Maciek Nowak

Pickup and Delivery with Split Loads

Splitting loads such that the delivery of certain loads is completed in multiple trips rather than one trip results in opportunities for a reduction in cost and the number of vehicles used. Several studies have shown the benefit of split deliveries for the vehicle routing problem, in which a vehicle operating out of a depot makes a series of deliveries on each route. In this paper, we quantify the benefit of using split loads for the pickup and delivery problem. A heuristic to solve the pickup and delivery problem with split loads is developed and applied to a set of random large-scale problem instances, revealing the potential benefit of split loads. This benefit is reduced when the heuristic is applied to a real-world trucking industry problem because of several problem instance characteristics. The benefit of split loads is found to be most closely tied to three characteristics: load size, cost associated with a pickup or delivery, and the frequency with which loads have origins or destinations in common. Prior to a discussion of these results, we define the pickup and delivery problem with split loads and prove that for a set of given origins and destinations the most benefit can occur with load sizes just above one half of vehicle capacity.

Workforce Management in Periodic Delivery Operations

Service quality and driver efficiency in the delivery industry may be enhanced by increasing the regularity with which a driver visits the same set of customers. However, effectively managing a workforce of drivers may increase travel distance, a traditional metric of the vehicle routing problem VRP. This paper evaluates the effect that workforce management has on routing costs, providing insight for managerial decision making. The analysis is presented in the context of the period vehicle routing problem PVRP, an extension of the VRP with vehicle routes constructed to service customers according to preset visit frequencies over an established period of time. We develop models to apply workforce management principles. Through a computational study with standard PVRP test cases and real-world delivery data, we show that multiobjective PVRP models can achieve a balance between workforce management and travel distance goals. With the proper parameters in place, workforce management principles may be successfully applied without sacrificing other operational objectives.

A multi-restart iterated local search algorithm for the permutation flow shop problem minimizing total flow time

A variety of metaheuristics have been developed to solve the permutation flow shop problem minimizing total flow time. Iterated local search (ILS) is a simple but powerful metaheuristic used to solve this problem. Fundamentally, ILS is a procedure that needs to be restarted from another solution when it is trapped in a local optimum. A new solution is often generated by only slightly perturbing the best known solution, narrowing the search space and leading to a stagnant state. In this paper, a strategy is proposed to allow the restart solution to be generated from a group of solutions drawn from local optima. This allows an extension of the search space, while maintaining the quality of the restart solution. A multi-restart ILS (MRSILS) is proposed, with the performance evaluated on a set of benchmark instances and compared with six state of the art metaheuristics. The results show that the easily implementable MRSILS is significantly better than five of the other metaheuristics and comparable to or slightly better than the remaining one.

An empirical study on the benefit of split loads with the pickup and delivery problem

Splitting loads such that the delivery of certain loads is completed in multiple trips rather than one trip has been shown to have benefit for both the classic Vehicle Routing Problem (VRP) and the Pickup and Delivery Problem (PDP). However, the magnitude of the benefit may be affected by various problem characteristics. In this paper, we characterize those real world environments in which split loads are most likely to be beneficial. Based on practitioner interest, we determine how the benefit is affected by the mean load size and variance, number of origins relative to the number of destinations, the percentage of origin-destination pairs with a load requiring service, and the clustering of origin and destination locations. We find that the magnitude of benefit is greatest for load sizes just over one half vehicle capacity as these loads can not be combined without splitting, while they are the easiest to combine on a vehicle with splitting; increases as the number of loads sharing an origin or destination increases because there are more potential load combinations to split at each stop; and increases as the average distance from an origin to a destination increases because splitting loads reduces the trips from origins to destinations.

Managing Inventory in Global Supply Chains Facing Port-of-Entry Disruption Risks

Ports-of-entry are critical components of the modern international supply chain infrastructure, particularly container seaports and airfreight hubs. The potential operational and economic impact resulting from their temporary closure is unknown but is widely believed to be very significant. This paper investigates one aspect of this potential impact, focusing specifically on the use of supply chain inventory as a risk mitigation strategy for a one supplier, one customer system in which goods are transported through a port-of-entry subject to temporary closures. Closure likelihood and duration are modeled using a completely observed, exogenous Markov chain. Order lead times are dependent on the status of the port-of-entry, including potential congestion backlogs of unprocessed work. An infinite-horizon, periodic-review inventory control model is developed to determine the optimal average cost ordering policies under linear ordering costs with backlogged demand. When congestion is negligible, the optimal policy is state invariant. In the more complex case of nonnegligible congestion, this result no longer holds. For studied scenarios, numerical results indicate that operating margins may decrease 10% for reasonable-length port-of-entry closures, that margins may be eliminated completely without contingency plans, and that expected holding and penalty costs may increase 20% for anticipated increases in port-of-entry utilization.

