Articles written in Sadhana

    • A mixed integer linear programming model for the vehicle routing problem with simultaneous delivery and pickup by heterogeneous vehicles, and constrained by time windows


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      In this work, we consider the Vehicle Routing Problem with Simultaneous Delivery and Pickup, and constrained by time windows, to improve the performance and responsiveness of the supply chain by transporting goods from one location to another location in an efficient manner. In this class of problem, each customer demands a quantity to be delivered as a part of the forward supply service and another quantity to be picked up as a part of the reverse recycling service, and the complete service has to be done simultaneously in a single visit of a vehicle, and the objective is to minimize the total cost, which includes the traveling cost anddispatching cost for operating vehicles. We propose a Mixed Integer Linear Programming (MILP) model for solving this class of problem. In order to evaluate the performance of the proposed MILP model, a comparison study is made between the proposed MILP model and an existing MILP model available in the literature, with the consideration of heterogeneous vehicles. Our study indicates that the proposed MILP model gives tighter lower bound and also performs better in terms of the execution time to solve each of the randomly generatedproblem instances, in comparison with the existing MILP model. In addition, we also compare the proposed MILP model (assuming homogeneous vehicles) with the existing MILP model that also considers homogeneous vehicles. The results of the computational evaluation indicate that the proposed MILP model gives much tighter lower bound, and it is competitive to the existing MILP model in terms of the execution time to solve each of the randomly generated problem instances.

    • Minimum cost berth allocation problem in maritime logistics: new mixed integer programming models


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      The berth allocation problem (BAP) involves decisions on how to allocate the berth space and to sequence maritime vessels that are to be loaded and unloaded at a container terminal involved in the maritime logistics. As the berth is a critical resource in a container terminal, an effective use of it is highly essential tohave efficient berthing and servicing of vessels, and to optimize the associated costs. This study focuses on the minimum cost berth allocation problem (MCBAP) at a container terminal where the maritime vessels arrive dynamically. The objective comprises the waiting time penalty, tardiness penalty, handling cost and benefit of early service completion of vessels. This paper proposes three computationally efficient mixed integer linear programming (MILP) models for the MCBAP. Through numerical experiments, the proposed MILP models arecompared to an existing model in the literature to evaluate their computational performance. The computational study with problem instances of various problem characteristics demonstrates the computational efficiency of the proposed models.

    • A comparative study on allocation/rationing mechanisms operational with/without backorder clearing in divergent supply chains


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      The management of inventory in a divergent supply chain involves inventory allocation/rationing in addition to the determination of order policy parameters. In the case of a stock point feeding product(s) to several downstream members, rationing mechanism can be viewed as a special case of the allocation mechanism. In a supply chain with multi-period ordering cycles, a rationing decision ensures that the entire inventory available with the feeder stock point is rationed to downstream members, whereas an allocation decision neednot allocate the entire inventory available, and it is at the discretion of the decision maker at the feeder stock point to retain inventory for possible high priority demands in future periods. In any supply chain permitting backordering of demands from downstream members, the clearing of backorders is a matter of concern. This study addresses the said issue by ensuring that the feeder stock point considers the current period demand for fulfilment only after clearing the backorders with respect to the downstream members. Through this study, anattempt is made to develop mathematical models for supply chains operating with installation-specific costs (holding and shortage) and ordering policy (base stock) over a finite time horizon with and without clearing backorders in the case of rationing as well as allocating inventory to downstream members. Specifically, thiswork appears to be the first comparative study on allocation and rationing mechanisms in association with/ without backorder clearing mechanisms in divergent supply chains, and their impact on the total supply chaincost.

    • Branch-and-bound algorithms for scheduling in an m-machine no-wait flowshop


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      In this paper, we develop branch-and-bound algorithms for objectives such as sum of weighted flowtime, weighted tardiness and weighted earliness of jobs, for an m-machine no-wait (continuous) flowshop. We believe that there has been no prior work on exact algorithms for this problem setup with a variety of objective functions. For the interest of space, we confine our discussion to a subset of certain combination of these objectives and the extension to other objective combinations is quite straight-forward. We explore the active nodes of a branch-and-bound tree by deriving an assignment-matrix based lower bound, that ensures oneto-one correspondence of a job with its due date and weight. This idea is based on our earlier paper on general m-machine permutation flowshop (Madhushini et al. in J Oper Res Soc 60(7):991–1004, 2009) and here weexploit the intricate features of a no-wait flowshop to develop efficient lower bounds. Finally, we conclude our paper with the numerical evaluation of our branch-and-bound algorithms.

