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This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions). The objective function under a constraint is imposed here in crisp and fuzzydoi:10.24297/jam.v15i0.7364 fatcat:ntn5rb7pbjcvbor7dfmyi5yl2u