Differentiation vs. standardisation in supply chain segmentation: a quantitative study

Figures & data

Figure 1. Example of the divergent and the serial networks.

Figure 2. Four candidate optimal safety stock policies.

Table 1. Comparison of cost and lead time parameters of responsive and economic segment.

Process	Economic segment	Responsive segment
Production	Longer lead time	Shorter lead time
	Higher fixed cost	Lower fixed cost
	Lower variable cost	Higher variable cost
Distribution	Longer lead time	Shorter lead time
	Lower variable cost	Higher variable cost

Table 2. Four scenarios: assumptions of the planning approaches and resulting network types.

Scenario I	• Production location and mode are SKU specific. Each production batch is assigned to a particular market. Pooling in production is not possible
	• Replenishment is SKU specific. Inventory of SKUs can be kept in any of the three stages depending on which policy is chosen by the model. Inventory pooling is not possible
	• Transport is SKU specific.
	• The resulting network is a serial network, referred as Network I.
Scenario II	• Production location and mode are product specific. Each production batch is for aggregated demand of SKUs of a product.
	• Replenishment is product specific. Inventory of products have to be kept in upstream stages. Keeping inventory only in the market is not a choice. This means that the fourth inventory policy is not in consideration and SKUs of a product are forced to be pooled in upstream.
	• Transport is product specific.
	• The resulting network is a divergent network, referred as Network II.
Scenario III	• Production location and mode are product specific. Each production batch is for aggregated demand of SKUs of a product.
	• Replenishment is product specific. Inventory of products can be kept in any of the three stages. If an inventory policy is chosen for a product, all SKUs of the product follow the same policy.
	• Transport is product specific.
	• The resulting network is a divergent network, referred as Network III.
Scenario IV	• Production location and mode are product specific. Each production batch is for aggregated demand of SKUs of a product.
	• Replenishment is group (pool) specific. The optimisation model decides the inventory placement of SKUs in consideration of pooling benefits in upstream stages. The SKUs of a product which are placed in the same location are seen as a group. A possible solution for a product sold to five markets can be divided into two groups with three SKUs in one group and two SKUs in the other. The optimisation model can also decide to put all SKUs in a product in the same stock pool, ending up with only one group. SKUs in a group follow the same inventory policies.
	• Transport is group specific.
	• The resulting network is a divergent network, referred as Network IV.

Figure 3. Differentiation and standardisation levels of the four networks.

Table 3. Values in the datasets.

Notation	Adapted real values value range	Synthetic values
Set
$\mathcal{N}$	3 locations	–
$\mathcal{R}$	3 locations	–
$\mathcal{M}$	21 locations	–
$\mathcal{S}$	2 modes	–
$\mathcal{P}$	50 products	–
$\mathcal{I}$	4 policies	–
Demand parameters
${\mu }_p$	[11, $28\mathrm{k}$]k units	–
${\sigma }_p$	[1, $21\mathrm{k}$]k units	–
cv	[0.01, 3]	–
Cost
$f_{i1}$	[60, 750]€/lot	500€/lot
$f_{i2}$	[12, 149]€/lot	100€/lot
$K_{i1}$	132, 000 k units	–
$K_{i2}$	170, 000 k units	–
$c_{i1}^{\mathrm{f}\mathrm{a}\mathrm{c}}$	[4.8, 11.8]€/$10\mathrm{k}$ units	9€/$10\mathrm{k}$ units
$c_{i2}^{\mathrm{f}\mathrm{a}\mathrm{c}}$	[7.1, 18.7]€/$10\mathrm{k}$ units	13.4€/$10\mathrm{k}$ units
$c_{ij1}^{\mathrm{u}\mathrm{p}}$	[0.09, 0.46]€/$10\mathrm{k}$ units	0.25€/$10\mathrm{k}$ units
$c_{ij2}^{\mathrm{u}\mathrm{p}}$	[0.19, 1.65]€/$10\mathrm{k}$ units	0.57€/$10\mathrm{k}$ units
$c_{j1wp}^{\mathrm{d}\mathrm{n}}$	[0.04, 3.95]€/$10\mathrm{k}$ units	0.70€/$10\mathrm{k}$
$c_{j2wp}^{\mathrm{d}\mathrm{n}}$	[0.07, 12.24]€/$10\mathrm{k}$ units	2.2€/$10\mathrm{k}$
$r^j$	0.1€/$10\mathrm{k}$ units	–
Lead time
$t_{i1}^{\mathrm{f}\mathrm{a}\mathrm{c}}$	1 month	–
$t_{i2}^{\mathrm{f}\mathrm{a}\mathrm{c}}$	0.2 month	–
$t_{ij1}^{\mathrm{u}\mathrm{p}}$	[0.10, 1.50] months	0.6 month
$t_{ij2}^{\mathrm{u}\mathrm{p}}$	[0.02, 0.50] months	0.15 month
$t_{j1p}^{\mathrm{d}\mathrm{n}}$	[0.04, 0.36] months	0.21 month
$t_{j2p}^{\mathrm{d}\mathrm{n}}$	[0.04, 0.18] months	0.08 month
Other parameters
h	–	0.25
${\lambda }_p$	–	3

Table 4. The operating cost and the number of SKUs allocated to inventory and resource segments.

