Some special fixed charge solid transportation problems of substitute and breakable items in crisp and fuzzy environments

•Uncertain special fixed charge STPs with substitute and breakable items are solved.•4-dimensional multi-item transportation problems (4DMITPs) are introduced and solved.•Marketing of substitute items from management's and customers' view points presented.•Items' breakabilities due to different routes' distances and vehicles are considered.•Items' fuzzy amount substitution due to its selling prices/in the lump implemented.

In this paper, some special fixed charge multi-item solid transportation problems which include damageability (breakability), substitutability and paths into consideration are developed and investigated in crisp and fuzzy environments. The breakability of substitute items varies due to the transported amount, conveyance type and traversed distance (path). The substitutability of the items depends on both the supply side by the management's discretion (ad hoc quantity), and the demand side by the item's price (price dependent). The vagueness of the model parameters is introduced by fuzzy set theories and then defuzzied applying possibility measure. Models are formulated as profit maximization problems, solved using generalized reduced gradient method and illustrated through numerical experiments. Sensitivenesses of profits on the degrees of substituteness are also presented numerically. Conventional solid (3D) and general (2D) transportation problems are derived as particular cases. Some useful managerial decisions are derived.

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