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Stochastic Mixed Garger Linear Programming (SMILP) Model

1791 Words8 Pages

ABSTRACT
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 …show more content…

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 nature of the logistic decisions encompasses procurement of raw materials from suppliers, production of finished product at factories, distribution of finished product to customers via distributors, and the storage of end product at factories and distributors. The proposed scheme of supply chain consists of three echelons (three suppliers, three factories, and three distributors) to serve four customers as shown in Figure …show more content…

EFFECT OF DEMAND MEAN AND NUMBER OF SCENARIOS

The relationship between demand mean and total expected profit has been studied at different values of scenarios of 1, 8, 27 and 64. Figures 2-6 show that the general shape of the relation between demand means and total expected profit is almost the same for a different number of scenarios. In general, the increase in demand mean increases the total expected profit as shown in Figure 6. The total expected profit is linearly proportional to the total demand. At transient ranges, it decreases slightly due to the shortage cost as it is not profitable to open an extra location. At certain demand mean, it is profitable to open another location to fulfill the extra demand. The same behavior continues with the increase in demand mean until the total demand exceeds the maximum permissible capacity of the network and it is not possible to open extra locations.

Figure 2: Relationship between demand mean and the total expected profit for 1 scenario.

Figure 3: Relationship between demand mean and the total expected profit for 8 scenarios.

Figure 4: Relationship between demand mean and the total expected profit for 27

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