In constrast to "ordinary" sensitivity analysis in linear programming, the tolerance approach considers simultaneous and independent changes in the objective function coefficients and in the right-hand side terms. This approach yields a maximum tolerance percentage such that, as long as selected...

Redundant constraints are constraints that can be omitted from a system of linear constraints without changing the feasible region. Implicit equalities are inequality constraints that can be replaced by equalities without changing the feasible region. We prove some theorems concerning the...

We develop a production planning model in the context of a system of assembly lines or production lines. The model is a large-scale linear program and we provide a polynomial column generation technique for its efficient solution. The column generation technique and the approach therein are also...

Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large-scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice. Multilevel...

Modelling planning problems that extend over many time periods as linear programs leads to a special structure called a "staircase" or "dynamic" linear program. In this special structure, the nonzero coefficients of the linear program appear in blocks along the "main diagonal" of the coefficient...

In this paper we consider a certain aggregate production planning model. This model permits regular and overtime production and allows for backordering of goods for a number of periods. Although the discussed model can be formulated as a linear programming problem a special (noniterative) method...

The attainment and enforcement of air quality standards is a complicated process. A crucial element in this process is the measurement of ambient air quality. The selection of locations for a limited number of monitors and their sampling frequencies is an important problem in the design of a...

An embedded network within a linear program is, roughly speaking, a subset of constraints that represent conservation of flow. We examine three broad classes of heuristic techniques---row-scanning deletion, column-scanning deletion, and row-scanning addition---for the extraction of large...

We pose the following problem: given m jobs, each of which requires a certain total amount of labour that must be performed within specified time periods, how should one schedule the jobs' execution to obtain a total workload that is as even as possible? A related question is: what is the...

Shift and days-off scheduling problems have received much attention in the literature of integer programming approaches to workforce scheduling. A typical managerial use would be to schedule full-time employees to minimize the number of labor hours while satisfying variable workforce...