A global MILP model for FMS scheduling

Flexible manufacturing systems (FMS) require intelligent scheduling strategies to achieve their principal benefit — combining high flexibility with high productivity. A mixed-integer linear programming model (MILP) is presented here for FMS scheduling. The model takes a global view of the problem and specifically takes into account constraints on storage and transportation. Both of these constrained resources are critical for practical FMS scheduling problems and are difficult to model. The MILP model is explained and justified and its complexity is discussed. Two heuristic procedures are developed, based on an analysis of the global MILP model. Computational results are presented comparing the performance of the different solution strategies. The development of iterative global heuristics based on mathematical programming formulations is advocated for a wide class of FMS scheduling problems.     

A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows

This paper presents a novel three-phase heuristic/algorithmic approach for the multi-depot routing problem with time windows and heterogeneous vehicles. It has been derived from embedding a heuristic-based clustering algorithm within a VRPTW optimization framework. To this purpose, a rigorous MILP mathematical model for the VRPTW problem is first introduced. Likewise other optimization approaches, the new formulation can efficiently solve case studies involving at most 25 nodes to optimality. To overcome this limitation, a preprocessing stage clustering nodes together is initially performed to yield a more compact cluster-based MILP problem formulation. In this way, a hierarchical hybrid procedure involving one heuristic and two algorithmic phases was developed. Phase I aims to identifying a set of cost-effective feasible clusters while Phase II assigns clusters to vehicles and sequences them on each tour by using the cluster-based MILP formulation. Ordering nodes within clusters and scheduling vehicle arrival times at customer locations for each tour through solving a small MILP model is finally performed at Phase III. Numerous benchmark problems featuring different sizes, clustered/random customer locations and time window distributions have been solved at acceptable CPU times.     

A Tabu Search Heuristic Procedure for Solving the Transportation Problem with Exclusionary Side Constraints

A new heuristic procedure for the transportation problem with exclusionary side constraints is developed and implemented. Tabu search, a meta-heuristic method, is used to guide the search to follow a path selectively to prevent from being trapped at local optimal solutions in order to find a global optimal or near global optimal solution. The simplex method on a graph is employed to lead the search from one solution to an adjacent solution in order to take advantage of the underlying network structure of the problem. In the procedure, net changes in cost and in infeasibility are used to measure the attractiveness of a move, and strategic oscillation is used to implement the intensification and diversification functions. A computational experiment was conducted to test the performance of the heuristic procedure and substantial computational results are reported. These results show that the new heuristic procedure finds very good quality solutions and outperforms an existing heuristic procedure in terms of both solution quality and CPU time.     

Mathematical programming modeling of the Response Time Variability Problem

The Response Time Variability Problem (RTVP) is a scheduling problem that has recently been defined in the literature. The RTVP has a broad range of real-life applications from manufacturing to services and information technology. A previous study developed a position exchange heuristic to apply to initial sequences for the RTVP, and a MILP (Mixed Integer Linear Programming) to obtain optimal solutions with a practical limit of 25 units to be scheduled. This paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality. The contribution of this paper is 4-fold: (i) larger instances can be solved to optimality by the off the shelf standard software; (ii) the new optimal solutions of the RTVP can be used to compare the results of heuristic procedures; (iii) the importance of modeling is demonstrated, as well as the huge impact that reformulation, redundant constraints and the elimination of symmetries have on the efficiency of MILPs is clearly established; finally (iv) a challenge to develop a customized optimization algorithm to rival the MILP solution efficiency for the RTVP is put forward.     

A transportation problem formulation for the MAC Airlift Planning problem

The Military Airlift Command (MAC) is responsible for planning the allocation of airlift resources for the movement of cargo and passengers. A heuristic algorithm, the Airlift Planning Algorithm (APA), has recently been developed under subcontract to the Oak Ridge National Laboratory to assist MAC in scheduling airlift resources. In this paper, we present a transportation problem formulation which can be used as a preprocessor to the APA or as an estimator for the APA. This paper examines the robustness and sensitivity of the transportation problem formulation. In particular, the performance of the APA improves by approximately 10% when the transportation problem is used as a preprocessor for two hypothetical problems and improves by up to 50% for derived airlift constrained problems.     

Heuristic algorithms for siting alternative-fuel stations using the Flow-Refueling Location Model

This paper presents three heuristic algorithms that solve for the optimal locations for refueling stations for alternative-fuels, such as hydrogen, ethanol, biodiesel, natural gas, or electricity. The Flow-Refueling Location Model (FRLM) locates refueling stations to maximize the flow that can be refueled with a given number of facilities. The FRLM uses path-based demands, and because of the limitations imposed by the driving range of vehicles, longer paths require combinations of more than one station to refuel round-trip travel. A mixed-integer linear programming (MILP) version of the model has been formulated and published and could be used to obtain an optimal solution. However, because of the need for combinations of stations to satisfy demands, a realistic problem with a moderate size network and a reasonable number of candidate sites would be impractical to generate and solve with MILP methods. In this research, heuristic algorithms—specifically the greedy-adding, greedy-adding with substitution and genetic algorithm—are developed and applied to solve the FRLM problem. These algorithms are shown to be effective and efficient in solving complex FRLM problems. For case study purposes, the heuristic algorithms are applied to locate hydrogen-refueling stations in the state of Florida.     

