paper summarizes what we know about chart design, and then reflects on what we do not know. In order to design charts that facilitate programing, we need a better understanding of how they are used in ho...

This paper designs a reliability distribution network with limited capacity under partial and complete facility disruptions. To increase the reliability of the distribution network, a new mixed integer linear programing model is developed by considering multiple mitigation strategies including diversification, fortification, and transshipment. The distribution network constitutes of reliable di...

In this short note we answer two questions that naturally arise while dealing with Hoffman’s celebrated 50-years-old cycling example for the primal simplex method to solve linear programs, where an angle θ and a scaling factor ω are adjustable parameters in his example. In particular, we determine what conditions have to be imposed on ω for cycling to occur with θ = 2π/5, and what on θ with |ω|...

in the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. in the second part we discuss some recent developments concurring the simplex algorithm. we describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.