# Janakiraman, Ganesh

Permanent URI for this collectionhttps://hdl.handle.net/10735.1/3183

Dr. Ganesh Janakiraman is a professor of Operations Management and was awarded an Asbel Smith Professorship in 2017. His current research is involved with inventory theory.

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Item Technical Note - On Optimal Policies for Inventory Systems with Batch OrderingHuh, Woonghee Tim; Janakiraman, GaneshWe study a periodically reviewed multiechelon inventory system in series such that order quantities at every stage have to be multiples of a given stage-specific batch size. The batch sizes are nested in the sense that the batch size for every stage is an integer multiple of the batch size for its downstream stage. The problem is that of determining the policy that minimizes the expected discounted sum of costs over a finite horizon. The result is that an echelon 4R1nQ5 policy is optimal when demands are independent across periods or, more generally, Markov-modulated. We also comment on algorithmic implications of our result and on extensions. © 2012 INFORMS.Item Robustness of Order-Up-To Policies in Lost-Sales Inventory Systems(INFORMS) Bijvank, Marco; Huh, Woonghee Tim; Janakiraman, Ganesh; Kang, WanmoWe study an inventory system under periodic review when excess demand is lost. It is known (Huh et al. 2009) that the best base-stock policy is asymptotically optimal as the lost-sales penalty cost parameter grows. We now show that this result is robust in the following sense: Consider the base-stock level which is optimal in a backordering system (with a per-unit-per-period backordering cost) in which the backorder cost parameter is a function of the lost-sales parameter in the original system. Then there is a large family of functions (mapping the lost-sales cost parameter to the backorder cost parameter) such that the resulting base-stock policy is asymptotically optimal. We also demonstrate the robustness phenomenon through a second result. We consider the base-stock level which is optimal in a backordering system in which a unit of backorder is charged a penalty cost only once (such a system has been studied by Rosling). We show that this base-stock policy is also asymptotically optimal. Furthermore, we show that a modification suggested by Archibald of this base-stock level also results in an asymptotically optimal policy. Finally, we numerically test the performance of this heuristic policy for a wide spectrum of values for the lost-sales penalty cost parameter and illustrate the superior performance of Archibald's method.Item Optimal Procurement Auctions under Multistage Supplier Qualification(INFORMS) Chen, W.; Dawande, Milind W.; Janakiraman, Ganesh; 0000-0001-6956-0856 (Dawande, MW); 0000-0001-7386-4318 (Jamakiraman, G); Dawande, Milind W.; Janakiraman, GaneshWe consider a firm that solicits bids from a fixed-sized pool of yet-to-be qualified suppliers for an indivisible contract. The contract can only be awarded to a supplier who passes a multistage qualification process. For each stage of the qualification process, the buyer incurs a fixed testing cost for each supplier she chooses to test. The buyer seeks an optimal mechanism-that is, one that minimizes her total expected cost. Motivated by the buyer's urgency (or the lack of it) of time for completing the qualification process, we obtain optimal mechanisms for two testing environments: (1) simultaneous testing, where in each stage, the buyer selects a subset of those suppliers who have passed all the previous stages and tests them simultaneously; and (2) nonsimultaneous testing, where the simultaneous-testing requirement is not imposed. Under simultaneous testing, the admission policy for selecting suppliers at each stage is based on nonuniformreserve-price thresholds. Under nonsimultaneous testing, too, the admission policy is threshold based, but the selection process is sequential in nature. The relative increase in cost due to the simultaneous-testing requirement is (under a mild condition) monotonically increasing in the number of suppliers, the expected multistage testing cost, and the overall passing probability. We also study the optimal sequencing of the qualification stages and show that the buyer should schedule the stages in increasing order of the ratio of their testing cost to their failing probability. Finally, for the simpler setting of a single-stage qualification process and a single supplier, we study a two-dimensional mechanism design problem where, in addition to cost, the passing probability is also private to the supplier. Here, too, threshold-based admission remains optimal, and the buyer offers either a pooling or a separating contract. Copyright: ©2018 INFORMS.Item Robustness of Order-Up-To Policies in Lost-Sales Inventory Systems(INFORMS) Bijvank, Marco; Huh, Woonghee Tim; Janakiraman, Ganesh; Kang, WanmoWe study an inventory system under periodic review when excess demand is lost. It is known (Huh et al. 2009) that the best base-stock policy is asymptotically optimal as the lost-sales penalty cost parameter grows. We now show that this result is robust in the following sense: Consider the base-stock level which is optimal in a backordering system (with a per-unit-per-period backordering cost) in which the backorder cost parameter is a function of the lost-sales parameter in the original system. Then there is a large family of functions (mapping the lost-sales cost parameter to the backorder cost parameter) such that the resulting base-stock policy is asymptotically optimal. We also demonstrate the robustness phenomenon through a second result. We consider the base-stock level which is optimal in a backordering system in which a unit of backorder is charged a penalty cost only once (such a system has been studied by Rosling). We show that this base-stock policy is also asymptotically optimal. Furthermore, we show that a modification suggested by Archibald of this base-stock level also results in an asymptotically optimal policy. Finally, we numerically test the performance of this heuristic policy for a wide spectrum of values for the lost-sales penalty cost parameter and illustrate the superior performance of Archibald's method.Item Fixed-Dimensional Stochastic Dynamic Programs: An Approximation Scheme and an Inventory Application(INFORMS) Chen, Wei; Dawande, Milind; Janakiraman, GaneshWe study fixed-dimensional stochastic dynamic programs in a discrete setting over a finite horizon. Under the primary assumption that the cost-to-go functions are discrete L♮-convex, we propose a pseudo-polynomial time approximation scheme that solves this problem to within an arbitrary prespecified additive error of ε > 0. The proposed approximation algorithm is a generalization of the explicit-enumeration algorithm and offers us full control in the trade-off between accuracy and running time. The main technique we develop for obtaining our scheme is approximation of a fixed-dimensional L♮-convex function on a bounded rectangular set, using only a selected number of points in its domain. Furthermore, we prove that the approximation function preserves L♮-convexity. Finally, to apply the approximate functions in a dynamic program, we bound the error propagation of the approximation. Our approximation scheme is illustrated on a well-known problem in inventory theory, the single-product problem with lost sales and lead times. We demonstrate the practical value of our scheme by implementing our approximation scheme and the explicit-enumeration algorithm on instances of this inventory problem.