		Resource segment		Inventory segment
Scenario	Operating cost	Economic	Responsive	1	2	3	4
I	471, 941	17	207	0	0	2	222
II	481, 733	56	168	0	6	218	0
III	466, 520	56	168	0	0	111	113
IV	463, 139	54	170	0	9	126	89

Table 5. The cost breakdown.

Scenario	Production	Transport	Throughput	Cycle stock	Pipeline stock	Safety stock
I	245, 912	34, 301	3, 268	15, 370	24, 439	148, 651
II	243, 020	37, 374	3, 268	11, 905	25, 006	161, 160
III	243, 020	37, 374	3, 268	11, 905	25, 006	145, 946
IV	243, 029	34, 489	3, 268	11, 900	25, 150	145, 302

Figure 4. % increase in cost compared with Scenario IV.

Figure 5. % increase in cost for Network I, II and III compared with cost for Network IV. (a) % increase in cost with respect to the % change of holding cost rate. (b) % increase in cost with respect to the % change of fixed cost in both modes. (c) % increase in cost compared with Scenario IV based on the both datasets and (d) % increase in cost compared with Scenario IV with segmented resources and single resource.

Table 6. Operating cost of a single resource segment in use compared with optimally segmented SC and allocations of resource (economic on the left and responsive on the right) and inventory segments for optimally segmented SC.

				Inventory segment
Network	Resource (allocation)	Operating cost	% Cost increase	1	2	3	4
I	segmented ($17|207$)	471, 941	–	0	0	2	222
	economic	503, 363	$6.66\mathrm{\%}$	0	0	0	224
	responsive	480, 153	$1.74\mathrm{\%}$	0	0	3	221
II	segmented ($56|168$)	481, 734	–	0	6	218	0
	economic	502, 132	$4.23\mathrm{\%}$	0	0	224	0
	responsive	492, 092	$2.15\mathrm{\%}$	0	4	220	0
III	segmented ($56|168$)	466, 519	–	0	0	111	113
	economic	484, 508	$3.86\mathrm{\%}$	0	0	115	109
	responsive	478, 174	$2.50\mathrm{\%}$	0	0	101	123
IV	segmented ($54|170$)	463, 139	–	0	0	126	89
	economic	481, 642	$4.00\mathrm{\%}$	0	0	148	76
	responsive	473, 283	$2.19\mathrm{\%}$	0	0	123	92

Figure 6. Total cost of product portfolios differing in number of products with identical SKU demands.

Table 7. % Cost saving from inventory pooling for mean product demand 1 m when supply chain is operated with optimal mode.

	Optimal mode
product cv	Serial (non-pool)	Divergent (pool)	% cost diff.
0.01	Economic	Economic	$23.77\mathrm{\%}$	11.9
0.1	Economic	Economic	$25.15\mathrm{\%}$	12.6
0.2	Economic	Economic	$26.55\mathrm{\%}$	13.3
0.3	Economic	Economic	$27.80\mathrm{\%}$	14.0
0.4	Economic	Economic	$28.94\mathrm{\%}$	14.5
0.5	Economic	Economic	$29.98\mathrm{\%}$	15.0
0.6	Responsive	Economic	$29.75\mathrm{\%}$	14.9
0.7	Responsive	Economic	$28.73\mathrm{\%}$	14.3
0.8	Responsive	Economic	$27.80\mathrm{\%}$	13.9
0.9	Responsive	Economic	$26.93\mathrm{\%}$	13.6
1.0	Responsive	Economic	$26.13\mathrm{\%}$	13.0
1.1	Responsive	Economic	$25.38\mathrm{\%}$	12.6
1.2	Responsive	Economic	$24.69\mathrm{\%}$	12.3
1.3	Responsive	Economic	$24.04\mathrm{\%}$	12.0
1.4	Responsive	Economic	$23.43\mathrm{\%}$	11.7
1.5	Responsive	Economic	$22.86\mathrm{\%}$	11.4
1.6	Responsive	Economic	$22.32\mathrm{\%}$	11.1
1.7	Responsive	Economic	$21.82\mathrm{\%}$	10.9
1.8	Responsive	Economic	$21.34\mathrm{\%}$	10.6
1.9	Responsive	Economic	$20.89\mathrm{\%}$	10.4
2.0	Responsive	Economic	$20.46\mathrm{\%}$	10.2
2.1	Responsive	Economic	$20.06\mathrm{\%}$	10.0
2.2	Responsive	Economic	$19.67\mathrm{\%}$	9.8
2.3	Responsive	Responsive	$19.69\mathrm{\%}$	9.9
2.4	Responsive	Responsive	$19.95\mathrm{\%}$	10.0
2.5	Responsive	Responsive	$20.20\mathrm{\%}$	10.1
2.6	Responsive	Responsive	$20.44\mathrm{\%}$	10.21
2.7	Responsive	Responsive	$20.68\mathrm{\%}$	10.45
2.8	Responsive	Responsive	$20.90\mathrm{\%}$	10.55
2.9	Responsive	Responsive	$21.12\mathrm{\%}$	10.68
3.0	Responsive	Responsive	$21.33\mathrm{\%}$	10.8

Figure 7. Graphic expression of pooling benefit in relation to optimal modes and demand variability.