    • Permutation flowshop scheduling to obtain the optimal solution/a lower bound with the makespan objective


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      This paper focuses on developing the optimal solution or a lower bound for N-job, M-machine Permutation Flowshop Scheduling (PFS) problem in a manufacturing system with the objective of minimizing the makespan using Lagrangian Relaxation (LR) technique. Even though LR technique is considered, in general,as a good method to obtain a lower bound, research in this direction with respect to our problem under study appears scarce. We address this gap by developing two MILP based Lagrangian Relaxation models, namely, Lagrangian Relaxation Method 1 (called Proposed Lagrangian Lower Bound Program (PLLBP)) and Alternate Lagrangian Relaxation Method 1 (called ALR) to find the optimal solution or a lower bound on the makespan. Basically, we develop these LR methods to overcome the possible limitation of the general LR procedureinvolving the sub-gradient approach. Benchmark PFS problem instances are used to evaluate the performance of these methods. It is observed that the PLLBP outperforms the ALR, and it provides better lower bounds than thelower bounds (in most instances) reported in the literature. Even though the PLLBP is superior in terms of solution quality, it has a limitation in that it cannot execute problem instances beyond 500 jobs due to the associated computational effort.

    • CARIMO - A heuristic approach to machine-part cell formation


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      This paper presents a correlation analysis-based heuristic for the machine-part cell formation in the context of cellular manufacturing systems. Two new indices, viz. ‘‘mean correlation index’’ for forming the part families and ‘‘relevance index-modified’’ for identifying the appropriate machine cells are proposed. Themachine-part cells formed by the proposed heuristic resulted in a higher grouping efficacy (GE) for 14.3% of the test instances gathered from the literature, and it performed equal to the best in class heuristics available in theliterature for 80% of the test instances. The method presented in this paper has set a new benchmark GE for 5 of the 35 test instances used by the researchers in the context of machine-part cell formation without singletons.

    • Priority fractional rationing (PFR) policy and a hybrid metaheuristic for managing stock in divergent supply chains


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      A distributor catering to demands of multiple retailers is considered in this paper and stockmanagement in this divergent supply chain is achieved through the deployment of periodic review base-stock (i.e. (R, S) policy) policy at every member. In the model of the supply chain considered in this study, in everytime-period, an attempt is made by the distributor to first transport backlogged-demands from the downstream members till the distributor’s previous instance-of-review even before considering demands from downstream members in recent time-periods. This practice of the distributor attempting first to satisfy backlogged-demands till its last instance of review will ensure that the shipment will reach the retailer, contemplating whom the order was made by the distributor. A Mixed Integer Linear Programming (MILP)-based mathematical formulation of the supply chain (with the objective of minimizing the Total Supply Chain Cost (TSCC)), to obtain optimum policy (R, S) parameters at each member of the supply chain, and inherently performing the allocation and rationing of stock over a finite planning horizon, is proposed through this paper. A new heuristic allocation and rationing mechanism for the distributor to distribute stock among retailers during the occurrence of shortage named as Priority Fractional Rationing (PFR) policy is also introduced in this study. A heuristic methodology which is a hybrid of Genetic Algorithm and Particle Swarm Optimization algorithm (HGA-PSO) combined with PFR policy is proposed through this study after analyzing the computational difficulty encountered and lack of tractability of stock-allocation and stock-rationing mechanism while the MILP-based mathematical formulation is solved to optimality. A local search technique as part of the Particle Swarm Optimization (PSO) algorithm, similar to mutation operation in Genetic Algorithm (GA) is introduced due to the observation of inferior results during pilot studies. The performance evaluation studies of the HGA-PSO with that of stand-alone GA, standalone PSO with new local search and the exact solution obtained by solving the MILP-based mathematical formulation is presented. The results indicate the superior performance of the hybrid algorithm in comparison with stand-alone GA and PSO.

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