Self-adaptive perturbation and multi-neighborhood search for iterated local search on the permutation flow shop problem

A self-adaptive perturbation for iterated local search is developed and found to be effective.Multi-neighborhood search performance is improved through the application of self-adaptive perturbation.The performance of the proposed methods are found to be superior to other compared algorithms.New best solutions are found for 20 benchmark instances. The flow shop scheduling problem minimizing total flow time is a famous combinatorial optimization problem. Among the many algorithms proposed to solve this problem, iterated local search (ILS) is a simple, effective and efficient one. Research shows that the perturbation method and neighborhood structure play key roles in the performance of ILS. However, existing ILS lacks the self-adaptive ability to adjust the degree of perturbation relative to the search status. Also, only one basic insertion neighborhood is often used, greatly limiting the size of the search space and the ability to escape from a local optimum. In this work, a self-adaptive strategy is proposed, evaluating the neighborhoods around the local optimum and adjusting the perturbation strength according to this evaluation. If neighboring solutions are found to be considerably worse than the best known solution, indicating that it may be hard to escape from the local optimum, then the perturbation strength is amplified. Additionally, a swap neighborhood is incorporated with an insertion neighborhood to form a new version of multi-neighborhood search. Experimental results on benchmark instances show that the self-adaptive search performs significantly better than three state of the art algorithms, particularly when tested with extended CPU time. The multi-neighborhood search performs even better, also outperforming two state of the art variable neighborhood search algorithms, indicating that the hybrid use of insertion and swap neighborhoods is effective for the discussed problem.

Precedence constrained pickup and delivery with split loads

A split load is a load having size no greater than the capacity of a single vehicle that is delivered using more than a single vehicle. The use of split loads can reduce the total transportation cost and the number of vehicles serving a set of loads. Several studies have shown the benefit of split loads as applied to the split delivery vehicle routing problem (SDVRP) and the pickup and delivery problem with split loads (PDPSL). While most research on the application of split loads to vehicle routing has revolved around heuristic methods, in this paper an exact solution method is used on a constrained version of the PDPSL. All origins to be visited must be served before any destination that is to be visited on each route, which we refer to as the precedence constrained-PDPSL (PC-PDPSL). Through this constraint, several structural characteristics that result from the SDVRP are shown to also hold for the PC-PDPSL. In particular, we develop a dynamic programming formulation of the PC-PDPSL and show that the state and action spaces of this problem are finite. We use the well-known A* ‘best-first’ search algorithm from artificial intelligence to find an exact solution to a wide range of data sets. Computational experiments support findings developed using heuristic methods for the PDPSL, showing that splitting loads can reduce costs and that there is a relationship between average load size and cost savings.

Assignment of swimmers to dual meet events

Every fall, thousands of high school swimming coaches across the country begin the arduous process of preparing their athletes for competition. With a grueling practice schedule and a dedicated group of athletes, a coach can hone the squad into a cohesive unit, poised for any competition. However, oftentimes all preparation is in vain, as coaches assign swimmers to events with a lineup that is far from optimal. This paper provides a model that may help a high school (or other level) swim team coach make these assignments. Following state and national guidelines for swim meets, we describe a binary integer model that determines an overall assignment that maximizes the total number of points scored by the squad based on the times for swimmers on the squad and for the expected opponent.

Planning Strategies for Home Health Care Delivery

In home health care (our motivating application), consistency is representative of the general health care principle of continuity of care, which is often correlated with quality of care. Much of the existing research involving consistency in routing uses planning horizons that are a week or shorter. Yet in many settings the relationship between an organization and its customers lasts much longer. Hence, this paper looks at how one should plan when seeking consistency in routes extends the impact of caregiver-patient assignments. Specifically, the paper examines appropriate planning horizon length and, with an extensive computational study, demonstrates that a long planning horizon can have significant potential for savings in terms of transportation costs and staffing levels. Initially, a deterministic setting is considered, with all patient requests during the planning horizon known a priori, and the routing cost of planning for two to three months is compared with the cost when planning is done on a weekly basis. With uncertainty inherent in planning for such a long time horizon, a methodology is presented that anticipates future patient requests that are unknown at the time of planning. Computational evidence shows that its use is superior to planning on a weekly, rolling horizon basis.

A self-adaptive iterated local search algorithm on the permutation flow shop scheduling problem

Iterated local search (ILS) is a simple, effective and efficient metaheuristic, displaying strong performance on the permutation flow shop scheduling problem minimizing total flow time. Its perturbation method plays an important role in practice. However, in ILS, current methodology does not use an evaluation of the search status to adjust the perturbation strength. In this work, a method is proposed that evaluates the neighborhoods around the local optimum and adjusts the perturbation strength according to this evaluation using a technique derived from simulated-annealing. Basically, if the neighboring solutions are considerably worse than the best solution found so far, indicating that it is hard to escape from the local optimum, then the perturbation strength is likely to increase. A self-adaptive ILS named SAILS is proposed by incorporating this perturbation strategy. Experimental results on benchmark instances show that the proposed perturbation strategy is effective and SAILS performs better than three state of the art algorithms.