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Approaches to Solve MID_CPLP Problem: Theoretical Framework and Empirical Investigation

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American Journal of Operations Research 2014年第3期4卷 142-154页

作者： renduchintala raghavendra kumar sharma Pritee Agarwal Department of Industrial and Management Engineering Indian Institute of Technology Kanpur India Department of Mathematics and Statistics Indian Institute of Technology Kanpur India

In two-stage warehouse location problem, goods are moved from plants to warehouses at stage-1 (which are larger sized warehouses), and from there to warehouses at stage-2 (which are smaller sized warehouses);and finally to the markets. We aim to minimize the sum of location costs of the warehouses at stage-1 and stage-2;plus the total distribution cost of goods to the markets. In this paper two-stage capacitated warehouse location problem (TSCWLP) is vertically decomposed into the smaller problems, which is attained by relaxing the associated flow balance constraints. This leads to three different versions of Capacitated Plant Location Problem (CPLP) referred as RHS_CPLP, MID_CPLP and LHS_CPLP (Verma and sharma REF _Ref387068711 \r \h [1]). In this paper MID_CPLP is reduced to RHS_CPLP and a single constraint 0-1 Knapsack problem by relaxing a difficult constraint. Interesting results and conjectures are given. Later two more valid constraints are added to MID_CPLP which are relaxed further to get additional results.

关键词： TSCWLP Location Transportation Distribution

Efficient Heuristic Based Methods for Two-Stage Transshipment Problem

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American Journal of Operations Research 2018年第4期8卷 281-293页

作者： Priyank Sinha renduchintala raghavendra kumar sharma Industrial and Management Engineering Department IIT Kanpur Kanpur India

In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by proposing a novel problem formulation for a two stage transshipment problem. Later, special structure of our problem formulation is utilized to devise two dual based heuristics solutions with computational complexity of O (n2), and O (n3) respectively. These methods are motivated by the methods developed by sharma and Saxena [1], Sinha and sharma [2]. Our methods differ in the initialization and the subsequent variation of the dual variables associated with the transshipment nodes along the shortest path. Lastly, a method is proposed to extract a very good primal solution from the given dual solutions with a computational complexity of O (n2). Efficacy of these methods is demonstrated by our numerical analysis on 200 random problems.

关键词： Two Stage Transshipment Problem Min Cost Flow Transportation Problem Dual Primal

Hybrid Formulation of the Multi-Item Capacitated Dynamic Lot Sizing Problem

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American Journal of Operations Research 2015年第6期5卷 503-513页

作者： Mayank Verma renduchintala raghavendra kumar sharma Department of Industrial and Management Engineering Indian Institute of Technology Kanpur Kanpur India

It is shown that when backorders, setup times and dynamic demand are included in capacitated lot sizing problem, the resulting classical formulation and one of the transportation formulations of the problem (referred to as CLSP_BS) are equivalent. And it is shown that both the formulations are “weak” formulations (as opposed to “strong” formulation). The other transportation version is a strong formulation of CLSP_BS. Extensive computational studies are presented for medium and large sized problems. In case of medium-sized problems, strong formulation produces better LP bounds, and takes lesser number of branch-and-bound (B&B) nodes and less CPU time to solve the problem optimally. However for large-sized problems strong formulation takes more time to solve the problem optimally, defeating the benefit of strength of bounds. This essentially is because of excessive increase in the number of constraints for the large sized problems. Hybrid formulations are proposed where only few most promising strong constraints are added to the weak formulation. Hybrid formulation emerges as the best performer against the strong and weak formulations. This concept of hybrid formulation can efficiently solve a variety of complex real life large-sized problems.

关键词： Capacitated Lot Sizing Linear Relaxation Strong Formulation Hybrid Formulation Branch-and-Bound

Computationally Efficient Problem Reformulations for Capacitated Lot Sizing Problem

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American Journal of Operations Research 2018年第4期8卷 312-322页

作者： renduchintala raghavendra kumar sharma Priyank Sinha Mananjay kumar Verma Industrial and Management Engineering Department IIT Kanpur Kanpur India

In this article, we propose novel reformulations for capacitated lot sizing problem. These reformulations are the result of reducing the number of variables (by eliminating the backorder variable) or increasing the number of constraints (time capacity constraints) in the standard problem formulation. These reformulations are expected to reduce the computational time complexity of the problem. Their computational efficiency is evaluated later in this article through numerical analysis on randomly generated problems.

关键词： Capacitated Lot Sizing Problem Efficient Problem Formulation Branch and Bound

Application of Modified Benders Decomposition to Single-Stage Multi-Commodity Multi-Period Warehouse Location Problem: An Empirical Investigation

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American Journal of Operations Research 2016年第3期6卷 245-259页

作者： renduchintala raghavendra kumar sharma Ankita Malviya Vimal kumar Vinay Singh Pritee Agarwal Department of Industrial & Management Engineering Indian Institute of Technology Kanpur India ABV Indian Institute of Information Technology & Management Gwalior India Department of Mathematics & Statistics Indian Institute of Technology Kanpur India

In the past, researchers have applied Bender’s decomposition to distribution problem and used feasibility constraint to speed up the performance of Bender’s decomposition. Further, the application of Branch and Bound to single-stage multi-commodity single-period warehouse location problem (SSMCSPWLP) with strong constraints has shown that they are more effective. It was also shown in the previous research (in the context of Branch and Bound Methodology) that hybrid formulation for the single-stage single-period multi-commodity warehouse location problem yielded superior results. In this paper we apply Benders’ decomposition to strong and weak formulations of single-stage multi-commodity multi-period warehouse location problem (SSMCMPWLP). As suggested in the previous literature we put feasibility constraints in the pure integer sub- problem to speed up the performance of Benders’ decomposition. We also develop an additional cut (constraint that is again added to pure integer sub-problem) and show that it further speeded up Benders’ Decomposition. This research led to the possibility of applying Benders’ Decomposition to the hybrid formulation of SSMCMPWLP in future.

关键词： Benders Decomposition SSMCMPWLP Strong and Weak Formulation Warehouse Location Distribution