Index sets ${f}_{1},\cdots ,F$ : set of factories. ${p}_{1},\cdots ,P$ : set of all different brands. ${d}_{1},\cdots ,D$ : set of all distributors. ${w}_{1},\cdots ,W$ : set of all internal warehouses. ${m}_{1},\cdots ,M$ : set of production lines at various factories. ${v}_{1},\cdots ,V$ : set of all vehicles in the transportation fleet. ${t}_{0},\cdots ,T$ : time frame considered. Parameters $\delta$ : amount of product p demanded by distributors d at time t. ${\eta }_{fcost}$ : operational cost of production line $m$ at factory f. ${\eta }_{cap}$ : production line m maximum production capacity of product p at factory f. ${S}_{cap}$ : warehouse w capacity. $\gamma$ : fuel price in litres. ${\rho }_{v}$ : the number of kilometers to be travelled by vehicle v per litre of fuel. ${\beta }_{v}$ : vehicle v maintenance cost per km. ${\nu }_{cap}$ : capacities of vehicles. ${\zeta }_{fd}$ : distance in km between factory f and distributors d. ${ϵ}_{fd}$ : fixed driver cost working between factory f and distributors d. ${\varphi }_{fd}$ : driver’s additional cost from factory f to distributors d. Variables ${\nu }_{fd}$ : vehicle v operational cost from factory f to distributors d. ${\sigma }_{act}$ : production line m activated at factory f at time t. ${A}_{prod}$ : Number of products p produced by production line m in factory f at time t. ${A}_{tfw}$ : Number of products p at the warehouse w at time t. ${A}_{twd}$ : Number of products p transported from factory warehouse using vehicle v to distributors d at time t. ${A}_{ware}$ : total products p in warehouse w at time t. VF: number of each vehicles v used at factory at time t. ${N}_{vfd}$ : number of vehicles v used to transport products at time t. ${T}_{vfd}$ : total number of vehicle v used to transport products. ${\alpha }_{fd}$ : driver total cost from factory f to distributors d.