Gyana R. Parija

A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.

Optimal batch size and raw material ordering policy for a production system with a fixed-interval, lumpy demand delivery system

Abstract The paper develops an ordering policy for raw materials, to meet the demands of a production facility which supplies a fixed quantity of finished products to outside buyers, at a fixed interval of time. In this model, an optimal multi-order policy for procurement of raw materials for a single manufacturing batch is developed to minimize the total cost. An integer approximation is adopted to refine the optimal solution. A worst-case scenario is also analyzed to demonstrate the effect of the setup costs on the total cost of the inventory system.

OPERATIONS PLANNING IN A SUPPLY CHAIN SYSTEM WITH FIXED-INTERVAL DELIVERIES OF FINISHED GOODS TO MULTIPLE CUSTOMERS

Raw material ordering policy and the manufacturing batch size for fixed-interval deliveries of finished goods to multiple customers play a significant role in economically managing the supply chain logistics. This paper develops an ordering policy for raw materials and determines an economic batch size for a product at a manufacturing center which supplies finished products to multiple customers, with a fixed-quantity at a fixed time-interval to each of the customers. In this model, an optimal multi-ordering policy for procurement of raw materials for a single manufacturing system is developed to minimize the total cost incurred due to raw materials and finished goods inventories. The carried over inventory of finished goods from the previous cycle is used as initial finished goods inventory, resulting in shifting the production schedule ahead for the next cycle. A closed-form solution to the problem is obtained for the minimal total cost. The algorithm is demonstrated for multiple customer systems.

On Bridging the Gap Between Stochastic Integer Programming and MIP Solver Technologies

Stochastic integer programs (SIPs) represent a very difficult class of optimization problems arising from the presence of both uncertainty and discreteness in planning and decision problems. Although applications of SIPs are abundant, nothing is available by way of computational software. On the other hand, commercial software packages for solvingdeterministic integer programs have been around for quite a few years, and more recently, a package for solving stochasticlinear programs has been released. In this paper, we describe how these software tools can be integrated and exploited for the effective solution of general-purpose SIPs. We demonstrate these ideas on four problem classes from the literature and show significant computational advantages.

Minimum Cost Resource Allocation for Meeting Job Requirements

We consider the problem of allocating resources for completing a collection of jobs. Each resource is specified by a start-time, finish-time and the capacity of resource available and has an associated cost, and each job is specified by a start-time, finish-time and the amount of the resource required (demand) during this interval. A feasible solution is a multiset of resources (i.e., multiple units of each resource may be picked) such that at any point of time, the sum of the capacities offered by the resources is at least the total demand of the jobs active at that point of time. The cost of the solution is the sum of the costs of the resources included in the solution (taking into account the units of the resources). The goal is to find a feasible solution of minimum cost. This problem arises naturally in many scenarios. For example, given a set of jobs, we would like to allocate some resource such as machines, memory or bandwidth in order to complete all the jobs. This problem generalizes a covering version of the knapsack problem which is known to be NP-hard. We present a constant factor approximation algorithm for this problem based on a Primal-Dual approach.

A Facet Generation Procedure for Solving 0/1 Integer Programs

This paper presents the Facet Generation Procedure (FGP) for solving 0/1 integer programs. The FGP seeks to identify a hyperplane that represents a facet of an underlying polytope to cut off the fractional solution to the linear programming relaxation of the integer programming problem. A set of standard problems is used to provide insight into the computational characteristics of the procedure.

Efficient Seat Utilization in Global IT Delivery Service Systems

Rapidly growing service delivery organizations need efficient tools to manage their business and reduce the cost of growth. These delivery businesses run round the clock due to demands coming from different geographical locations for different shifts. Cost of adding new physical infrastructure and space to tap incoming business is a key inhibitor of growth. Physical space availability and its effective management is the key infrastructure enabler for effective business delivery apart from human resources. A considerable impact can be realized if space utilization can be increased by optimal allocation around different work shifts. Optimal space utilization can bring down the number of physical seats required to serve the existing demand and also allow service delivery organizations to commit to new business needs with the existing capacity. The paper addresses this business problem and proposes an effective seat utilization planning solution using a mathematical programming approach to meet various strategic and tactical business objectives in this setting.

