Process variability analysis in make-to-order production systems

Figures & data

Figure 1. Production system for license vehicle number plate production

Table 1. Arrival rate (λ) vs. process rate (μ) of jobs at the plants

Plant	λ (pr/h)	μ (pr/h)
Awka	111	222
Gwagwalada	158	222
Lagos	383	444
Lagos State	114	167

Figure 2. Process time of the production lines

Table 2. Variability parameters of the plants

Plant	$\overline{x}$ (h)	σ (h)	C V	Variability level	Implication for performance case
Awka	0.46	0.29	0.63	Low	Between best case practical worst case
Gwagwalada	0.39	0.29	0.74	Low	Between best case practical worst case
Lagos	0.46	0.25	0.54	Low	Between best case practical worst case
Lagos State	0.36	0.21	0.58	Low	Between best case practical worst case

Table 3. Expected performance measures of the plants after pooling

Plant	λ (pr/h)	μ p (pr/h)	$\overline{x}$ (h)	σ (h)	C v	ρ	P 0	L q(pr)	L (pr)	Wq (h)
Awka	111	475	0.32	0.10	0.31	0.23	0.77	77	78	0.72
Gwagwalada	158	535	0.25	0.06	0.24	0.30	0.70	66	67	0.41
Lagos	383	769	0.34	0.10	0.29	0.50	0.50	1,478	1,479	3.82
Lagos State	114	341	0.26	0.08	0.31	0.33	0.67	60	61	0.55

Figure 3. Effect of variability reduction by pooling on average number of plates on queue for Gwagwalada plant

Figure 4. Effect of variability reduction by pooling on average number of plates in queue for Awka plant

Table 4. Cost benefit of pooling

Type of operation	X (pairs)	SP ($₦$)	FC ($₦$)	VC ($₦$)	Annual variable cost ($₦$)	Annual net income ($₦$)
Pooled operation	1,003,023	5,000 ($25)	500,000,000 ($2.5 m)	398 m ($1.99 m)	399,200,000 ($1.99 m)	4,124,939,050 ($20.62)
Un-pooled operation	436,788	5,000 ($25)	500,000,000 ($2.5 m)	896.05 m ($1.95 m)	391,383,405 ($1.95 m)	1,292,556,113 ($6.4 m)
Profit						2,832,382,937 ($14.16 m)

Note:

Exchange rate $1.00 = $₦$200.00.

Table 5. Data from screen printing lines

Sample no.	Awka plant	Gwagwalada plant	Lagos plant	Lagos State plant
1	12.45	11.92	11.58	12.79
2	12.12	12.02	12.12	13.50
3	11.93	12.10	11.93	12.44
4	15.81	12.02	11.88	12.54
5	12.71	11.97	12.71	12.16
6	11.88	11.54	14.81	12.26
7	14.98	11.21	12.11	12.16
8	12.11	12.01	12.17	12.57
9	12.58	12.16	12.30	12.16
10	12.17	12.02	11.23	12.27
11	12.30	12.65	12.00	13.27
12	12.23	11.22	12.23	12.33
13	12.03	11.78	12.03	13.38
14	12.51	12.27	12.51	12.15
15	12.66	11.67	12.66	12.89
16	12.79	11.58	12.43	12.30
17	13.50	12.28	11.88	12.15
18	12.44	12.19	11.92	12.14
19	12.54	11.99	12.02	11.59
20	12.16	12.11	12.10	12.00