Kamlesh Mathur

Stochastic Vehicle Routing Problem with Restocking

In this paper, a stochastic vehicle routing problem is considered. In particular, customer demand is assumed to be uncertain, and actual demand is revealed only upon the visit to the customer. Instead of adopting the simple recourse action of returning to the depot whenever the vehicle runs out of stock, the points along the route at which restocking is to occur are designed into the route. The restocking points may be before a stockout actually occurs. Two heuristic algorithms are developed to construct both single and multiple routes that minimize total travel cost. The computational results show that the heuristic procedures produce quality solutions and are efficient.

A set-partitioning-based exact algorithm for the vehicle routing problem

In this paper, we discuss a computationally viable algorithm based on a set-partitioning for-mulation of the Vehicle Routing Problem (VRP). Implementation strategies based on theoretical as well as empirical results are developed. Some computational results are presented. It is shown that a set-partitioning formulation to the VRP, although well known for a long time, deserves considerable research efforts beyond those we present here.

Reverse logistics: simultaneous design of delivery routes and returns strategies

A reverse logistics problem, motivated by blood distribution of the American Red Cross, is examined where containers in which products are delivered from a central processing point to customers (stops) in one period are available for return to the central point in the following period. Any container not picked up in the period following its delivery incurs a penalty cost resulting primarily from operating costs and customer dissatisfaction. The result is a dynamic logistics planning problem where in each delivery period the vehicle dispatcher needs to design a multi-stop vehicle route while determining the container quantities to be picked up at each stop. This research is unique in that route design and pickup strategies are developed simultaneously, where stop volumes are known only probabilistically over a planning horizon. A heuristic procedure is developed for treating the route design-pickup strategy planning problem.

Vehicle Routing and Scheduling with Full Truckloads

Truckload carriers are constantly faced with the problem of shipping full truckloads of goods at minimum cost between pairs of cities or customers, using a fleet of trucks located at one or more depots. In this paper, a new branch-and-bound algorithm for solving an integer-programming formulation of this vehicle-routing problem (VRP) with full truckloads is developed. The algorithm also takes into consideration the time-window constraints and waiting costs. The resulting efficiency, validated by computational tests on random problems, is due to a column-generation scheme that exploits the special structure of the problem to solve the linear-programming relaxation problems that arise at the nodes.

A branch and search algorithm for a class of nonlinear knapsack problems

This paper discusses a class of nonlinear knapsack problems where the objective function is quadratic. The method is a branch and search procedure which includes an efficient algorithm to find the continuous (relaxed) solution and a reduction rule which computes tight lower and upper bounds on the integer variables.

An Efficient Heuristic Algorithm for a Two-Echelon Joint Inventory and Routing Problem

With an increasing emphasis on coordination in the supply chain, the inventory and distribution decisions, which in most part had been dealt with independently of each other, need to be considered jointly. This research considers a two-echelon distribution system consisting of one warehouse and N retailers that face external demand at a constant rate. Inventories are kept at retailers as well as at the warehouse. The products are delivered to the retailers by a fleet of vehicles with limited capacity. We develop an efficient heuristic procedure that finds a reorder interval for the warehouse, the replenishment quantities (and associated reorder interval) for each retailer, and the delivery routes so as to minimize the long-run average inventory and transportation costs.

Value considerations in three-dimensional packing — A heuristic procedure using the fractional knapsack problem

Abstract Not much work has been done on three-dimensional bin packing problem because of the larger number of complexities occurring as compared to packing problems in lower dimensions. Almost all solution procedures developed for bin packing are heuristic in nature. A heuristic algorithm has been presented here for packing a given set of regular sized boxes of different values into a given set of regular containers. The objective is to maximize the total value of the boxes packed into the given containers. The heuristic is based on an Integer Programming formulation that uses the fractional knapsack problem as a column generation subproblem.

An integer-programming-based heuristic for the balanced loading problem

This paper presents an efficient heuristic algorithm for the one-dimensional loading problem in which the goal is to pack homogeneous blocks of given length and weight in a container in such a way that the center of gravity of the packed blocks is as close to a target point as possible. The proposed algorithm is based on the approximation of this problem as a knapsack problem. This algorithm has the same computational complexity but a better worst-case performance than the algorithm recently proposed by Amiouny et al. [Oper. Res. 40 (1992) 238]. Moreover, the computational results also show that, in general, it performs better on randomly generated problems.

A note on a general non-linear knapsack problem

This paper discusses a general non-linear knapsack problem with a concave objective function and a single conves constraint. in particular, it includes an efficient procedure to find the continuous (relaxed) solution and a reduction process which computes tight lower and upper bounds on the integer variables. Some implicit enumeration criteria to be used in an enumeration algorithm are also suggested.

A surrogate relaxation based algorithm for a general quadratic multi-dimensional knapsack problem

In this paper, we develop a framework to solve a General Quadratic Multi-dimensional Knapsack Problem using surrogate relaxation. This paper exploits the fact that a continuous single constraint quadratic knapsack problem can be solved by inspection by the procedure given by Mathur et al. [6]. A preliminary computational study indicates that the proposed algorithm is much more efficient than some of the alternate procedures.