A perturbation-based heuristic for the capacitated multisource Weber problem

This paper proposes a perturbation-based heuristic for the capacitated multisource Weber problem. This procedure is based on an effective use of borderline customers. Several implementations are considered and the two most appropriate are then computationally enhanced by using a reduced neighbourhood when solving the transportation problem. Computational results are presented using data sets from the literature, originally used for the uncapacitated case, with encouraging results.     

Improved MILP models for two-machine flowshop with batch processing machines

In this paper, we consider the problem of scheduling jobs in a flowshop with two batch processing machines such that the makespan is minimized. Batch processing machines are frequently encountered in many industrial environments such as heat treatment operations in a steel foundry and chemical processes performed in tanks or kilns. Improved Mixed Integer Linear Programming (MILP) models are presented for the flowshop problem with unlimited or zero intermediate storage. An MILP-based heuristic is also developed for the problem. Computational experiments show that the new MILP models can significantly improve the original ones. Also, the heuristic can obtain the optimal solutions for all the test problem instances.     

A tabu search heuristic procedure for the capacitated facility location problem

A tabu search heuristic procedure is developed, implemented and computationally tested for the capacitated facility location problem. The procedure uses different memory structures. Visited solutions are stored in a primogenitary linked quad tree. For each facility, the recent move at which the facility changed its status and the frequency it has been open are also stored. These memory structures are used to guide the main search process as well as the diversification and intensification processes. Lower bounds on the decreases of total cost are used to measure the attractiveness of the moves and to select moves in the search process. A specialized network algorithm is developed to exploit the problem structure in solving transportation problems. Criterion altering, solution reconciling and path relinking are used to perform intensification functions. The performance of the procedure is tested through computational experiments using test problems from the literature and new test problems randomly generated. It found optimal solutions for almost all test problems from the literature. As compared to the heuristic method of Lagrangean relaxation with improved subgradient scheme, the tabu search heuristic procedure found much better solutions using much less CPU time.     

Successive Linear Approximation Procedure for Generalized Fixed-Charge Transportation Problems

In this paper, we develop a new heuristic procedure for solving a generalization of the fixed-charge transportation problem in which there are resource losses in addition to the fixed charges. The losses may be evaporation losses when the commodity is a liquid, heat losses in an electrical distribution network, or deterioration losses in distribution networks involving perishable commodities such as, for example, food items. The proposed procedure consists of solving a sequence of pro-rated problems. It is different from heuristic procedures that have been developed for solving the standard fixed charge transportation problem, in that it is not based on extreme point enumeration. We experiment with problems involving up to 2100 arcs with fixed charges and resource losses. The results show that the proposed approach is viable for solving medium-to-large sized problems.     

A mixed integer linear programming model for reliability optimisation in the component deployment problem

Component deployment is a combinatorial optimisation problem in software engineering that aims at finding the best allocation of software components to hardware resources in order to optimise quality attributes, such as reliability. The problem is often constrained because of the limited hardware resources, and the communication network, which may connect only certain resources. Owing to the non-linear nature of the reliability function, current optimisation methods have focused mainly on heuristic or metaheuristic algorithms. These are approximate methods, which find near-optimal solutions in a reasonable amount of time. In this paper, we present a mixed integer linear programming (MILP) formulation of the component deployment problem. We design a set of experiments where we compare the MILP solver to methods previously used to solve this problem. Results show that the MILP solver is efficient in finding feasible solutions even where other methods fail, or prove infeasibility where feasible solutions do not exist.     

Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem

In this paper new MILP formulations for the multiple allocation p-hub median problem are presented. These require fewer variables and constraints than those traditionally used in the literature. An efficient heuristic algorithm, based on shortest paths, is described. LP based solution methods as well as an explicit enumeration algorithm are developed to obtain exact solutions. Computational results are presented for well known problems from the literature which show that exact solutions can be found in a reasonable amount of computational time. Our algorithms are also benchmarked on a different data set. This data set, which includes problems that are larger than those used in the literature, is based on a postal delivery network and has been treated by the authors in an earlier paper.     

An integrated framework for inventory management and transportation of refined petroleum products: Pipeline or marine?

