The Effect of demand distribution pattern and demand variance on

The effect o f the proposed IRP model on the demand distribution factor is examined by considering Normal and Poisson distributions for identical retailers. The mean values for Normal and Poisson distributions are set equal to the mean o f the current demand distribution used in the study. However, the value o f the variance parameter for the Poisson distribution is slightly different as a result o f the characteristic of Poisson distribution since the variance value is equal to the mean value. Further, five different variance values o f the Normal distribution are considered in this analysis, namely, the condition when the variance is approximately similar to the current setting, Normal( 10,2.24), the condition when the model have a lower variance value, Normal (10,2.0) and Normal (10,1.0) as well as the condition when the model have a higher variance value, Normal (10,2.5) and Normal (10,3.0) in order to examine the effect of the IRP model w ith regard to the variation o f demand.

The effect o f different demand distributions that may have similar mean and variance with current demand distribution used in the IRP model on the optimal inventory control parameters that minimises the total cost is shown in Table 5.13.

Table 5.13: Optimal inventory control parameters and total cost for different demand distributions

Demand "Order-up- "Must-deliver" "Can-deliver" Optimal

Distribution to" level level level total cost

Normal (10,2.24) 19 0 11 22.9644

Poisson(lO) 19 0 10 23.7606

Binomial(20,0.5) 19 0 13 22.9528

With a similar warm-up period and length o f simulation execution, it is found that the behaviour o f the model is consistent, even with different demand distributions, since the optimal inventory control parameter is similar for Normal (10, 2.24), Poisson (10) and Binomial (20, 0.5). Thus, it is anticipated that the model will behave similarly for demand distributions that have similar characteristics. However, different total cost values occur as a result o f different values o f demand data generated with regards to the demand pattern behaviours. Consistent with ANOVA analysis findings reported in

Mustaffa and Disney (2006), the IRP model performance measurement is highly influenced by the demand distribution factor. W ith regard to the impact o f demand variations, it can be seen in Table 5.14 that shortage cost is increased as the demand variance is increased, which is as expected.

Table 5.14: Effect of demand variance on inventory control parameters and costs

Parameters

Is also been discovered that the optimal combination o f inventory control parameters have shown an interesting pattern in the results. Basically, in theory a higher “must- deliver” level is needed in order to deal with high demand variance. However, the findings from Table 5.14 suggest that a lower “must-deliver” level is more economical when there is opportunity to coordinate the replenishment between retailers via the “can-deliver” level by considering o f the transportation cost in the performance measurement. A higher “must-deliver” level may increase the number o f delivery trips where probably only one or two retailers that reach the “must-deliver”

level and “can-deliver” level are required to be delivered in one delivery trip.

Therefore, another delivery trip needs to be scheduled in the next period in order to fulfil the requirement for others retailer. Hence, more frequent delivery is required and this phenomenon will cause a higher transportation cost and holding cost.

However less total cost will occur with a low “must-deliver” level since the probability to deliver to all retailers in one delivery trip is higher. This is because, there is a gap between the replenishment periods as none o f the retailers have reached the “must-deliver” level and no replenishment is required at some period. As a result,

the inventory level for all retailers may decrease unvaryingly and all retailers can be consolidated together for each replenishment time. As a result, fewer delivery trips are required. Therefore, less total cost is incurred with a reduction o f transportation cost and holding cost even though it may cause a slightly higher shortage cost.

5.9 Conclusion

This chapter has examined the opportunity for a supplier to consolidate retailers’

replenishment through an inventory control policy called the “can-deliver” policy.

The analysis was carried out using a spreadsheet simulation. The steady state period was determined using the well-known W elch’s method. The simulation was executed with multiple replications to ensure accuracy. At the 95 percent and 99 percent confidence level, three replications were found appropriate for this simulation model.

The performance o f the “can-deliver” policy was evaluated in 3 phases. First, we examined the model by varying the inventory control parameter with the constant costs parameter. Results showed that the total costs decreased as the “can-delivery”

level is increased. However, the benefit seemed to saturate out with high flexibility.

The experiment is expanded by varying the cost parameters using the experimental design approach based on the Taguchi methods to get the rough idea o f model behaviour. The experiment showed that the “must-deliver” level, holding cost and transportation cost factors had a large impact on the model performance measurement as expected. Then, the sensitivity analysis o f the model is analysed by determining the optimal combination o f inventory control parameters that minimised the total cost.

Total cost o f the model is a function o f holding cost, shortage cost and transportation cost. 125 combinations o f these costs were analysed using the brute-force approach to determine the optimal total cost. Results showed that the “can-delivery” level minimised the total cost for the combination o f costs. The result suggested that it is economical to replenish all retailers when there is the opportunity to make replenishment and the ratio o f transportation cost is high compared to holding cost. In other situations, the results showed that the minimum total cost existed at a certain flexibility level. The dynamic relationship between costs parameter and the inventory control parameters was visualized using the causal-loop diagram.

Finally, in order to evaluate this m odel’s performance, comparison analysis was performed between the “can-delivery” policy and the (s,S) policy as well as the (s,S-1,5) policy by changing the setting o f the “can-delivery” level. The results showed that with the periodic “can-deliver” policy it was possible to get the maximum 17.6% saving compared to the (s,S) policy. On the other hand, only a small additional cost would be incurred if replenishment was made to all retailers at each delivery time.

So far, the optimal routing strategy for the proposed IRP model has been determined based on the route that minimises the total distance travelled during the replenishment activities. However, as the quantity o f delivery at each retailer is different based on the condition o f retailers and the cost function, further analysis o f the optimal sequence o f delivery between retailers based on distance, weight o f vehicle and the weight o f replenishment that minimises the costs and vehicle energy and maximises the overall vehicle effectiveness needs to be carried out. Such analysis is presented in the following chapter.