Mixed-Integer Programming Models

Given the heterogeneous nature of supply chains, optimization often cannot be performed with respect to a single objective. Multi-objective programming models seek an optimal solution with regard to multiple objectives. These models rely on judgmental assessment of the relative importance of each objective. 

Generally, as one moves from linear programming to more complex mathematical programming models, the validity of representing real-world problems is improved at the expense of model development and solving simplicity. Specialized model-solving algorithms are often required to solve complex problems. 

---

Grossmann, I. E. and J. Hooker. Logic Based Approaches for Mixed Integer Programming Models and Their Application in Process Synthesis. FOCAPD Proceedings, AIChE Symp. Ser. 96 (323) 70-83 (2000). 

Chemical-industry related literature addressing value chain management focuses on production and supply chain management as well as selectively procurement. Companies in the oil and chemical industries have been leaders for almost 50 years in the development and use of linear and mixed integer programming models to support decision-making at all levels of planning (Shapiro 2004). 

Jimenez, G.A. and Rudd, D.F. (1987) Use of a recursive mixed-integer programming model to detect an optimal integration sequence for the Mexican petrochemical industry. Computers e[ Chemical Engineering, 11, 291. 

A mixed-integer programming model for designing an integration and coordination policy among multiple refineries and a petrochemical network was presented. 

In the steady state case example, because the data were sparse and there were more unknowns than constraining equations, an additional restriction to the linear programming method was needed. This was done by utilizing a mixed integer-programming model such as in a stepwise multiple regression solution. In the multiple regression method, the identification problem was formulated as follows ... 

Shelton, M. R., and Grossmann, I. E. Optimal Synthesis of Integrated Refrigeration Systems. I Mixed-integer Programming Model, Comput. Chem. Eng. 10, 445 (1986a). 

K.L. Croxton and B. Gendron and T.L. Magnanti, A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems. Management Science, 49, 9 (2003) 1268-1273... 

Considering that Beta s main objective of its restructuring plan is the maximization of a potential cost saving accrued from centralization of warehouses, we propose a single-objective, mixed-integer programming model as our decision-aid tool. The proposed model is designed to find the optimal number of warehouses in the restructured network under capacity limits and service requirements. 

To address the above issues systematically, we develop a mixed-integer programming model that... 

This problem is extensively studied in the hterature with various solution methods and several modelling approaches. One of the first Mixed Integer Programming models for the problem was developed by Manne [7] in 1960 and adopted here as described by Conway et al. [2]. 

Demirel NO, Gokfen H (2008) A mixed integer programming model for reananufacturing in reverse logistics environment. Int J Adv Manuf Technol 39 1197-1206... 

The mixed integer programming models of Chen et al. (2000, 2001) includes constraints for order promising and fulfillment, finished product inventory, material/component inventory, material requirements, capacity utilization, and material compatibility. We highlight the major constraints as follows. 

Looking ahead, this type of quantity discount structure also appears in Chapter 5, where we discuss techniques for representing this "all-unit-discount" cost structure in mixed-integer programming models. 

The above model contains many parameters and constraints, which makes it a large-scale and complex stochastic linear mixed integer programming model. The components of the model are described and explained as follows ... 

In addition to other real variables, the model also has 0-1 decision variables. Therefore, the model is a typical chance-constrained mixed integer programming model. 

The above model is a large-scale fiizzy random linear mixed integer programming model with many parameter and restrictions. The explanation of the components is as follows ... 

Mathematical programming is the most prominent tool used in supply chain configuration, specifically for establishing the supply chain network, because of its ability to deal with spatial issues effectively. This chapter presents the generic mixed-integer programming model used in configuration. Application of this... 

The authors have formulated the problem as a mixed integer programming model as follows firstly defining the parameters and variables ... 

In this paper, we study an SET with sequence-dependent setup times and job release times. First of all, we present a mixed integer programming model for the problem. But it is well known that the SET is NP-hard (Baker and Scudder 1990 Garey et al. 1988), and then, a big-sized problem cannot be solved in a reasonable computation time. Therefore, we concentrate on developing heuristics, by which not optimal but good solution for realistic big-sized problem can be acquired in a reasonable computing time. 

---