Incorporating uncertainty in optimal decision making: Integrating mixed integer programming and simulation to solve combinatorial problems

C.T. Bauer College of Business, Department of DISC, 334 Melcher Hall, 4800 Calhoun Road, University of Houston, Houston, TX 77204-6021, USA
Computers & Industrial Engineering (Impact Factor: 1.78). 02/2009; 56(1):106-112. DOI: 10.1016/j.cie.2008.04.003
Source: DBLP


We introduce a novel methodology that integrates optimization and simulation techniques to obtain estimated global optimal solutions to combinatorial problems with uncertainty such as those of facility location, facility layout, and scheduling. We develop a generalized mixed integer programming (MIP) formulation that allows iterative interaction with a simulation model by taking into account the impact of uncertainty on the objective function value of previous solutions. Our approach is generalized, efficient, incorporates the impact of uncertainty of system parameters on performance and can easily be incorporated into a variety of applications. For illustration, we apply this new solution methodology to the NP-hard multi-period multi-product facility location problem (MPP-FLP). Our results show that, for this problem, our iterative procedure yields up to 9.4% improvement in facility location-related costs over deterministic optimization and that these cost savings increase as the variability in demand and supply uncertainty are increased.

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    • "Then, the feedback works two ways: too high service times lead to more strict capacity constraints in the MIP, too low service times lead to less strict constraints. Acar et al. (2009) give a generalized procedure for simulation feedback for optimization under uncertainty. They develop a general MILP formulation , for which firstly a deterministic solution is determined. "
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    ABSTRACT: Dynamics in product quality complicate the design of logistics networks for perishable products, like flowers and other agricultural products. Complications especially arise when multiple products from different origins have to come together for processes like bundling. This paper presents a new MILP model and a hybrid optimization–simulation (HOS) approach to identify a cost-optimal network design (i.e. facility location with flow and process allocation) under product quality requirements. The MILP model includes constraints on approximated product quality. A discrete event simulation checks the feasibility of the design that results from the MILP assuming uncertainties in supply, processing and transport. Feedback on product quality from the simulation is used to iteratively update the product quality constraints in the MILP. The HOS approach combines the strengths of strategic optimization via MILP and operational product quality evaluation via simulation. Results, for various network structures and varying degrees of dynamics and uncertainty, show that if quality decay is not taken into account in the optimization, low quality products are delivered to the final customer, which results in not meeting service levels and excess waste. Furthermore, case results show the effectiveness of the HOS approach, especially when the change from one iteration to the next is in the choice of locations rather than in the number of location. It is shown that the convergence of the HOS approach depends on the gap between the product quality requirements and the quality that can be delivered according to the simulation.
    Computers & Industrial Engineering 10/2015; 88:26-38. DOI:10.1016/j.cie.2015.06.017 · 1.78 Impact Factor
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    • "Similar to our problem, Syam (2008) formulates a facility location model with staff allocation considerations in order to minimize the expected waiting times in the service facilities and uses a Lagrangian relaxation method to solve the problem. We use a similar optimization framework as Vardar et al. (2006) and Acar et al. (2009) to locate POD sites with uncertain performance to design a robust response system for a major public health concern. An emergency such as an influenza outbreak or a bioterrorist attack may require PODs to perform well on several performance measures. "
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    ABSTRACT: We formulate a p-median facility location model with a queuing approximation to determine the optimal locations of a given number of dispensing sites (Point of Dispensing-PODs) from a predetermined set of possible locations and the optimal allocation of staff to the selected locations. Specific to an anthrax attack, dispensing operations should be completed in 48 hours to cover all exposed and possibly exposed people. A nonlinear integer programming model is developed and it formulates the problem of determining the optimal locations of facilities with appropriate facility deployment strategies, including the amount of servers with different skills to be allocated to each open facility. The objective of the mathematical model is to minimize the average transportation and waiting times of individuals to receive the required service. The mathematical model has waiting time performance measures approximated with a queuing formula and these waiting times at PODs are incorporated into the p-median facility location model. A genetic algorithm is developed to solve this problem. Our computational results show that appropriate locations of these facilities can significantly decrease the average time for individuals to receive services. Consideration of demographics and allocation of the staff decreases waiting times in PODs and increases the throughput of PODs. When the number of PODs to open is high, the right staffing at each facility decreases the average waiting times significantly. The results presented in this paper can help public health decision makers make better planning and resource allocation decisions based on the demographic needs of the affected population.
    Biocontrol Science and Technology 10/2014; 4(4). DOI:10.1080/19488300.2014.965394 · 0.94 Impact Factor
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    ABSTRACT: Closure of facilities is quite common among both business firms and public sector institutions like hospitals and schools. Although the facilities location problem has been studied extensively in the literature, not much attention has been paid to the closure of facilities. Unlike the location problem, the existing facilities and the corresponding network impose additional constraints on the closure or elimination of facilities and to highlight the difference between the two, we have called this the facilities delocation problem. In this article, we study a firm with an existing distribution network with known retailer and distributor locations that needs to downsize or shrink its distribution chain due to other business reasons. However, it is not a reallocation of demand nodes among the retained distributors. An important condition stipulates that all demand nodes must continue to get their supplies from their respective current distributors except when the current source itself is delocated, and only such uprooted demand nodes will be supplied by a different but one of the retained suppliers. We first describe the delocation problem and discuss its characteristics. We formulate the delocation problem as an integer linear programming problem and demonstrate its formulation and solution on a small problem. Finally, we discuss the solution and its implications for the distribution network.
    International Journal of Systems Science 03/2010; 41(3):271-280. DOI:10.1080/00207720903326860 · 2.10 Impact Factor
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