A tactical supply chain planning model with multiple flexibility options: an empirical evaluation

Abstract

Supply chain flexibility is widely recognized as an approach to manage uncertainty. Uncertainty in the supply chain may arise from a number of sources such as demand and supply interruptions and lead time variability. A tactical supply chain planning model with multiple flexibility options incorporated in sourcing, manufacturing and logistics functions can be used for the analysis of flexibility adjustment in an existing supply chain. This paper develops such a tactical supply chain planning model incorporating a realistic range of flexibility options. A novel solution method is designed to solve the developed mixed integer nonlinear programming model. The utility of the proposed model and solution method is evaluated using data from an empirical case study. Analysis of the numerical results in different flexibility adjustment scenarios provides various managerial insights and practical implications.

Appendix: Parameters and decision variables

Input parameters

d _iet :

Demand for product i in end-user e at period t

f _pt :

Fixed cost of opening and operating plant p at period t

$f'_{wt}$ :

Fixed cost of opening and operating DC w at period t

$a_{ipt}^{1st}$ :

Unit production cost in regular-time (in the first period of plant opening) for product i in plant p at period t

$a_{\ ipt}^{' 1st}$ :

Unit production cost in overtime (in the first period of plant opening) for product i in plant p at period t

a _ipt :

Unit production cost in regular-time (from the second period onward) for product i in plant p at period t

$a'_{ipt}$ :

Unit production cost in overtime (from the second period onward) for product i in plant p at period t

r _ipt :

Unit cost of outsourcing product i by plant p at period t

h _cpt :

Unit holding cost of component c in plant p at period t

$h'_{ipt}$ :

Unit holding cost of product i in plant p at period t

b _iet :

Cost of backlogging product i in end-user e at period t

ϕ _ci :

Quantity of component c used to produce one unit of product i

ω _cpt :

Maximum holding capacity of component c in plant p at period t

$\overline{\omega}_{ipt}$ :

Maximum holding capacity of product i in plant p at period t

ν _iet :

Maximum allowed backlog for product i in end-user e at period t

ρ _ipt :

Maximum capacity for regular-time production of product i in plant p at period t

$\overline{\rho}_{ipt}$ :

Maximum capacity for overtime production of product i in plant p at period t

ζ _ipt :

Maximum capacity for outsourcing product i in plant p at period t

pc _cspt :

Base purchasing cost (highest rate at lowest quantity range) for the acquisition of component c from supplier s for plant p at period t

α _cspt :

Discount multiplier for purchasing component c from supplier s for plant p at period t

$pq_{cspt}^{low}$ :

Lower quantity break-point for component c offered by supplier s to plant p at period t

$pq_{cspt}^{up}$ :

Upper quantity break-point for component c offered by supplier s to plant p at period t

π _cspt :

Lower discount rate (for medium quantity range) for purchasing component c from supplier s for plant p at period t

ψ _cspt :

Higher discount rate (for large quantity range) for purchasing component c from supplier s for plant p at period t

$pq_{cspt}^{\min}$ :

Minimum allowed purchase quantity of component c from supplier s for plant p at period t

$pq_{cspt}^{\max}$ :

Maximum capacity of supplier s for component c to supply plant p at period t

$\varepsilon_{s}^{\min}$ :

Minimum purchase quantity from supplier s during the planning horizon

τ _ipwlmt :

Unit transportation cost for the shipment of product i from plant p to DC w by logistics provider l using transport mode m at period t

$\overline{\tau}_{iwelmt}$ :

Unit transportation cost for the shipment of product i from DC w to end-user e by logistics provider l using transport mode m at period t

$\overline{\overline{\tau}}_{ipelmt}$ :

Unit transportation cost for the shipment of product i from plant p to end-user e by logistics provider l using transport mode m at period t

$tq_{ipwlmt}^{\min}$ :

Minimum allowed shipping quantity of product i from plant p to DC w by logistics provider l using mode m at period t

$tq_{ipwlmt}^{\max}$ :

Maximum allowed shipping quantity of product i from plant p to DC w by logistics provider l using mode m at period t

$\overline{tq}_{iwelmt}^{\,\min}$ :

Minimum allowed shipping quantity of product i from DC w to end-user e by logistics provider l using mode m at period t

$\overline{tq}_{iwelmt}^{\,\max}$ :

Maximum allowed shipping quantity of product i from DC w to end-user e by logistics provider l using mode m at period t

$\overline{\overline{tq}}_{ipelmt}^{\,\min}$ :

Minimum allowed shipping quantity of product i from plant p to end-user e by logistics provider l using mode m at period t

$\overline{\overline{tq}}_{ipelmt}^{\,\max}$ :

