network
In Tanzania, the 2012 national population census revealed the annual population growth to be 2.7% [83]. Hence there will be an increase in demand of the maize crop. We have therefore studied the performance of the extended network based on the projected demands in the next five and ten years. We have denoted the projected demand by ˆDl. This is calculated from Dl
by considering a percentage increase for annual demand (denoted by Dl(↑) in Table 5.25) in
each corresponding number of years. In particular, we have considered the annual demand increase of 5%, 10% and 12% as indicated in Table 5.25. Apart from the new demand, the remaining inputs used for optimization are the same as those used in section 5.6 for eight DCs. For this experiment we have used the mathematical model for the extended network presented with the equations (5.39) - (5.40). The results are summarized in Table 5.25 where the notations used in the columns are the same as those found in the text.
The results in Table 5.25 indicate the sustainability of the extended network for the next five and ten years where up to 12% annual demand increase is possible. This is from the fact that the current total capacity for eight DCs is 337,500 tons while the maximum observed total capacity to be utilized is 319,317 tons. This is for 12% annual demand increase in the
Table 5.25: Summary results for the increased demand Years |L| P l=1 ˆ Dl Dl(↑) |Ks| |Ks| P k=1 Vr k DC1 DC2 DC3 DC4 DC5 DC6 DC7 DC8 5 181,430 5% 7 181,571 25,000 - 39,000 18,144 29,000 39,000 18,144 13,283 217,716 10% 8 217,783 25,000 26,000 45,000 24,000 33,000 25,000 26,500 13,283 232,230 12% 7 232,288 28,500 - 45,144 24,000 39,000 53,000 26,500 16,144 10 217,716 5% 8 217,783 25,000 26,000 45,000 24,000 33,000 25,000 26,500 13,283 290,288 10% 7 290,573 39,361 - 59,000 34,000 38,929 63,000 43,000 13,283 319,317 12% 8 319,361 39,361 26,000 63,000 34,000 45,000 53,000 43,000 16,000
next ten years (see last row in Table 5.25 under
|Ks|
P
k=1
Vkr). The number of DCs to be used in projected demand ˆDl, are seven and eight (see column under |Ks| in Table 5.25). Notice
that under the current demand Dl, only six DCs were found to be optimal.
The last eight columns under DC1 to DC8 in Table 5.25, indicate the capacity for each
selected DC. DC3 and DC6 mostly appear to have higher selected capacities than others
while DC8 has the lowest selected capacity. This is due to the number of CPs together with
their demands being higher for DC3 and DC6. These two DCs are located in semi-arid areas
where there is always deficit of maize crop harvest every year.
The results obtained with the above experiment clearly suggest that the government’s plan to build three new DCs with suggested maximum capacities is appropriate, given the increased demands.
Chapter 6
Conclusions and future research
6.1
Conclusions
The capacitated two-level facility location problem (FLP) has been studied in this thesis. The study involves a model that integrates three layers namely: production centers (PCs), distribution centers (DCs) and customer points (CPs).
Using the mathematical model, a distribution network is established with minimum cost for transportation of maize crop from PCs to CPs through DCs. We have studied both a deterministic and a stochastic version of our model using a case study in Tanzania. The consideration of the deterministic model in this thesis is mainly for comparison with the results of the stochastic model. In both cases, we have studied two types of distribution networks, the existing distribution network and an extended distribution network. The existing distribution network is when five DCs are used while in the extended distribution network, the same five DCs are used together with the three new proposed DCs. In these two networks, the general goal is to satisfy the customers’ demand with minimum overall distribution cost. We have considered four PCs, eight DCs and 93 CPs. These are the ingredients of the studied network.
The following are the summary results that have been revealed in the existing distribution network for the deterministic model as detailed in Chapter 4:
(a) The manually operated network was found not to be optimal. This is due to the observed overall cost saving that results from reallocation of PCs, DCs and CPs compared to the manually operated network. The details are presented in section 4.2.2, Chapter 4.
(b) Through optimization, an improved network was established, resulting in an average cost saving of $564 thousand, compared to the manually operated network. The model predicted 4.27% of cost reduction from the cost of manually operated network. The improved results show that only four DCs should be used out of the five DCs considered.
When considering the sustainability of the network over a period of time (e.g. five or ten years to come) with maximum annual demands being satisfied, we have also studied and analysed the extended network using eight DCs. This is based on high production capacities in PCs and future increased demands. The results for this extended network are stated below:
• By using eight DCs, an improvement in terms of cost reduction was achieved compared
to the existing network.
• The results for eight DCs have reduced the cost obtained in the existing network
in part (b) above by 3%. This is equivalent to a saving of $357 thousand. When we compared to the cost of the manually operated existing network, the extended network had reduced the cost by 7.27% (3% + 4.27%). This is a significant saving which has been achieved through the extended network. In this experiment, only six DCs are selected out of eight DCs where two of the six selected DCs are the newly proposed DCs.
The stochastic model presented in Chapter 5 is an extension of the deterministic model by considering the effect of rainfall in the transportation network. In the computational experiments for the stochastic model, we have observed an overall network cost increase as
compared to the cost of the corresponding deterministic model. Furthermore, the analysis on location-allocations for PCs, DCs and CPs, also have been addressed in Chapter 5. We have carried out these computations in the existing network and the extended network. The computational results for the stochastic model are as follows:
(i) In the existing network, an average cost increase of 13.06% was observed compared to the corresponding cost of the deterministic model.
(ii) In the case of the extended network using eight DCs, the cost increase for the stochastic model is 11.32% as compared to the corresponding cost of the deterministic model. This cost increase obtained for the extended network, is lower than that of the existing network (13.06%) as presented in (i) above. This also clearly indicates the potential of using extended network for cost reduction.
Generally, the cost increase due to stochastic rainfall is an important factor to be considered prior to transportation planning. This is due to the fact that the condition of road networks, in Tanzania, can be affected by rainfall (see Longido case in Appendix D). The Tanzanian government is encouraged to consider this factor as suggested by this study.
The results obtained show that optimization as a decision tool in logistic problems is important. It can be used by all stakeholders and practitioners in their planning. The results of extended network also give more potential for future planning (e.g. expansion of PCs’ and DCs’ capacities), and that this should be done using optimization as one of the decision tools. The Tanzanian government is encouraged to use the results from this study for reviewing its existing maize crop distribution network.
We have also studied the structure of the optimized extended network using increased annual demand of maize crop over five and ten year horizons. Results show that in both horizons,
period of 10 years.