## Solving Multiplicative Programs by Binary-encoding the Multiplication Operation

Multiplicative programs in the form of maximization and/or minimization have numerous applications in conservation planning, game theory, and multi-objective optimization settings. In practice, multiplicative programs are challenging to solve because of their multiplicative objective function (a product of continuous or integer variables). These challenges are twofold: 1. As the number of factors in the objective … Read more

## Mixed-Integer Linear Programming for Scheduling Unconventional Oil Field Development

The scheduling of drilling and hydraulic fracturing of wells in an unconventional oil field plays an important role in the profitability of the field. A key challenge arising in this problem is the requirement that neither drilling nor oil production can be done at wells within a specified neighborhood of a well being fractured. We … Read more

## Extended formulations for convex hulls of some bilinear functions

We consider the problem of characterizing the convex hull of the graph of a bilinear function \$f\$ on the \$n\$-dimensional unit cube \$[0,1]^n\$. Extended formulations for this convex hull are obtained by taking subsets of the facets of the Boolean Quadric Polytope (BQP). Extending existing results, we propose the systematic study of properties of \$f\$ … Read more

## A polynomially solvable case of the pooling problem

Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border … Read more

## Discrete flow pooling problems in coal supply chains

The pooling problem is a nonconvex nonlinear programming problem (NLP) with applications in the refining and petrochemical industries, but also the coal mining industry. The problem can be stated as follows: given a set of raw material suppliers (inputs) and qualities of the supplies, find a cost-minimising way of blending these raw materials in intermediate … Read more

## A special case of the generalized pooling problem arising in the mining industry

Iron ore and coal are substantial contributors to Australia’s export economy. Both are blended products that are made-to-order according to customers’ desired product qualities. Mining companies have a great interest in meeting these target qualities since deviations generally result in contractually agreed penalties. This paper studies a variation of the generalized pooling problem (GPP) arising … Read more

## New multi-commodity flow formulations for the pooling problem

The pooling problem is a nonconvex nonlinear programming problem with numerous applications. The nonlinearities of the problem arise from bilinear constraints that capture the blending of raw materials. Bilinear constraints are well-studied and significant progress has been made in solving large instances of the pooling problem to global optimality. This is due in no small … Read more