An available-to-promise stochastic model for order promising based on dynamic resource reservation policy

Figures & data

Table 1. Classification of Demand Class.

Order	Profit Margin
Demand class	High Profit	Medium Profit	Low Profit
Stage 1 (current actual)	Class 1	Class 3	Class 5
Stage 2 (future forecast)	Class 2	Class 4	Class 6

Figure 1. Promising current orders in the push-pull based ATP model.

In the push-pull based ATP model, these are five possible demand scenarios at Stage 1 for an initial availability a and the reservation level R.

Figure 2. Promising current orders in the pull-based ATP model.

In the pull-based ATP model, these are four possible demand scenarios at Stage 1 for an initial availability a without reservation.

Figure 3. Promising future customer orders (with given remaining critical resource b).

In the push-pull based ATP model, there are four possible scenarios in Stage 2 for a given remaining critical resource b.

Table 2. Characteristics of Demand Classes

Order	Profit Margin
Stage	High Profit	Medium Profit	Low Profit
Stage 1 (current actual)	$v_1=940$CNY	$v_3=761$CNY	$v_5=616$CNY
	$w_1=94$CNY	$w_3=76$CNY	$w_5=61$CNY
	$\mu {}_1=1474$ units	${\mu }_3=1783$ units	${\mu }_5=2157$ units
	${\sigma }_1=85.6$ units	${\sigma }_3=103.5$ units	${\sigma }_5=125.1$ units
Stage 2 (future forecast)	$v_2=846$CNY	$v_4=685$CNY	$v_6=555$CNY
	$w_2=85$CNY	$w_4=68$CNY	$w_6=55$CNY
	${\mu }_2=1621$ units	${\mu }_4=1961$ units	${\mu }_6=2372$ units
	${\sigma }_2=94.1$ units	${\sigma }_4=113.8$ units	${\sigma }_6=137.6$ units

Figure 4. Best fitness value in each generation versus iteration number.

GA stops at the 51st generation, the optimal reservation level R* turns out to be 2463 units, and the corresponding maximal expected total profit is 4352000 CNY.

Figure 5. Impact of dynamic resource reservation policy.

It reflects the impact of different reservation levels on the expected total profit and the average total profit and shows that the total profit rises with the increasing reservation level till its peak value and then falls to a certain level.

Figure 6. Impact of initial availability on reservation level (for low availability scenarios).

It reflects the different reservation levels on the expected total profit and the average total profit under three low initial availability scenarios and shows that the optimal reservation level experiences an increasing trend due to increasing availability.

Figure 7. Impact of initial availability on reservation level (for high availability scenarios).

It reflects the different reservation levels on the expected total profit and the average total profit under three high initial availability scenarios and shows that the proposed dynamic resource reservation policy becomes less important when there are abundant critical resources.

Figure 8. Impact of per-unit denial penalty cost of different ratio levels on reservation level.

Under different ratio levels of per-unit denial penalty cost, the optimal reservation level experiences little change, and the optimal price level stays around 2461 units.

Figure 9. Impact of per-unit denial penalty cost with the same value on the reservation level.

Under different per-unit denial penalty costs, the optimal reservation level still experiences little change, and the corresponding reservation level stays around 2461 units.

Figure 10. Impact of per-unit denial penalty cost of class 1 on reservation level.

Under different per-unit denial penalty cost w1, the optimal reservation level still experiences little change, and the corresponding reservation level stays around 2461 units.

Figure 11. Impact of per-unit denial penalty cost of both class 1 and class 2 on reservation level.

The optimal reserve level is volatile within a very small range when per-unit denial penalty cost w1 and w2 are set to different values.

Figure 12. Impact of inventory holding cost g and h on reservation level.

When the per-unit component inventory cost g is fixed, the optimal reserve level has a very small fluctuation with the change of the per-unit component inventory cost h, whereas, when h is fixed, the optimal reservation level experiences a step down with the growth of g.

Figure 13. Impact of future pricing level on the total profit.

The optimal price level v2 = 885 CNY exists, maximising the total profit when combining dynamic resource reservation policy.

Figure 14. Impact of future pricing level on the reservation level and total profit.

The optimal reservation level shows an obvious growing trend with the reduction of future pricing levels.

Data availability statement

The data that support the findings of this study are available from the corresponding authors, W.Q. and Y. L., upon reasonable request.

Acknowledgements

The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (No. 51775348).