A review of mathematical models for supporting the order promising process under Lack of Homogeneity in Product and other sources of uncertainty

•The OPP combined with LHP is little researched.•The OPP with uncertainty conditions in variables is little researched.•The OPP combined with LHP and uncertainty becomes a research stream. This paper presents a review of mathematical programming models for supporting the order promising process (OPP) under Lack of Homogeneity in Product (LHP) conditions and uncertainty in a modelling approach. LHP appears in productive processes with raw materials, which directly stem from nature and/or production processes with operations that confer heterogeneity to the characteristics of the outputs obtained, even when the inputs used are homogenous. LHP has a direct impact on the company’s service level, mainly when the customer needs to be served with homogeneous units of the same product. LHP leads to inherent sources of uncertainty due to the natural physical characteristics of the supply chain. This research aims to determine the way that LHP, and uncertainties related either to LHP or different variables that confer more realistic conditions to OPP, have been modelled in different LHP sectors, or others affected by uncertainty. This result may provide the opportunity to transfer knowledge among them and to identify gaps for further research. Accordingly, and in order to set the basis for future research into the OPP topic, for cases affected by LHP and for uncertainties inherent to LHP conditions, or due to other possible uncertain variables, this research needs to consider both mathematical model types: (i) mathematical programming models of the OPP that consider some LHP characteristic and (ii) mathematical programming models of the OPP that consider any type of uncertainty in the modelling approach. We propose a taxonomy approach to classify and analyse the literature based on the main characteristics of its environment, order promising approach, customer order characteristics, modelling characteristics, and LHP and uncertainty modelling. The main finding of this research was that research into OPP modelling, combined with LHP characteristics and uncertainty, are lacking. We provide some starting points for further research in this field.