We study the integrated problem of managing inventory of refined petroleum products, and their multi-modal (ships and pipeline) transportation between a refinery and the served distribution centers. It is important that the transportation decisions are driven not just by the inventory levels and customer demand, but also the environmental risks associated with different refined products. A bi-objective mixed integer linear programming optimization model (MILP) is proposed, where constituent components were independently developed and then interfaced to capture the complexity of the resulting integrated model. A time-based decomposition heuristic is also employed to solve the integrated problem. The proposed framework was used to study a number of problem instances generated using a realistic infrastructure in the United States, and the resulting analyses lead to the following inferences: pipeline is the preferred mode of transportation only when cost is the sole consideration; on the other hand, when environmental risks are considered marine is the preferred mode for most of the refined petroleum products, except for heavier oils; and, the proportion of traffic on the two modes is a function of the type and volume of products, and the number of vessels available at the start of the planning horizon.     

A parallel clustering technique for the vehicle routing problem with split deliveries and pickups

In this paper, a parallel clustering technique and route construction heuristic have been developed for the vehicle routing problem (VRP) with split deliveries and pickups. An MILP formulation for determining the exact solution to the problem has also been included. It has been shown through extensive experimentation that the algorithm proposed in this paper statistically produces better results than the only heuristic existing for this class of problems in literature. We also form a basis of comparison between this class of problems and the VRP with simultaneous deliveries and pickups. We note that while heuristics for simultaneous deliveries and pickups cannot be applied in situations where customers' delivery or pickup demands exceed the vehicle capacity, heuristics allowing split deliveries and pickups can, in fact, be applied in every situation, even producing superior results under the combined objective of minimization of the fixed charge and mileage associated with vehicle routes. A guideline as to which heuristic could be used under what parametric conditions and objective functions, has also been provided.     

Synchronization of inventory and transportation under flexible vehicle constraint: A heuristics approach using sliding windows and hierarchical tree structure

This paper investigates the integrated inventory and transportation planning under flexible vehicle constraint. To offer better services at lower prices, more and more companies turn to outsource transportation functions to other professional service providers, namely 3rd party logistics companies. Under these vehicle rental arrangements, the number of vehicles is a decision variable instead of a fixed number, and the transportation cost includes not only the delivery cost but also the cost of vehicle rental that is proportional to the number of vehicles rented in a given planning horizon. In this paper, the problem is formulated as a mixed integer programming problem. A heuristic algorithm is developed, in which sliding windows are applied to approximate the problem by repeatedly solving a series of overlapping short-term subproblems, and a hierarchical tree structure is used to evaluate the closeness of different groups of retailers. Numerical experiments show that a better tradeoff between the inventory cost and transportation cost can be achieved through the proposed heuristic algorithm.     

Capacitated Multiple Item Ordering with Incremental Quantity Discounts

This paper presents a heuristic algorithm for determining order quantities for multiple items given incremental quantity discounts and a single resourse constraint. The heuristic is based on Lagrangian relaxation. The performance of the heuristic is compared, for small problems, with a procedure that generates optimal solutions. Results from computational experiments are given that demonstrate the quality and computational efficiency of the heuristic algorithm.     

Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection

We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.     

A Modification of the Silver-Meal Heuristic to Handle MRP Purchase Discount Situations

This paper introduces an alternative approach for determining lot sizes for purchased components in MRP environments where discounts are available from vendors. This new method is a variation of the least period cost procedure, which was previously found to be a poor performer relative to the least unit cost, McLaren's order moment, and the Chung et al. procedures. The performance of this new version of the least period cost procedure, which actually is a modified version of the original Silver-Meal heuristic, is found to be excellent relative to alternative procedures. In fact, when flexibility of the method to operate in diverse environments and computational time are considered, this modified least-period cost heuristic may be the best procedure available.     

Heuristic sensitivity analysis in a combinatoric environment: An exposition and case study

Sensitivity orpost-optimality analysis investigates the effect of parametric changes on heuristic robustness and solution quality. This approach is relatively unexplored for combinatorial optimization problems, and yet is of considerable interest in analyzing performance characteristics of heuristic approaches. The purpose of this paper is to: (1) develop the semantics and rationale of parametric analysis within the combinatoric environment; (2) present as an example the design and implementation of sensitivity analysis procedures for a newly developed heuristic — theVariable-Depth-Search Heuristic (VDSH) — to solve the Generalized Assignment Problem (GAP). The concepts and methodology discussed in this paper may as well be applied to other heuristics, or in developing a heuristic sensitivity analysis procedure for a large-scale optimization method.     

Large-scale optimization planning methods for the distribution of United States army munitions

Coordinating the distribution of ammunition and scheduling strategic transportation resources during military contingency operations is a complex process. This paper presents a large-scale optimization-based planning method that uses column generation to schedule the movement of ammunition and transportation resources through a time-space network representation of the distribution system. The optimization-based planner is initialized using a feasible solution generated by a heuristic planning method. Both the optimization-based planner and the heuristic planner generate plans with improved ship utilization and delivery tardiness values as compared to plans generated using current planning techniques. In addition, the heuristic planner is implemented within a closed-loop planning and control framework, and is used to generate plans on a rolling horizon basis.