Table 7.

Notations and parametric assumptions

Parameters		Assumptions
N	: Initial market size of potential adopters	$N\in \mathbb{N}$
${\mathrm{\Xi }}_t$	: Remaining potential adopters at period t	$\{{\cup }_{m=t}^T{\mathrm{\Xi }}_m{\}}_{t=1}^T$
T	: Length of the finite selling horizon	$T\in \mathbb{N}$
t	: Subscript denoting period	${\{t\}}_{t=1}^T$
$\mathcal{T}$	: Set of production strategies characterized by $(T_{A\to M},T_{M\to A})$	$\mathcal{T}\in {\{T_{A\to M},T_{M\to A}\}}^T$
$T_{A\to M}$	: Technology-switching time when the manufacturer switches from AM to MC	$0\le T_{A\to M}<T_{M\to A}$
$T_{M\to A}$	: Technology-switching time when the manufacturer switches from MC to AM	$T_{A\to M}<T_{M\to A}<T+1$
$\mathrm{\Phi }$	: Virtual space of horizontally differentiated products	$\mathrm{\Phi }=[0,1]$
$\varphi$	: Customer’s ideal product variant	${\mathbb{P}}_{\varphi }=\mathcal{U}([0,1])$
$\tau$	: Customer’s ideal buying time	see Lacroix et al. (2021)
p, q	: Bass innovation and imitation coefficients, respectively	$p,q\in {\mathbb{R}}^{+}$
$\xi$	: Random customer characterized by $\tau$ and $\varphi$	$\xi =(\tau ,\varphi )$ with ${\mathbb{P}}_{\xi }={\mathbb{P}}_{\tau }\varnothing$
n	: Number of mass-customized variants to offer to customers under MC	$1\le n\le n_{\mathit{max}}$
$\mathcal{X}$	: Set of mass-customized product variants offered under MC	$\mathcal{X}=\{x_1,\dots ,x_n\}\subset {[0,1]}^n$
j	: Subscript denoting the mass-customized variant	$j\in \{1,\dots ,n\}$
$x_j$	: Location of product variant j on the virtual product space	$\forall j\in \{1,\dots ,n\}$
$w_t(\tau )$	: Customer’s willingness-to-pay at period t	$\omega (\tau )\in {\mathbb{R}}^{+}$
$\gamma (\tau )$	: Buying time-sensitivity coefficient	$\gamma \in {\mathbb{R}}^{+}$
$\lambda (\tau )$	: Product variant sensitivity coefficient, incurred only under MC technology	$\lambda \in {\mathbb{R}}^{+}$
$U^{\mathcal{T}}(\xi ,t)$	: Customer $\xi$’s utility at period t, dependent on the production strategy $\mathcal{T}$ (1)
$p_t$	: Selling price at period t	$0\le p_t\le max\{0,U^{\mathcal{T}}\}$, $\forall j\in \mathrm{\Phi }$
$\ast$	: Subscript denoting the demand forecast method	$\ast {=}_c{,}_u$
${}_{\ast }{D}_{j,t}^{\prime }$	: Demand forecast of variant j at time t
D j, t	: Observed demand for product variant j at time t
$I_{j,t}^{\prime }$	: Target inventory level of variant j at time t
I j, t	: Observed inventory level of variant j at time t
$K^A$	: Constant production capacity under AM
$K^M$	: Constant production capacity under MC	Equally distributed among n
$\kappa$	: Production capacity magnitude	$\kappa \in {\mathbb{R}}^{+}$
$\rho$	: Production capacity ratio between AM and MC	$\rho \in {\mathbb{R}}^{+}$
$S_t$	: Sales at period t
$L_t$	: Lost sales at period t
$Q_{j,t}$	: Optimal production quantity for each variant j at time t
$c^A$	: Constant marginal production cost under AM	$c^A=$ constant $>0$
$c^b$	: Unit production base cost under MC	$c^b=$ constant $>0$
$c^M(n)$	: Unit production cost under MC depending on n	$c^M(n)=c_b(1+(n-1)\delta )>0$
$k^A$	: One-time fixed cost for AM technology	$k^A=$ constant $>0$
$k^M$	: One-time fixed cost for MC technology	$k^M=$ constant $>0$
h	: Inventory holding cost per unit per period, common to all product variants	$h\in {\mathbb{R}}^{+}$
s	: Stockout cost incurred when excess demand is lost per unit of unmet demand,	$h<s$
	common to all product variants
v	: Salvage value of remaining inventory at the end of MC period	$p_t>v>c^M(n)$