A contract portfolio perspective on the role of customer order lead times in demand fulfilment processes with supply shortage

Figures & data

Figure 1. Example of two different scenarios for the realisation of the order fulfilment process after an initial allocation, where the only difference is in the order lead time (on the left, customer A orders first; on the right customer B orders first).

Figure 2. Rolling horizon scheme for customer ordering behaviour driven allocation planning.

Table 1. Contract portfolios for numerical case study.

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	Total
Customers	16	12	13	13	16	14	14	16	15	14	143
Orders	105	98	131	136	197	185	153	210	214	215	1644
Average ${\overline{\mathit{\text{acc}}}}_i$	85%	79%	82%	93%	91%	88%	68%	87%	91%	99%	86%
Average ${\mathit{\text{olt}}}_i$	2.20	3.38	3.07	1.87	1.47	3.44	2.98	2.82	3.15	2.98	2.73
Average ${\overline{\mathit{\text{err}}}}^{\mathit{\text{acc}}}$(in-sample)	0.03	0.19	0.27	0.31	0.41	0.38	0.40	0.44	0.51	0.65	0.36
Average ${\overline{\mathit{\text{err}}}}^{\mathit{\text{acc}}}$(out-of-sample)	0.04	0.21	0.29	0.30	0.38	0.39	0.40	0.46	0.48	0.59	0.35
$r\left({\mathit{\text{olt}}}_i,{\mathit{\text{acc}}}_i\right)$	0.28	−0.42	−0.18	0.43	0.05	−0.39	0.11	−0.03	0.32	0.23	0.04

Table 2. On-time service levels per ADI accuracy error and number of customer segments.

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
${\overline{\mathit{\text{err}}}}^{\mathit{\text{acc}}}$	0.03	0.19	0.27	0.31	0.41	0.38	0.40	0.44	0.51	0.65
|K| = 2	23%	31%	35%	22%	31%	25%	28%	29%	23%	28%
|K| = 4	24%	33%	35%	24%	31%	26%	32%	32%	25%	35%
|K| = 6	28%	34%	39%	25%	35%	29%	33%	34%	28%	37%
|K| = |I|	35%	41%	43%	29%	42%	33%	37%	37%	29%	31%

Figure 3. (a) Relative difference in on-time service level by upward nesting level, (b) relative service level-optimal upward nesting level by error of ADI accuracy.

Figure 4. Average on-time service level performance of contract portfolios.

Table 3. Service-level-optimal weight factors.

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10
${\overline{\mathit{\text{err}}}}^{\mathit{\text{acc}}}$	0.03	0.19	0.27	0.31	0.41	0.38	0.40	0.44	0.51	0.65
$\alpha$	0.6	0.5	0.4	0.5	0.4	0.4	0.3	0.2	0.1	0.0
$\omega$	0.4	0.4	0.6	0.4	0.5	0.6	0.7	0.8	0.8	1.0
$\pi$	0.0	0.1	0.0	0.1	0.1	0.0	0.0	0.0	0.1	0.0

Table 4. Impact of portfolio-specific parametrisation.

	OTSL
	–	$\alpha \text{,}\omega \text{,}\pi$	$\alpha \text{,}\omega \text{,}\pi \text{,}\left|K\right|$	$\left|K\right|\text{,}n$	$\alpha \text{,}\omega \text{,}\pi \text{,}n$	$\alpha \text{,}\omega \text{,}\pi \text{,}n\text{,}\left|K\right|$
P1	32.2%	34.7%	34.7%	34.2%	35.9%	35.9%
P2	40.2%	41.0%	41.0%	40.6%	41.8%	41.8%
P3	43.2%	43.2%	43.2%	43.9%	43.9%	43.9%
P4	31.6%	33.1%	33.1%	31.6%	33.1%	33.1%
P5	42.9%	43.7%	43.7%	42.9%	43.7%	43.7%
P6	40.3%	40.3%	40.3%	40.3%	40.3%	40.3%
P7	36.4%	38.2%	38.2%	36.4%	38.2%	38.2%
P8	38.7%	40.7%	40.7%	40.9%	41.3%	41.3%
P9	34.0%	34.5%	34.5%	34.7%	35.4%	35.4%
P10	29.7%	32.3%	34.5%	35.4%	33.2%	36.2%
Average	36.9%	38.2%	38.4%	38.1%	38.7%	39.0%

Table 5. The value of considering order lead time, ADI accuracy and profitability in demand fulfilment.

	OTSL
	$\pi =1$	$\alpha =1$	$\omega =1$	All
P1	25.6%	28.7%	35.1%	35.9%
P2	26.8%	29.9%	37.3%	41.8%
P3	27.8%	31.2%	38.5%	43.9%
P4	26.3%	25.9%	32.1%	33.1%
P5	26.1%	30.5%	39.8%	43.7%
P6	28.9%	28.2%	37.0%	40.3%
P7	28.3%	28.5%	36.6%	38.2%
P8	24.5%	27.1%	37.2%	41.3%
P9	26.6%	26.4%	35.0%	35.4%
P10	27.0%	26.1%	35.8%	36.2%

Figure 5. On-time service level in dependence of (a) the average customer order lead time; (b) the correlation of order lead time and advance demand information bias.