A multi-objective flexible job shop scheduling problem (FJSSP) that considers transportation time using mathematical programming is proposed to optimise three conflicting objectives: minimising makespan, total cost, and total lateness. The proposed model was developed and verified in three stages. In the first stage, only one objective was considered. The minimisation of the makespan and total cost was considered separately in the first stage. In the second stage, only two objectives were considered. In this stage, the minimisation of the makespan and total cost was considered instantaneously. In the third stage, a model was developed to optimise the three objectives. The proposed model was formulated using mixed-integer nonlinear programming (MINLP) and solved using the DICOPT solver based on general algebraic modelling system (GAMS) optimisation software. This model includes the transportation times between machines in the FJSSP, and the problem is called the “flexible job shop scheduling problem with transportation time” (TT-FJSSP). The proposed model gave better results in comparison with the other recent developed models. The effect of changing the maximum allowable deviation when optimising the three objectives was studied to achieve more-practical results.

This research is a development of a stochastic mixed integer linear programming (SMILP) model considering stochastic customer demand, to tackle the multi-product SCND problems. It also considers multi-period, multi-echelons, products inventories, considering locations capacities and associated cost elements. The model represents both location and allocation decisions of the supply chain which maximize the total expected profit. The effect of demand mean on the total expected profit and the effect of the number of scenarios on the CPU time are studied. The results have shown the effect of customers’ demands for each product in each period on the quantities of material delivered from each supplier to each factory, the quantities of products delivered from each factory and factory store to each distributor, the inventory of each product in each factory and distributor, the quantities of each type of product delivered from each distributor to each customer in each period. The model has been verified through a detailed example.