Contact center scheduling with strict resource requirements

Consider the following problem which often arises in contact center scheduling scenarios. We are given a set of employees where each employee can be deployed for shifts consisting of L consecutive time units. Further, each employee specifies a set of possible start times, and can be deployed for a bounded number of shifts only. At each point of time t, we are also given a lower bound rt on the number of employees that should be present at this time. The goal is to find a schedule for the employees such that the number of time slots whose requirements are met is maximized. Such problems naturally arise in many other situations, e.g., sensor networks and cloud computing. The strict nature of the resource requirement makes this problem very hard to approximate. In this paper, we give a bicriteria approximation algorithm for this problem. Given a parameter e > 0, we give an O(1/e3 log 1e)-approximation algorithm for this problem, where we count those time slots for which we satisfy at least (1-e)-fraction of the requirement. Our techniques involve a configuration LP relaxation for this problem, and we use non-trivial structural properties of an optimal solution to solve this LP relaxation. We even consider the more general problem where shift lengths of different employees can vary significantly. In this case, we show that even finding a good bicriteria approximation is hard (under standard complexity theoretic assumptions).

Learning to Propagate Rare Labels

Label propagation is a well-explored family of methods for training a semi-supervised classifier where input data points (both labeled and unlabeled) are connected in the form of a weighted graph. For binary classification, the performance of these methods starts degrading considerably whenever input dataset exhibits following characteristics - (i) one of the class label is rare label or equivalently, class imbalance (CI) is very high, and (ii) degree of supervision (DoS) is very low -- defined as fraction of labeled points. These characteristics are common in many real-world datasets relating to network fraud detection. Moreover, in such applications, the amount of class imbalance is not known a priori. In this paper, we have proposed and justified the use of an alternative formulation for graph label propagation under such extreme behavior of the datasets. In our formulation, objective function is the difference of two convex quadratic functions and the constraints are box constraints. We solve this program using Concave-Convex Procedure (CCCP). Whenever the problem size becomes too large, we suggest to work with a k-NN subgraph of the given graph which can be sampled by using Locality Sensitive Hashing (LSH) technique. We have also discussed various issues that one typically faces while sampling such a k-NN subgraph in practice. Further, we have proposed a novel label flipping method on top of the CCCP solution, which improves the result of CCCP further whenever class imbalance information is made available a priori. Our method can be easily adopted for a MapReduce platform, such as Hadoop. We have conducted experiments on 11 datasets comprising a graph size of up to 20K nodes, CI as high as 99:6%, and DoS as low as 0:5%. Our method has resulted up to 19:5-times improvement in F-measure and up to 17:5-times improvement in AUC-PR measure against baseline methods.

RISE: Resolution of Identity Through Similarity Establishment on Unstructured Job Descriptions

Identity resolution of job description involving cross organizational data would go a long way in addressing several high valued business problems. Job data normalization/sanitation, automated creation of better job descriptions with context preference, description reuse and validation across different sources, semantic classification of jobs, routing of candidates to suitable jobs across different organization etc. are some of the business centric functionalities that can be efficiently built by resolving job description identities. Job descriptions are highly unstructured with free flow textual data consisting of lines describing important attributes of job requirements, like education, skills, experience, role, responsibility etc. Much of the problem is due to the highly unstructured nature of job descriptions. Further, the attributes that are representative of the information in a job description are not readily available from the description. Thus, the process of resolution involves deep data cleansing, classification, attributes identification, and building highly scalable similarity detection algorithms. In this paper, we propose RISE - that uses values of attributes in the underlying job description data and similarity observed in the attributes to resolve identities across organizations. It proposes classification followed by similarity establishment processes that eventually provides high quality of resolution. Through extensive experiments performed on corpus of job descriptions from several real world recruitment systems, we demonstrate that RISE can resolve the identities with high precision and recall.