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Controlling lead times and minor ordering costs in the joint replenishment problem with stochastic demands under the class of cyclic policies
Author(s) -
Braglia Marcello,
Castellano Davide,
Santillo Liberatina,
Song Dongping
Publication year - 2021
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12571
Subject(s) - mathematical optimization , heuristic , class (philosophy) , computer science , minor (academic) , economic shortage , holding cost , fraction (chemistry) , order (exchange) , upper and lower bounds , lead time , function (biology) , benchmarking , operations research , mathematics , operations management , economics , mathematical analysis , linguistics , philosophy , chemistry , management , organic chemistry , finance , artificial intelligence , evolutionary biology , government (linguistics) , political science , law , biology
In this paper, we consider the periodic review joint replenishment problem under the class of cyclic policies. For each item, the demand in the protection interval is assumed stochastic. Moreover, a fraction of shortage is lost, while the other quota is backordered. We suppose that lead times and minor ordering costs are controllable. The problem concerns determining the cyclic replenishment policy, the lead times, and the minor ordering costs in order to minimize the long‐run expected total cost per time unit. We established several properties of the cost function, which permit us to derive a heuristic algorithm. A lower bound on the minimum cost is obtained, which helps us to evaluate the effectiveness of the proposed heuristic. The heuristic is also compared with a hybrid genetic algorithm that is specifically developed for benchmarking purposes. Numerical experiments have been carried out to investigate the performance of the heuristic.