Revenue sharing contract for a VMI with one for one period policy

Figures & data

Figure 1. A serial supply chain consisting of a supplier, a vendor, and a retailer.

Figure 2. The inventory level of the product at the vendor.

Table 1. The parameters’ values for numerical example

Decision variables	Retailer’s parameters			Vendor’s parameters
$\mu$	$p$	$\pi$	$h_R$	$A$	$h_v$
12	100	20	14	20	12

Table 2. The optimal solution in centralized control

$I^{\ast }$	$m^{\ast }$	$T^{\ast }$	${\rho }^{\ast }$	$T{C}^{\ast }$
6.73	6	0.09	0.93	−936.73

Table 3. Bargaining process through Algorithm 2

Step	$I$	$m$	$\rho$	$\phi$	$CV$	$\mathrm{C}\mathrm{R}$	$\mathrm{T}\mathrm{C}$	$\mathrm{\Delta }\mathrm{T}\mathrm{C}$
1	4.13	6	0.89	0.5000	−409.55	−506.00	−915.55
2	5	6	0.90	0.4980	−409.73	−519.16	−928.88	−13.33
3	6	6	0.92	0.4920	−410.66	−524.89	−935.55	−6.67
4	6.2	6	0.92	0.4905	−410.90	−525.23	−936.13	−0.58
5	6.5	6	0.93	0.4884	−410.95	−525.67	−936.62	−0.49
6	6.73	6	0.93	0.4867	−410.99	−525.74	−936.73	−0.11

Table 4. Final optimal replenishment policy for different values of ${\phi }_{\mathrm{m}\mathrm{a}\mathrm{x}}$

${\phi }_{\mathrm{m}\mathrm{a}\mathrm{x}}$	Step	$I$	$m$	$\rho$	$\phi$	$CV$	$\mathrm{C}\mathrm{R}$	$\mathrm{T}\mathrm{C}$	$\mathrm{\Delta }\mathrm{T}\mathrm{C}$
0.1	1	5.75	6	0.92	0.1000	−844.09	−90.45	−934.54	–
	2	6	6	0.92	0.0992	−844.10	−90.72	−934.82	−0.28
	3	6.5	6	0.93	0.0986	−844.51	−92.12	−936.62	−1.81
	4	6.73	6	0.93	0.0979	−844.54	−92.19	−936.73	−0.11
0.7	1	3.03	6	0.85	0.7000	−200.13	−680.04	−880.17	–
	2	3.50	6	0.87	0.6950	−204.56	−694.20	−898.76	−18.59
	3	4	6	0.88	0.6900	−207.75	−704.96	−912.72	−13.95
	4	4.5	6	0.90	0.6850	−210.08	−712.28	−922.35	−9.64
	5	5	6	0.91	0.6800	−211.78	−717.10	−928.88	−6.53
	6	5.5	6	0.91	0.6750	−213.03	−720.08	−933.10	−4.22
	7	6	6	0.92	0.6700	−213.92	−721.64	−935.55	−2.45
	8	6.5	6	0.93	0.6650	−214.53	−722.10	−936.62	−1.07
	9	6.73	6	0.93	0.6628	−214.62	−722.11	−936.73	−0.11