Distribution free approach on electrical energy supply chain using geometric shipment policy

Figures & data

Table

$Q$ Power consumption of the customers

$q_1$ Size of the first shipment from the power plant to the customer

$D$ Average of electricity demand rate of the customers

$P$ Power supply rate of the power plant $P>D$

$S$ Power plant’s setup cost per setup

$\lambda$ Geometric growth factor

$k_1$ Backup factor of batch 1

$k_2$ Backup factor of batch 2,3,,,m

$T_s$ Setup and transportation time

$T_t$ Transportation time

$g$ Electricity power distribution factor from the distribution substation to the customers

in one production cycle

$p$ Electricity power distribution factor from the transmission substation to the

distribution substation in one production cycle

$m$ Electricity power distribution factor from the power plant to the transmission

substation in one production cycle

$\sigma$ Standard deviation of electricity demand of the customers

$t$ Average of time consumption of the customers

$E$ Customers energy consumption, $(E=Q.t)$

$A$ Ordering cost of the customers

$E_c$ Electricity price of the customers

$C_p$ Production cost incurred by the power plant

$C_t$ Transmission and distribution rates paid by the power plant

$h_t$ Holding cost of the transmission substation

$h_p$ Holding cost of the power plant

$\pi$ Backorder cost per electricity consumption of the customers

$\delta$ power factor correction

$P_{dt}$ Transmission and distribution rates paid by the power plant

$D_d$ Distribution network from the distribution substation to the customers

$D_t$ Transmission network from the transmission substation to the distribution substation

$D_p$ Transmission network from the power plant to the transmission substation

$W_d^x$ Maximum capacity of distribution substation

$W_t^x$ Maximum capacity of transmission substation

$W_p^x$ Maximum capacity of power plant

$W_d^y$ Actual capacity of distribution substation

$W_t^y$ Actual capacity of transmission substation

$W_p^y$ Actual capacity of power plant

$\alpha$ Power supply loss factor

Table 1. Outline of the algorithm for this problem

$g$	$p$	$m$	$q_1$	Actual capacity on dis.subs			Actual capacity on trans.subs			Actual capacity on power plant			$k_1$	$k_2$	$JETC$
				$W_d^y$	$\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$	$q_1$	$W_t^y$	$\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$	$q_1$	$W_p^y$	$\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$	$q_1$
1	1	1	103.8014	3114		103.8014	3114		103.8014	3114		103.8014	2.8115	0.9608	17,979
1	1	2	56.8224	1704.67		56.8224	1704.67		56.8224	3409.34		56.8224	2.8500	0.9210	15,875
1	3	3	41.5335	1246.01		41.5335	3738.02		41.5335	11,214.05		41.5335	2.7221	0.8625	15,606
1	4	4	34.1676	1025.028		34.1676	4100.11		34.1676	16,400.45		34.1676	2.5683	0.8059	15,728
1	3	5	29.5015	885.05		29.5015	2655.14		29.5015	13,275.68		29.5015	2.5631	0.7992	16,057

Table 2. The summary of results

Decision variables	Unit	Values
Electrical power distribution factor on the power plant	times	3
Electrical power distribution factor on the transmission substation	times	3
Electrical power distribution facotr on the distribution substation	times	1
Energy produced by the power plant $(E_p=q_{1}tgpm)$	kWh	8971
Energy supplied by the transmission substation $(E_t=q_{1}tgp)$	kWh	2990
Energy supplied by the distribution substation $(E_d=q_{1}tg)$	kWh	996.80
Actual power plant capacity	kVA	11,214
Actual transmission substation capacity	kVA	3738
Actual distribution substation capacity	kVA	1246

