1 S ystems Analysis Laboratory Helsinki University of Technology Goal intervals in dynamic multicriteria problems The case of MOHO Juha Mäntysaari

2 S ystems Analysis Laboratory Helsinki University of Technology Decision problem of space heating consumers Under time varying electricity tariff space heating consumers can save in heating costs by –Storing heat in to the house during low tariff hours –Trading living comfort to costs savings A dynamic decision problem

3 S ystems Analysis Laboratory Helsinki University of Technology Space heating problem Space heating consumers try to –MIN “Heating costs” –MAX “Living comfort” subject to Dynamic price of the electricity Dynamics of house Other (physical) constraints

4 S ystems Analysis Laboratory Helsinki University of Technology Dynamics of the house Q(t)=Q(t-1)+  tq(t-1)-d(t-1) where d(t) =  t(T(t) - T out (t)) Q(t) = T(t)/C, (  = 1/C)  T(t) = T(t-1) +  tq(t-1) -  t  T(t-1) - T out (t-1)) Units: [Q] = kWh, [  ] = kW/  C, [C] = kWh/  C T Q T out q d

5 S ystems Analysis Laboratory Helsinki University of Technology Example houses House 1 House 2

6 S ystems Analysis Laboratory Helsinki University of Technology Information summary Q d T ref  q  q max T out p T min  T  T max 

7 S ystems Analysis Laboratory Helsinki University of Technology Goal models 1. Hard constraint (pipe is hard) 3. Hard constraint with a goal inside (pipe with a goal) 2. Soft constraints (pipe is soft) “Interval goal programming”

8 S ystems Analysis Laboratory Helsinki University of Technology Hard constraints

9 S ystems Analysis Laboratory Helsinki University of Technology Soft constraints

10 S ystems Analysis Laboratory Helsinki University of Technology Hard constraints with a goal

11 S ystems Analysis Laboratory Helsinki University of Technology Goal models (summary) 3. Hard constraints with a goal 1. Hard constraints 2. Soft constraints

12 S ystems Analysis Laboratory Helsinki University of Technology MultiObjective Household heating Optimization (MOHO)

13 S ystems Analysis Laboratory Helsinki University of Technology Idea of MOHO Minimize heating costs using hard lower and upper bounds for indoor temperature –The case of hard constraints Ask: “How many percents would you like to decrease the heating costs from the current level?” Solve again trying to achieve the desired decrease in cost by relaxing the indoor temperature upper bound –The  -constraints method (upper bound must be active in order to succeed)

14 S ystems Analysis Laboratory Helsinki University of Technology Example: House 2 (1/4) Minimized heating costs:

15 S ystems Analysis Laboratory Helsinki University of Technology Example: House 2 (2/4) Decreased costs by 5 %

16 S ystems Analysis Laboratory Helsinki University of Technology Example: House 2 (3/4) Decreased again by 5 %

17 S ystems Analysis Laboratory Helsinki University of Technology Example: House 2 (4/4) And again by 5 %

18 S ystems Analysis Laboratory Helsinki University of Technology Summary Model and parameters of the house identified Depending on the definition of the “living comfort” different multicriteria models can be used Benefits of the simplified approach: –Only bounds of the indoor temperature asked –Comparison and tradeoff only with heating costs