39 Recovery Analysis of Domestic Electric Storage Water Heaters
599
returns and for serviceable products. Set-up and unit costs are assumed for production, remanufacturing, discard and inspection of returns. Costs related to returns
depend on their quality: top qualities imply higher costs for inventory and lower
costs for remanufacturing and discard. Demand and returns quantities as well as the
different cost values are assumed known in advance for each one of the periods within
the planning horizon. The objective is to determine the quantities to be inspected,
remanufactured, discarded and produced at each period in order to meet the demand
requirements on time, minimizing the sum of all the involved costs.
39.4.2 Description of the Mathematical Formulation
The hybrid production-remanufacturing system stated above can be modelled as a
Mixed-Integer Linear Programming (MILP). We provide below a description of the
objective function and constraints of the model. The detailed MILP formulation can
be found in (Devoto and Fernández 2019). We also note that it can be considered an
extended version of that presented in (Devoto et al. 2019) for a hybrid system of a
single item and without capacity constraints.
• Objective function: sum of the costs related to the production, remanufacturing,
discard, inspection and holding inventories.
• Constraints to establish that a set-up cost is incurred whenever a positive amount
is produced, remanufactured, discarded or inspected.
• Inventory balance equations for serviceable, incoming returns and inspected-andgraded returns.
• Initial inventory equations.
• Capacity constraints for the inventory of serviceable items and for the production
and recovery lines.
• Specific constraints of Rivomark about the type of products that can be produced
and/or remanufactured in the same period.
• Constraints for rounding the quantities of graded returns.
• Set of domains for the variables (continuous, integers and binary values).
We note that the MILP formulation has (I × T + Q × I×T + T) variables and
(Q × I×T + Q × I + I × T ) constraints, where T is the number of periods, Q the
number of quality levels, and I the number of products.
39.4.3 Resolution Procedure and Analysis of Results
In order to evaluate the impact of including recovery options, we compare the solution
obtained with the model of above for the hybrid system, against the solution of
a MILP model developed for the current production system of Rivomark without
returns options. More specifically, we compare the costs of holding inventories and
599
returns and for serviceable products. Set-up and unit costs are assumed for production, remanufacturing, discard and inspection of returns. Costs related to returns
depend on their quality: top qualities imply higher costs for inventory and lower
costs for remanufacturing and discard. Demand and returns quantities as well as the
different cost values are assumed known in advance for each one of the periods within
the planning horizon. The objective is to determine the quantities to be inspected,
remanufactured, discarded and produced at each period in order to meet the demand
requirements on time, minimizing the sum of all the involved costs.
39.4.2 Description of the Mathematical Formulation
The hybrid production-remanufacturing system stated above can be modelled as a
Mixed-Integer Linear Programming (MILP). We provide below a description of the
objective function and constraints of the model. The detailed MILP formulation can
be found in (Devoto and Fernández 2019). We also note that it can be considered an
extended version of that presented in (Devoto et al. 2019) for a hybrid system of a
single item and without capacity constraints.
• Objective function: sum of the costs related to the production, remanufacturing,
discard, inspection and holding inventories.
• Constraints to establish that a set-up cost is incurred whenever a positive amount
is produced, remanufactured, discarded or inspected.
• Inventory balance equations for serviceable, incoming returns and inspected-andgraded returns.
• Initial inventory equations.
• Capacity constraints for the inventory of serviceable items and for the production
and recovery lines.
• Specific constraints of Rivomark about the type of products that can be produced
and/or remanufactured in the same period.
• Constraints for rounding the quantities of graded returns.
• Set of domains for the variables (continuous, integers and binary values).
We note that the MILP formulation has (I × T + Q × I×T + T) variables and
(Q × I×T + Q × I + I × T ) constraints, where T is the number of periods, Q the
number of quality levels, and I the number of products.
39.4.3 Resolution Procedure and Analysis of Results
In order to evaluate the impact of including recovery options, we compare the solution
obtained with the model of above for the hybrid system, against the solution of
a MILP model developed for the current production system of Rivomark without
returns options. More specifically, we compare the costs of holding inventories and