Table A1. Data generation.

	Tested dataset A	Tested dataset B
network ($\mathcal{N},\mathcal{R},\mathcal{M},\mathcal{P}$)	$(5,5,10,15)$	$(6,3,8,10)$
mean demand per period	${\mu }_{wp}=U[50,5000]$	–
coefficient of variation of demand	$v_{wp}=U[0.1,2]$	–
service factor	${\lambda }_{wp}=U[1,3]$	–
factory capacity	$K_{is}=V_0/3$	–
setup cost per batch (economic) at factory i	$f_{i1}=U[500,1000]$	–
setup cost per batch (express) at factory i	$f_{i2}=f_{i1}U[0.1,0.2]$
production cost per unit (economic) at factory i	$c_{i1}=U[20,40]$
production cost per unit (express) at factory i	$c_{i2}=c_{i1}(1+U[0.2,0.5\left]\right)$	$c_{i2}=1.5c_{i1}(1+U[0.2,0.5\left]\right)$
production lead time (economic) at factory i	$t_{i1}=U[2,5]$	–
production lead time (express) at factory i	$t_{i2}=t_{i1}U[0.1,0.3]$	–
transport cost (economic) per unit from factory i to DC j	$c_{ij1}=0.5\alpha D_{ij}$	–
transport cost (express) per unit from factory i to DC j	$c_{ij2}=c_{ij1}(1+U[0.2,0.5\left]\right)$	$c_{ij2}=1.2c_{ij1}(1+U[0.2,0.5\left]\right)$
transport cost (economic) per unit from DC j to factory i	$c_{jw1}=\alpha D_{jw}$	$c_{jw1}=0.2\alpha D_{jw}$
transport cost (express) per unit from DC j to warehouse w	$c_{jw2}=c_{jw1}(1+U[0.2,0.5\left]\right)$	–
order lead time (economic) from factory i to DC j	$t_{ij1}=U[0.5,2]$	–
order lead time (express) from factory i to DC j	$t_{ij2}=t_{ij1}U[0.1,0.3]$	–
order lead time (economics) from DC j to warehouse w	$t_{jw1}=U[0.1,0.5]$	$t_{jw1}=U[1,5]$
order lead time (express) from DC j to warehouse w	$t_{jw2}=t_{jw1}U[0.1,0.3]$	–

Table A2. The operating cost and the number of SKUs allocated to inventory and resource segments for dataset A.

		Resource segment		Inventory segment
Scenario	Operating cost	Economic	Responsive	1	2	3	4
I	24, 546, 986	49	101	0	0	0	150
II	22, 241, 047	80	70	0	0	150	0
III	22, 241, 047	80	70	0	0	150	0
IV	22, 237, 883	80	70	0	0	147	3

Table A3. The cost breakdown for dataset A.

Scenario	Production	Transport	Throughput	Cycle stock	Pipeline stock	Safety stock
I	13, 305, 763	2, 030, 344	34, 700	223, 197	1, 341, 449	7, 611, 533
II	12, 287, 773	2, 420, 175	34, 700	86, 019	1, 868, 727	5, 543, 654
III	12, 287, 773	2, 420, 175	34, 700	86, 019	1, 868, 727	5, 543, 654
IV	12, 287, 773	2, 411, 978	34, 700	86, 019	1, 870, 302	5, 547, 112

Table A4. The operating cost and the number of SKUs allocated to inventory and resource segments for dataset B.

		Resource segment		Inventory segment
Scenario	operating cost	Economic	Responsive	1	2	3	4
I	17, 054, 204	49	31	0	0	0	80
II	17, 523, 098	56	24	0	0	80	0
III	17, 478, 972	56	24	0	0	64	16
IV	17, 219, 645	56	24	0	16	41	23

Table A5. The cost breakdown for dataset B.

Scenario	Production	Transport	Throughput	Cycle stock	Pipeline stock	Safety stock
I	5, 852, 918	799, 254	21, 602	143, 293	3, 358, 848	6, 878, 289
II	5, 734, 004	570, 647	21, 602	51, 594	4, 342, 603	6, 802, 648
III	5, 734, 004	570, 647	21, 602	51, 594	4, 342, 603	6, 758, 522
IV	5, 752, 925	712, 095	21, 602	53, 268	3, 801, 789	6, 877, 964