Maximum allowed shipping quantity of product i from plant p to end-user e by logistics provider l using mode m at period t

$\overline{\varepsilon}_{l}^{\,\min}$ :

Minimum allowed shipment quantity delegated to logistics provider l during the planning horizon

k _iwt :

Unit storage cost for holding product i in self-owned DC w at period t

$k'_{iwt}$ :

Unit storage cost for holding product i in rental warehouse w at period t

γ _iwt :

Storage multiplier for holding product i in self-owned DC and/or rental warehouse w at period t

η _iwt :

Maximum capacity of self-owned DC w for storing product i at period t

$\overline{\eta}_{iwt}$ :

Maximum capacity of rental warehouse w for storing product i at period t

Independent decision variables

Q _cspt :

Quantity of component c purchased from supplier s for plant p at period t

A _ipt :

Quantity of product i produced in regular-time in plant p at period t

$A'_{ipt}$ :

Quantity of product i produced in overtime in plant p at period t

R _ipt :

Quantity of product i outsourced by plant p at period t

X _cpt :

Quantity of component c stored in plant p at period t

$X'_{ipt}$ :

Quantity of product i stored in plant p at period t

J _ipwlmt :

Quantity of product i shipped from plant p to DC w by logistics provider l using transport mode m at period t

$J'_{iwelmt}$ :

Quantity of product i shipped from DC w to end-user e by logistics provider l using transport mode m at period t

$J'_{ipelmt}$ :

Quantity of product i shipped from plant p to end-user e by logistics provider l using transport mode m at period t

Y _iwt :

Quantity of product i stored in the self-owned DC w and the linked rental warehouse w at period t

B _iet :

Quantity of product i backlogged in end-user e at period t

G _pt =:

$\left \{ \begin{array}{l@{\quad }l} 1, &\mbox{if plant}\ p\ \mbox{is open at period}\ t\\ 0, &\mbox{otherwise} \end{array} \right .$

$G'_{wt} =$ :

$\left \{ \begin{array}{l@{\quad}l} 1, &\mbox{if DC}\ w\ \mbox{is open at period}\ t \\ 0, &\mbox{otherwise} \end{array} \right .$

U _cspt =:

$\left \{ \begin{array}{l@{\quad}l} 1, &\mbox{if component}\ c\ \mbox{is purchased form supplier}\ s\ \mbox{for plant}\ p\ \mbox{at period}\ t\\ 0, &\mbox{otherwise} \end{array} \right .$

V _ipwlmt =:

$\left \{ \begin{array}{l@{\quad}l} 1, &\mbox{if product}\ i\ \mbox{is shipped from plant}\ p\ \mbox{to DC}\ w\ \mbox{by logistics}\ \mbox{provider}\ l \\ & \mbox{using transport mode}\ m\ \mbox{at period}\ t \\ 0, &\mbox{otherwise} \end{array} \right .$

$V'_{iwelmt} =$ :

$\left \{ \begin{array}{l@{\quad}l} 1, &\mbox{if product}\ i\ \mbox{is shipped from DC}\ w\ \mbox{to}\ \mbox{end-user}\ e\ \mbox{by}\ \mbox{logistics}\ \mbox{provider}\ l \\ & \mbox{using}\ \mbox{transport}\ \mbox{mode}\ m\ \mbox{at period}\ t \\ 0, &\mbox{otherwise} \end{array} \right .$

$V''_{ipelmt} =$ :

$\left \{ \begin{array}{l@{\quad}l} 1, &\mbox{if product}\ i\ \mbox{is shipped from plant}\ p\ \mbox{to end-user}\ e\ \mbox{by logistics provider}\ l\\ & \mbox{using transport mode}\ m\ \mbox{at period}\ t\\ 0, &\mbox{otherwise} \end{array} \right .$

Dependent decision variables

$\alpha_{cspt} = \left \{ \begin{array}{l@{\quad}l} 1 & pq_{cspt}^{\min} \leq Q_{cspt} \leq pq_{cspt}^{low} \\[3pt] \pi_{cspt} & pq_{cspt}^{low} < Q_{cspt} \leq pq_{cspt}^{up} \\[3pt] \psi_{cspt} & pq_{cspt}^{up} < Q_{cspt} \leq pq_{cspt}^{\max} \end{array} \right . \quad \forall c, s,p, t$

$\gamma_{iwt} = \left \{ \begin{array}{l@{\quad}l} 1, &Y_{iwt} \leq \eta_{iwt} \\[3pt] 0, &\eta_{iwt} < Y_{iwt} \leq \eta_{iwt} + \overline{\eta}_{iwt} \end{array} \right . \quad \forall i, w, t$