In this paper, bi-level programming is proposed for designing a competitive supply chain network. A two-stage stochastic programming approach has been developed for a multi-product supply chain comprising a capacitated supplier, several distribution centers, retailers and some resellers in the market. The proposed model considers demand’s uncertainty and disruption in distribution centers and transportation links. Then, Stackelberg game is used to formulate the competition among the component of supply chain. A bi-level mixed integer programming is used for developing a supply chain performed currently, then the impacts of the strategic facility location on the operational decisions such as inventory and shipments, have been investigated. To solve the model, we have used Bender’s decomposition algorithm, which is an exact algorithm for solving mixed integer programming. Finally, the outputs of the model are illustrated for investigating the efficiency of proposed model. Then, some discussions have been done through several numerical examples and some managerial insight has been suggested for the situations similar to the assumed problem.

We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is developed. The proposed method of cuts generation, separation and strengthening is compared to the Gomory, linear branching and coordinated cutting plane methods. The computational results show that the proposed method is promising but becomes complicated as number of variables increases.

The present study proposes an integrated model for hub location problem in a Multi-location, Multi-period, Multi-commodity (3M), three echelon supply chain. The problem is formulated as a mixed integer programming model and solved using GAMS software. As the developed model is a mixed integer non leaner programming and NP-hard, a new algorithm for re-formulation is proposed to change it to a mixed integer leaner programming and also a new heuristic algorithms is proposed to solve it in a reasonable time. To prove the applicability of the model, the well-known real CAB data set is used. Numerical examples show the benefit of the proposed model in both solution time and result quality.

Today, many transportation systems use hub and spoke structures to transfer flow (good, message, passenger, etc.) from origin to destination. In such systems, the manager must plan for the location of the hubs and the allocation of other demand points to the hubs and other decisions during the planning horizon. Also, if the planning horizon is continuous time, the manager must also determine the timing of implementing the decisions. To determine the optimal decisions during the planning horizon and the best time for implementing decisions (i.e., breakpoints) according to sustainability aspects. In this research, a mathematical programming model is presented for a sustainable multi-period hub location problem in which the transportation demand between different origin-destination pairs is time-dependent and the planning horizon is continuous-time. The problem is formulated as a nonlinear multi-objective mixed integer programming model. Sustainability aspects are considered as objectives of the model. These objectives are minimizing transportation system costs, minimizing emissions in the transportation network, and maximizing fixed and variable job opportunities created by hubs during the planning horizon. Also, some valid inequalities are presented for strengthening the formulation of the problem. To solve the problem, we first use the Augmented Epsilon Constraint method version 2 (AUGMECON2) and then, use a dynamic programming approach to determine the optimal values of the breakpoints of the planning horizon. Using the proposed dynamic programming method, in each stage, some of decision variables are fixed and the number of variables in the original problem is reduced and instead of a nonlinear mixed integer programming problem, we solve a mixed integer linear programming problem that is easier to solve. The results of the solution methods are presented for a sample problem on the Turkish network dataset. Also, the CAB dataset is used to validate the dynamic programming method. The results show that the dynamic programming approach can solve problems with up to 25 nodes and 6 time periods.

The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper investigates development of a local branching approach for the SCP. This solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. The algorithm parameters are tuned by design of experiments approach. The proposed method is tested on the several standard instances. The results show that the algorithm outperforms the best heuristic approaches found in the literature.

This paper proposes a mixed integer programming model for single-item capacitated lot sizing problem with setup times, safety stock, demand shortages, outsourcing and inventory capacity. Due to the complexity of problem, three meta-heuristics algorithms named simulated annealing (SA), vibration damping optimization (VDO) and harmony search (HS) have been used to solve this model. Additionally, Taguchi method is conducted to calibrate the parameters of the meta heuristics and select the optimal levels of the algorithm’s performance influential factors. Computational results on a set of randomly generated instances show the efficiency of the HS against VDO and SA.

In this paper, a mixed integer programming formulation for flexible flow shop scheduling problem with unrelated machines and sequence dependent setup times is proposed in order to minimize sum of earliness and tardiness. Due to the fact that this problem is NP-Hard, a SA-based heuristic as well as a PSO-based heuristic are proposed to tackle the complexity of the problem. Later, the parameters of these algorithms are set by Taguchi method and then, these meta-heuristic algorithms are compared with each other by 410 test problems. At the end, a number of topics are proposed for future research.

This paper considers a bi-objective mathematical model for locations of landfills, transfer stations and material recovery facilities (MRFs) in order to serve the entire regions and simultaneously identify the capacities of landfills. This is a mixed-integer programming (MIP) model, whose objectives are to minimize the total cost and pollution simultaneously. To validate the model, a numerical example is solved an augmented ε-constraint method and the associated computational results are presented to show the number of solid waste facilities and location of sites for solid waste facilities.

Despite the dynamic nature of real life scheduling problems, few studies focus on stochastic resource constrained project scheduling problem and its variants. In this study, we consider stochastic resource possibilities and propose a new chance constraint, piecewise-linear and mixed integer programming model. Model is tested and verified with known project instances. One of the main strengths of the proposed model is it can be used to construct baseline schedules with a predetermined confidence interval. This gives scheduler an opportunity to construct proactive actions in order to minimize disruptions.

The present study introduced a novel hierarchical hub set covering problem with capacity constraints. This study showed the significance of fixed charge costs for locating facilities, assigning hub links and designing a productivity network. The proposed model employs mixed integer programming to locate facilities and establish links between nodes according to the travel time between an origin-destination pair within a given time bound.