A Surrogate Model-Based Hybrid Approach for Stochastic Robust Double Row Layout Problem

The double row layout problem is to arrange a number of machines on both sides of a straight aisle so as to minimize the total material handling cost. Aiming at the random distribution of product demands, we study a stochastic robust double row layout problem (SR-DRLP). A mixed integer programming (MIP) model is established for SR-DRLP. A surrogate model is used to linearize the nonlinear term in the MIP to achieve a mixed integer linear programming model, which can be readily solved by an exact method to yield high-quality solutions (layouts) for small-scale SR-DRLPs. Furthermore, we propose a hybrid approach combining a local search and an exact approach (LS-EA) to solve large-scale SR-DRLPs. Firstly, a local search is designed to optimize the machine sequences on two rows and the clearance from the most left machine on row 1 to the left boundary. Then, the exact location of each machine is further optimized by an exact approach. The LS-EA is applied to six problem instances ranging from 8 to 50 machines. Experimental results show that the surrogate model is effective and LS-EA outperforms the comparison approaches.

An Exact Algorithm for Large-Scale Continuous Nonlinear Resource Allocation Problems with Minimax Regret Objectives

We study a large-scale resource allocation problem with a convex, separable, not necessarily differentiable objective function that includes uncertain parameters falling under an interval uncertainty set, considering a set of deterministic constraints. We devise an exact algorithm to solve the minimax regret formulation of this problem, which is NP-hard, and we show that the proposed Benders-type decomposition algorithm converges to an [Formula: see text]-optimal solution in finite time. We evaluate the performance of the proposed algorithm via an extensive computational study, and our results show that the proposed algorithm provides efficient solutions to large-scale problems, especially when the objective function is differentiable. Although the computation time takes longer for problems with nondifferentiable objective functions as expected, we show that good quality, near-optimal solutions can be achieved in shorter runtimes by using our exact approach. We also develop two heuristic approaches, which are partially based on our exact algorithm, and show that the merit of the proposed exact approach lies in both providing an [Formula: see text]-optimal solution and providing good quality near-optimal solutions by laying the foundation for efficient heuristic approaches.

The Study of Depot Position Effect on Travel Distance in Order Picking Problem

Research of travel distance on single - depot position in warehouse is tremendous. This study focuses more on the effect of two-depot position on travel distance in order picking problem (OPP) by using the concept of traveling salesman problem (TSP) and exact method – Branch and Bound (B\&B) algorithm. The total distance of one-depot position is shorter than two-depot position for single and double block warehouses and the difference is less than 5%. The total distance is also compared with approximate methods – SA and TS which show that the differences are less than 5%. The sequence of location visit for one depot and two depot is similar about two third from the total location visits. For order picking problem that has more than 25 location visits, one need to consider to apply approximate approach to get the solution faster even the difference will be higher from exact approach when the number of location visit or aisle increases.