the risk of delay. Scenario 3 shows that increasing only warehouse capacity does not make any sense on the
model unless the suppliers’ capacities are increased at the same time. As it is shown in scenario 4, increasing all
these capacities together will result in transporting many more products from suppliers to warehouse in the
early periods. The result of that is an important decreasing in delaying cost which would tolerate a little
increasing in warehousing costs. Scenarios 5 and 6 show that increasing starting inventories will both decrease
transported product quantities from suppliers to warehouse and allow the quick transport of the products to
the manufacturer. Although the transportation and delaying costs decrease, it should be noticed that the warehousing
cost increases 2 and 3 times, respectively. This situation indicates that the model is sensitive to the unit
cost values. In the last two scenarios, even though there is an increase in warehousing cost, the total cost continues
decreasing since they combine the advantages of scenarios 4, 5 and 6.
The above-mentioned scenario results can be followed clearly in Fig. 2. The only thing that was not mentioned
above is that the transportation cost between warehouse and manufacturer is constant because of having
certain and imperatively satisfied demands and constant unit transportation costs.
4.2. Sensitivity analysis
In the scenario analysis section, numerical results of the model has analyzed for various scenarios. In that
section, a model’s sensitivity to some capacity and cost parameters are represented but the explosion of the
presentation volume is avoided by not giving the detailed system parameters. First, we motivated the analysis
with relaxing the capacity restriction of suppliers to show the sensitivity of the model to this parameter. The
capacities of all suppliers, which were the 300, 400, 200 and 300 pallets/period, respectively, in the model application,
are increased 16 times in steps of 50 pallets. Fig. 3 shows the changes of all objective values and the
totals. The warehousing cost and transportation cost between warehouse and manufacturers are not affected
by supplier capacity increases. However, delaying cost results in decreasing rates and transportation cost
between suppliers and warehouse reduces at the beginning and then increases. Since the decreasing amount
in delaying cost is relatively higher than transportation cost, the overall total cost decreases continuously
and in decreasing rate.
To explain the reasons of these changes, transported quantities from the suppliers are given in Fig. 4, while
the capacities are relaxing. In the first two capacity increases, supplier 1 and supplier 4, which have long transportation
time but low unit costs, increase transported products quantities and the others decreases. Then the
supplier having the lowest transportation cost increases transportation rate until the increase of 600 pallets.
Also, it should be noticed that relatively more expensive but faster suppliers (supplier 2 and supplier 3) start
to transport more products after an increase of 350 pallets and 200 pallets, respectively. The reason for this
marginal reduction rate of delaying cost becomes greater than the reduction of the transportation cost
between suppliers and warehouse.