SENSITIVITY ANALYSIS AND SCENARIO EVALUATION

To ensure the reliability and robustness of the decisions suggested by the mathematical programming model, a sensitivity analysis is conducted with respect to the factors that are potentially influential to the results. In addition, in order to generate more managerial insights, the MIP model is applied to different scenarios.

Sensitivity analysis

Three factors are considered in the sensitivity analysis: the fixed facility cost, the overall demand level, and the cost difference between the DC inbound and outbound transportation cost.

Taichung DC

Taichung DC Customers

Changhua DC

1. Fixed facility cost: The fixed facility cost, i.e., fi in the objective function (1), covers the cost items involved in setting up a DC and is independent of the capacity. The most important item is the IT system and the communication equipment. The implication of varying the value of fi is to adjust the class of these hardware and software systems. Meanwhile, it can also be viewed as raising the level of safety inventory (Nozick and Turnquist, 1998). It is found that if fi is reduced from 3,000,000 to 1,000,000 TW dollars, the number of DCs is increased to four. In addition to the three DC previously set up in northern, central, and southern Taiwan (Keelung, Changhua, and Kaohsiung), one more is to be established in Taichung, also in central Taiwan. The split of the demand nodes in central Taiwan as well as the exact location of the fourth DC are illustrated in Figure 5. On the other hand, if fi is increased to 5,000,000 TW dollars, the decision for locating DCs remains unchanged. However, if fi is further increased to 10,000,000 TW dollars, the DC in southern Taiwan (Kaohsiung) is dropped, and the customers are assigned to the DC in central Taiwan (Changhua). Nonetheless, even though only two DCs are set up, the logistics cost per liter is only increased slightly. The total cost is increased to 127,819,600 TW dollars (a 15%

increase when compared to the based case), and the ratio of the fixed cost to the variable cost becomes 2:8, a result due to the adjustment made by the model.

Figure 5 – The fourth DC due to the reduction of fixed cost or the increase of demand

2. Overall demand level: The demand parameter for each demand node (hj) is estimated by assuming the overall annual demand of 20,000,000 liters. However, for the past several decades, the sales of KKL have been growing steadily. In order to understand how KKL should re-act to the possible demand increase, the overall demand level is increased gradually to test the MIP model. It is found that once the overall demand is higher than 30,000,000 liters, one more DC should be set up, and the location of the fourth DC is also at Taichung, as the one shown in Figure 5. The original DC at Changhua is close to the sea port in central Taiwan. However, the

DC at Taichung is adjacent to the heavily populated Taichung metropolitan. The increase of the demand makes it feasible to pay for the fixed cost for another DC by being compensated by the reduction of the DC outbound transportation cost.

3. Cost difference between DC inbound and outbound transportation: The base rate for the land transportation is assumed to be 0.035(1-a) and 0.035(1+a) NT dollars per km for DC inbound and outbound transportation links to reflect the natures of the shipments into and out of the DCs.

The value of the parameter a is initially set as 10%. The value of a is adjusted from 0 to 30% to test its effect. It is found that the decision regarding the number and location of the DCs remains unchanged, though the total cost is changed slightly (within 2%).

Scenario evaluation

Before the study, KKL initially considered setting up only one DC in Taiwan so as to minimize the administrative complexity. The best location for this single DC can be determined by the MIP model (1) to (5) plus one extra constraint of limiting the sum of the binary decision variables (Xi’s) to be 1. It is found the best location is Changhua in central Taiwan, and the total logistics is increased from 110,786,400 to 165,786,400 TW dollars, an almost 50% increase when compared to that of the optimal solution. Therefore, KKL’s initial thought may be preferable from the administration point of view, but the extremely high transportation cost incurred makes the idea not viable.

In general, the customers of KKL are quite stable over time, as most of the wholesalers have been in the business for a long period of time. However, it is possible that the wholesalers may relocate their warehouses. Besides, the possibility of more new comers for this business cannot be ruled out. As the liquor consumption is closely related to population, the set of demand nodes and the amount of the associated demand are adjusted. The annual demand of 20,000,000 liters is re-allocated to 17 hypothetical demand nodes, which are the location of the local governments. In addition, the amount of demand for each node is set to be proportional to the population in the area. The results shows there are still three DCs to be established (one in northern, central, and southern Taiwan respectively). However, the DC in central Taiwan is moved from Changhua to Taichung, where the population and then the demand are higher.

CONCLUSIONS

Located on an island apart from the main island of Taiwan, KKL sells over 90% of its produced liquor domestically. In 2007, KKL’s revenue has reached 11.2 billion TW dollars. In order to raise its profit margin and provide better service, KKL has been retrieving the amounts of sales from the agents and is planning to establish the distribution centers in Taiwan.

This study aims to provide the decision support, especially from a quantitative aspect, for KKL’s strategic plan for establishing the DCs in Taiwan. The classical fixed charge model is modified to take into consideration the inbound and outbound transportation costs associated with the DCs as well as the variable and fixed components of the DC facility costs. This study collects and estimates the values of the associated parameters in the model. The results indicate that the total cost is 110,786,400 TW dollars per year, and three DCs are to be established in Keelung, Changhua, and Kaohsiung in northern, central, southern Taiwan respectively. The sum of the transportation cost for all four links is 84,395,530 TW dollars, making the unit transportation cost to be 4.2 TW dollars per liter. The total facility cost is 26,390,870 TW dollars, and the ratio of transportation cost to facility cost is about 76%

to 24%.

The sensitivity analysis is performed with respect to three factors. The result shows that the changes in fixed cost and demand level are the most influential factors for locating the DCs. If the fixed cost is reduced from 3,000,000 to 1,000,000 NT dollars, the number of the DCs is increased from three to four.

One more DC will be established at Taichung in central Taiwan. On the other hand, if the fixed cost is creased to 10,000,000 TW dollars, the DC in southern Taiwan (Kaohsiung) is dropped, and the customers are assigned to the DC in central Taiwan (Changhua).

In the scenario evaluation, it is found that KKL’s initial thought of setting up only one DC in Taiwan is not economically feasible, thought the administrative complexity can be significantly reduced. The total logistics is increased from 110,786,400 to 165,786,400 TW dollars, an almost 50%

increase. In the second scenario, instead of being distributed according to the locations of the current wholesalers, the overall demand is re-allocated according to the population in the counties and cities. It is found the optimal decision for locating the DCs appears to be not very sensitive to the demand distribution, as the locations of the DCs are only slightly changed.

The number of binary variables in the MIP of (1) to (5) is not many, and the optimal solution can be solved easily. However, this formulation relies on several assumptions and simplifications, which leads to the direction of future research for this case study. First, transportation cost is assumed to be linear, and the freight transportation is independent of volume. However, it is common that transportation exhibits significant scale of economy. The decision for locating the DCs should be re-examined if the cost curves of the transportation links are concave. Second, at this moment, inventory cost is not considered in the model, as KKL does not maintain a high level of safety inventory due to its superior market power. However, the business environment changes rapidly, and KKL may need to raise its safety inventory and the customer service level in the future. The decisions for locating the DCs should also take inventory into consideration.

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