Related papers: Improved Approximation Algorithms for Inventory Pr…
The economic warehouse lot scheduling problem is a foundational inventory-theory model, capturing computational challenges in dynamically coordinating replenishment decisions for multiple commodities subject to a shared capacity constraint.…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
The paper considers single-machine scheduling problems with a non-renewable resource. In this setting, we are given a set jobs, each of which is characterized by a processing time, a weight, and the job also has some resource requirement.…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another…
We consider an assortment optimization problem under the multinomial logit choice model with general covering constraints. In this problem, the seller offers an assortment that should contain a minimum number of products from multiple…
In this work, we investigate the problem of order batching and picker routing in warehouse storage areas. These problems are known to be capital and labour intensive, and often contribute to a sizable fraction of warehouse operating costs.…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number…
In the Scheduling Machines with Capacity Constraints problem, we are given k identical machines, each of which can process at most m_i jobs. M jobs are also given, where job j has a non-negative processing time length t_j >= 0. The task is…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available…
Sequence optimization, where the items in a list are ordered to maximize some reward has many applications such as web advertisement placement, search, and control libraries in robotics. Previous work in sequence optimization produces a…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…