Table 3. Sensitivity analysis for different key parameters

	$\mathrm{\%}$	$JETC$		$\mathrm{\%}$	$JETC$
	$+50\mathrm{\%}$	18,478		$+50\mathrm{\%}$	15,902
$A$	$+25\mathrm{\%}$	15,914	$W_p^x$	$+25\mathrm{\%}$	15,891
	$-25\mathrm{\%}$	15,576		$-25\mathrm{\%}$	15,902
	$-50\mathrm{\%}$	15,394		$-50\mathrm{\%}$	15,910
	$+50\mathrm{\%}$	16,021		$+50\mathrm{\%}$	15,908
$\pi$	$+25\mathrm{\%}$	15,984	$W_t^x$	$+25\mathrm{\%}$	15,912
	$-25\mathrm{\%}$	15,870		$-25\mathrm{\%}$	15,917
	$-50\mathrm{\%}$	15,825		$-50\mathrm{\%}$	16,023
	$+50\mathrm{\%}$	16,706		$+50\mathrm{\%}$	16,706
$P$	$+25\mathrm{\%}$	16,293	$t$	$+25\mathrm{\%}$	17,168
	$-25\mathrm{\%}$	15,506		$-25\mathrm{\%}$	17,337
	$-50\mathrm{\%}$	15,158		$-50\mathrm{\%}$	17,183

Table 4. Outline of the algorithm for this problem

$g$	$p$	$m$	$q_1$	Actual capacity on dis.subs			Actual capacity on trans.subs			Actual capacity on power plant			$k_1$	$k_2$	$JETC$
				$W_d^y$	$\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$	$q_1$ revised	$W_t^y$	$\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$	$q_1$ revised	$W_p^y$	$\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$
1	1	1	103.8014	3114		103.8014	3114		103.8014	3114		103.8014	2.8115	0.9608	17,979
1	1	2	56.8224	1704.67		56.8224	1704.67		56.8224	3409.34		56.8224	2.8500	0.9210	15,875
1	3	3	41.5335	1246.01		41.5335	3738.02		41.5335	11,214.05		41.5335	2.7221	0.8625	15,606
1	4	4	34.1676	1025.028		34.1676	4100.11		34.1676	16,400.45		34.1676	2.5683	0.8059	15,728
1	3	5	29.5015	885.05		29.5015	2655.14		29.5015	13,275.68		29.5015	2.5631	0.7992	16,057

Table 5. The summary of results

Decision variables	Unit	Values
Electrical power distribution factor on the power plant	times	3
Electrical power distribution factor on the transmission substation	times	3
Electrical power distribution facotr on the distribution substation	times	1
Energy produced by the power plant (Ep = q1tgpm)	kWh	8971
Energy supplied by the transmission substation (Et = q1tgp)	kWh	2990
Energy supplied by the distribution substation (Ed = q1tg)	kWh	996.80
Actual power plant capacity	kVA	11,214
Actual transmission substation capacity	kVA	3738
Actual distribution substation capacity	kVA	1246

Table 6. Sensitivity analysis for different key parameters

Parameters	changes in %	JETC	Parameters	changes in %	JETC
	$+50\mathrm{\%}$	18,478		$+50\mathrm{\%}$	15,902
$A$	$+25\mathrm{\%}$	15,914	$W_p^x$	$+25\mathrm{\%}$	15,891
	$-25\mathrm{\%}$	15,576		$-25\mathrm{\%}$	15,902
	$-50\mathrm{\%}$	15,394		$-50\mathrm{\%}$	15,910
	$+50\mathrm{\%}$	16,021		$+50\mathrm{\%}$	15,908
$\pi$	$+25\mathrm{\%}$	15,984	$W_t^x$	$+25\mathrm{\%}$	15,912
	$-25\mathrm{\%}$	15,870		$-25\mathrm{\%}$	15,917
	$-50\mathrm{\%}$	15,825		$-50\mathrm{\%}$	16,023
	$+50\mathrm{\%}$	16,706		$+50\mathrm{\%}$	16,706
$P$	$+25\mathrm{\%}$	16,293	$t$	$+25\mathrm{\%}$	17,168
	$-25\mathrm{\%}$	15,506		$-25\mathrm{\%}$	17,337
	$-50\mathrm{\%}$	15,158		$-50\mathrm{\%}$	17,183

Figure 1. Change of parameter $A$ in total cost

Figure 2. Change of parameter $\pi$ in total cost

Figure 3. Change of parameter $P$ in total cost

Figure 4. Change of parameter $W_p^x$ in total cost

Figure 5. Change of parameter $W_t^x$ in total cost

Figure 6. Change of parameter $t$ in total cost