diff --git a/prism/src/explicit/MDPModelChecker.java b/prism/src/explicit/MDPModelChecker.java
index 4f2c16b5..47b686a2 100644
--- a/prism/src/explicit/MDPModelChecker.java
+++ b/prism/src/explicit/MDPModelChecker.java
@@ -32,6 +32,7 @@ import java.util.Iterator;
 import java.util.List;
 import java.util.Map;
 
+import common.IterableStateSet;
 import parser.VarList;
 import parser.ast.Declaration;
 import parser.ast.DeclarationIntUnbounded;
@@ -42,6 +43,7 @@ import prism.PrismDevNullLog;
 import prism.PrismException;
 import prism.PrismFileLog;
 import prism.PrismLog;
+import prism.PrismNotSupportedException;
 import prism.PrismUtils;
 import strat.MDStrategyArray;
 import acceptance.AcceptanceReach;
@@ -1292,6 +1294,126 @@ public class MDPModelChecker extends ProbModelChecker
 		return res;
 	}
 
+	/**
+	 * Compute total expected rewards.
+	 * @param mdp The MDP
+	 * @param mdpRewards The rewards
+	 * @param min Min or max rewards (true=min, false=max)
+	 */
+	public ModelCheckerResult computeTotalRewards(MDP mdp, MDPRewards mdpRewards, boolean min) throws PrismException
+	{
+		if (min) {
+			throw new PrismNotSupportedException("Minimum total expected reward not supported in explicit engine");
+		} else {
+			// max. We don't know if there are positive ECs, so we can't skip precomputation
+			return computeTotalRewardsMax(mdp, mdpRewards, false);
+		}
+	}
+
+	/**
+	 * Compute maximal total expected rewards.
+	 * @param mdp The MDP
+	 * @param mdpRewards The rewards
+	 * @param noPositiveECs if true, there are no positive ECs, i.e., all states have finite values (skip precomputation)
+	 */
+	public ModelCheckerResult computeTotalRewardsMax(MDP mdp, MDPRewards mdpRewards, boolean noPositiveECs) throws PrismException
+	{
+		ModelCheckerResult res = null;
+		int n;
+		long timer;
+		BitSet inf;
+
+		// Local copy of setting
+		MDPSolnMethod mdpSolnMethod = this.mdpSolnMethod;
+
+		// Switch to a supported method, if necessary
+		if (!(mdpSolnMethod == MDPSolnMethod.VALUE_ITERATION || mdpSolnMethod == MDPSolnMethod.GAUSS_SEIDEL || mdpSolnMethod == MDPSolnMethod.POLICY_ITERATION)) {
+			mdpSolnMethod = MDPSolnMethod.GAUSS_SEIDEL;
+			mainLog.printWarning("Switching to MDP solution method \"" + mdpSolnMethod.fullName() + "\"");
+		}
+
+		// Start expected total reward
+		timer = System.currentTimeMillis();
+		mainLog.println("\nStarting total expected reward (max)...");
+
+		// Store num states
+		n = mdp.getNumStates();
+
+		long timerPre;
+
+		if (noPositiveECs) {
+			// no inf states
+			inf = new BitSet();
+			timerPre = 0;
+		} else {
+			mainLog.println("Precomputation: Find positive end components...");
+
+			timerPre = System.currentTimeMillis();
+
+			ECComputer ecs = ECComputer.createECComputer(this, mdp);
+			ecs.computeMECStates();
+			BitSet positiveECs = new BitSet();
+			for (BitSet ec : ecs.getMECStates()) {
+				// check if this MEC is positive
+				boolean positiveEC = false;
+				for (int state : new IterableStateSet(ec, n)) {
+					if (mdpRewards.getStateReward(state) > 0) {
+						// state with positive reward in this MEC
+						positiveEC = true;
+						break;
+					}
+					for (int choice = 0, numChoices = mdp.getNumChoices(state); choice < numChoices; choice++) {
+						if (mdpRewards.getTransitionReward(state, choice) > 0 &&
+								mdp.allSuccessorsInSet(state, choice, ec)) {
+							// choice from this state with positive reward back into this MEC
+							positiveEC = true;
+							break;
+						}
+					}
+				}
+				if (positiveEC) {
+					positiveECs.or(ec);
+				}
+			}
+
+			// inf = Pmax[ <> positiveECs ] > 0
+			//     = ! (Pmax[ <> positiveECs ] = 0)
+			inf = prob0(mdp, null, positiveECs, false, null);  // Pmax[ <> positiveECs ] = 0
+			inf.flip(0,n);  // !(Pmax[ <> positive ECs ] = 0) = Pmax[ <> positiveECs ] > 0
+
+			timerPre = System.currentTimeMillis() - timerPre;
+			mainLog.println("Precomputation took " + timerPre / 1000.0 + " seconds, " + inf.cardinality() + " infinite states, " + (n - inf.cardinality()) + " states remaining.");
+		}
+
+		// Compute rewards
+		// do standard max reward calculation, but with empty target set
+		switch (mdpSolnMethod) {
+		case VALUE_ITERATION:
+			res = computeReachRewardsValIter(mdp, mdpRewards, new BitSet(), inf, false, null, null, null);
+			break;
+		case GAUSS_SEIDEL:
+			res = computeReachRewardsGaussSeidel(mdp, mdpRewards, new BitSet(), inf, false, null, null, null);
+			break;
+		case POLICY_ITERATION:
+			res = computeReachRewardsPolIter(mdp, mdpRewards, new BitSet(), inf, false, null);
+			break;
+		default:
+			throw new PrismException("Unknown MDP solution method " + mdpSolnMethod.fullName());
+		}
+
+		// Finished expected total reward
+		timer = System.currentTimeMillis() - timer;
+		mainLog.println("Expected total reward took " + timer / 1000.0 + " seconds.");
+
+		// Update time taken
+		res.timeTaken = timer / 1000.0;
+		res.timePre = timerPre / 1000.0;
+
+		// Return results
+		return res;
+	}
+
+
 	/**
 	 * Compute expected reachability rewards.
 	 * @param mdp The MDP
diff --git a/prism/src/explicit/ProbModelChecker.java b/prism/src/explicit/ProbModelChecker.java
index 488e2c0d..b1334ae2 100644
--- a/prism/src/explicit/ProbModelChecker.java
+++ b/prism/src/explicit/ProbModelChecker.java
@@ -1080,6 +1080,8 @@ public class ProbModelChecker extends NonProbModelChecker
 			res = ((CTMCModelChecker) this).computeTotalRewards((CTMC) model, (MCRewards) modelRewards);
 			break;
 		case MDP:
+			res = ((MDPModelChecker) this).computeTotalRewards((MDP) model, (MDPRewards) modelRewards, minMax.isMin());
+			break;
 		default:
 			throw new PrismNotSupportedException("Explicit engine does not yet handle the " + expr.getOperatorSymbol() + " reward operator for " + model.getModelType()
 					+ "s");