Large scale stochastic inventory routing problems with split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC

Solving the Task Variant Allocation Problem in Distributed Robotics

We consider the problem of assigning software processes (or tasks) to hardware processors in distributed robotics environments. We introduce the notion of a task variant, which supports the adaptation of software to specific hardware configurations. Task variants facilitate the trade-off of functional quality versus the requisite capacity and type of target execution processors. We formalise the problem of assigning task variants to processors as a mathematical model that incorporates typical constraints found in robotics applications; the model is a constrained form of a multi-objective, multi-dimensional, multiple-choice knapsack problem. We propose and evaluate three different solution methods to the problem: constraint programming, a constructive greedy heuristic and a local search metaheuristic. Furthermore, we demonstrate the use of task variants in a real instance of a distributed interactive multi-agent navigation system, showing that our best solution method (constraint programming) improves the system’s quality of service, as compared to the local search metaheuristic, the greedy heuristic and a randomised solution, by an average of 16, 31 and 56% respectively

Scheduling Projects with Labor Constraints

In this paper we consider a labor constrained scheduling problem (LCSP) which is a simplification of a practical problem arising in industry. Jobs are subject to precedence constraints and have specified processing times. Moreover, for eachjob the labor requirement varies as the job is processed. Given the amount of labor available in each period, the problem is to finish all the jobs as soon as possible, that is, to minimize makespan, subject to the precedence and labor constraints. Several Integer Programming #IP# formulations for this problem are discussed and valid inequalities for these di#erent models are introduced. It turns out that a major drawback in using the IP approach is the weakness of the lower bound relaxations. However, we report computational experiments showing how the solution of the linear relaxation of the IP models can be used to provide good schedules. Solutions arising from these LP-based heuristics are considerably improved by local search procedures. We further exploit the capabilities of local search for LCSP by designing a Tabu Search algorithm. The computational experiments on a benchmark data set show that the Tabu algorithm generates the best known upper bounds for almost all these instances. We also show how IP can be used to provide reasonably good lower bounds for LCSP when the makespan is replaced by suitably modified objective functions. Finally some directions for further investigations which may turn IP techniques into a more interesting tool for solving such a problem are suggested

Transportation Procurement with Seasonally Varying Shipper Demand and Volume Guarantees

2007-2008 > Academic research: refereed > Publication in refereed journa

Dynamic lot-sizing problem with demand time windows and container-based transportation cost

10.1007/s11590-006-0042-1Optimization Letters2139-5