Robust production planning and control for multi-stage systems with flexible final assembly lines

Figures & data

Figure 1. Scheme of the analysed process chain.

Table 1. The applied notation.

Sets
	set of production orders
	set of products
	set of working shifts (macro-periods)
	set of micro-time periods
	set of product modules
	set of machines
	set of operators in the machinery
Parameters
	product of order i
	volume of order i [pcs.]
	due date of order i [shift]
	the total manual norm cycle time of product p
	machine setup time of module m [min]
	manual operation time of module m [min]
	machining time of module m [min]
	duration of a working shift (macro-period length) [min]
	length of a micro-period [min]
	ratio of the macro- and micro-periods’ length:
	lead time of module m in the shared resources segment
	inventory holding cost (product or module) [cost/part/shift]
	late delivery cost [cost/product/shift]
	deviation cost of order i in shift t
	cost of a setup
	cost of an operator per shift
	the max. number of operators working in the same shift
Variables
	production of order i in shift t (binary)
	production of product p in shift t (binary indicator variable)
	produced volume from product p in shift t (integer)
	number of operators working in shift t (integer)
	volume of module m machined in time on machine j
	production of module m in time on machine j (binary indicator variable)
	setup on machine j for module m in time (indicator variable)
	inventory level of module m in time
	assignment of operator o and machine j in time
	volume of module m machine by operator o in time on machine j

Figure 2. Production planning workflow.

Figure 3. Results of the capacity prediction for a sample assembly line.

Table 2. Benchmark of robust production planning methods.

		Lateness [%]						Objective [%]						CPU Time [s]
	Orders	NTP	RPN	RCT	RCO	ITR		NTP	RPN	RCT	RCO	ITR		NTP	RPN	RCT	RCO	ITR
24	Normal	98	73	79	82	83		95	97	100	98	95		8.8	8.8	14.0	14.1	209.2
24	High	100	87	79	83	95		91	94	100	95	91		9.3	10.9	81.5	18.4	90.0
24	Extreme	99	92	79^(8)	87	97		29	33	100^(8)	35	30		11.2	131.1	68.3^(8)	368.3	52.0
30	Normal	100	78	70	73	85		93	96	100	97	93		10.2	11.7	40.4	21.5	141.0
30	High	98	93	81	88	98		84	89	100	91	84		10.9	15.5	370.3	81.0	25.0
30	Extreme	99	90	86^(10)	85^(2)	95		22	25	100^(10)	29^(2)	23		134.8	517.9	116.4^(10)	764.7^(2)	331.7
36	Normal	100	78	75	85	90		93	96	100	97	93		11.4	12.0	61.9	26.7	362.5
36	High	95	93	84^(1)	87	95		22	26	100^(1)	30	22		13.8	68.8	659.3	137.4^(1)	76.1
36	Extreme	95	93	84^(9)	87^(4)	95		22	26	100^(9)	30^(4)	22		41.6	567.0	225.9^(9)	708.1^(4)	184.6
42	Normal	99	87	78	83	93		93	96	100	97	93		13.3	44.6	261.9	86.2	146.7
42	High	99	89	80^(5)	87	95		49	51	100^(5)	52	49		16.9	38.7	1097.2^(5)	240.6	36.9
42	Extreme	97	91	85^(9)	88^(7)	98		26	31	100^(9)	50^(7)	26		112.2	797.4	227.6^(9)	1090.8^(7)	165.1

Figure 4. Total lateness (left) and cost (right) results of the benchmark with the five different planning methods.

Table 3. Module parameters in the test case.

Module1	1.22	0.76	0.6	127	32
Module2	0.59	1	0.75	131	30
Module3	2.14	0.81	0.53	101	32
Module4	1.28	0.76	0.8	140	50
Module5	0.16	0.86	0.56	123	30
Module6	2.57	0.83	0.56	115	25
Module7	1.65	0.7	0.56	121	29
Module8	1.82	0.66	0.78	113	57
Module9	2.67	0.9	0.78	108	20
Module10	1.56	1	0.81	104	41
Module11	1.78	0.95	0.78	106	22
Module12	2.34	0.68	0.56	111	52
Module13	0.31	0.86	0.8	144	53
Module14	2.77	1	0.8	119	52

Table 4. Simulation analysis: execution of the production plans (pre-inventory processes).

Scenario				[pcs.]
1	1	1	86	0	0.0%
2	1	1	93	0	0.0%
3	1	1	100	0	0.0%
4	1	1.30	86	0	0.0%
5	1	1.30	93	4	0.0%
6	1	1.30	100	0	0.0%
7	1	1.60	86	111	0.8%
8	1	1.60	93	255	1.9%
9	1	1.60	100	111	0.8%
10	1.30	1	86	5	0.0%
11	1.30	1	93	5	0.0%
12	1.30	1	100	5	0.0%
13	1.30	1.30	86	5	0.0%
14	1.30	1.30	93	42	0.3%
15	1.30	1.30	100	5	0.0%
16	1.30	1.60	86	196	1.5%
17	1.30	1.60	93	336	2.5%
18	1.30	1.60	100	196	1.5%
19	1.60	1	86	55	0.4%
20	1.60	1	93	74	0.6%
21	1.60	1	100	55	0.4%
22	1.60	1.30	86	110	0.8%
23	1.60	1.30	93	262	2.0%
24	1.60	1.30	100	110	0.8%
25	1.60	1.60	86	492	3.7%
26	1.60	1.60	93	599	4.5%
27	1.60	1.60	100	492	3.7%